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Venn Diagrams- Basics, Problems, Maxima and Minima
by Total Gadha - Tuesday, 18 September 2007, 04:49 PM
  cat 2009 cat 2010 venn diagrams set theory mba 2009 xat 2010 For all the CAT aspirants taking CAT in 2009 or 2010, this chapter should provide some insight into Venn diagrams and methods for solving the problems. This chapter comes on the demand of some high octane TG users who are responsible for my lack of sleep and excessive intake of caffeine last night. I hope this resolves many of their problems in Venn diagrams.

 

 
Venn diagrams are pictorial representations used to display mathematical or logical relationships between two or more given sets (groups of things). The drawing consists of two or more circles, each representing a specific group. Each Venn diagram begins with a rectangle representing the universal set.  Then each set in the problem is represented by a circle.  Any values that belong to more than one set will be placed in the sections where the circles overlap. A typical venn diagram is shown in the figure below:

cat mba

In the figure, set A contains the multiples of 2 which are less than 30 and set B contains multiples of 3 which are less than 25. Therefore, A = {2, 4, 6, 8, 10, 12... 26, 28} and B = {3, 6, 9, 12... 21, 24}. The various areas in the above diagram depict the following relationships:

·          Intersection (A∩B)- Denotes the set of elements that are shared by two or more given sets. In the figure
given below, the intersection of the two sets is shown.

cat mba

            A ∩ B = {6, 12, 18, 24}

·          ˜Only A or ˜Only B- The part of set A, or set B, which is not shared by any other set is known as "only A," or "only B." In the figure given below, the two parts are shown:

cat mba

            Only A = {2, 4, 8, 10, 14, 16, 20, 22, 26, 28}, only B = {3, 9, 15, 21}

·          Union (AUB)- Denotes all the elements of the given sets taken once.

cat mba

            A U B = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 28}

It can be seen that

cat mba

The venn diagram for three sets is shown below:

cat mba

It can be shown that

cat mba

Problem-solving through Venn diagrams:

I use the following method to solve problems through Venn diagrams:

cat mba

Solved Examples:

Of all the users on Totalgadha.com, 80% spend time in CAT Quant-DI forum whereas 60% spend time in CAT verbal forum. If only those users will crack CAT who spend time in both the forums, what percentage of users of TotalGadha

·          will crack CAT?
·          will not crack CAT?

Answer: n(AUB) = n(A) + n(B) - n(A∩B) Þ 100% = 80% + 60% - n(A∩B) Þ n(A∩B) = 40%
Therefore, 40% users of TG will crack CAT. And 60% of users (only A + only B) will not crack CAT.

NOTE: See that the surplus (superfluous part) can only be adjusted inside the area denoted for the intersection of the sets, a fact we will use in maxima- minima type of questions.

A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options — air conditioning, radio and power windows — were already installed. The survey found:

15 had air conditioning
2 had air conditioning and power windows but no radios
12 had radio
6 had air conditioning and radio but no power windows
11 had power windows
4 had radio and power windows
3 had all three options.

What is the number of cars that had none of the options? (CAT 2003)
1. 4                                           2. 3                                           3. 1                                           4. 2

Answer: We make the Venn diagram and start filling the areas as shown:

cat mba

Total Number of cars according to the diagram = 2 + 6 + 3 + 1 + 5 + 2 + 4 = 23.
Therefore, number of cars having none of the given options = 25
- 23 = 2.

New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani, and 3 projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved. (CAT 2003- Leaked)

What is the number of projects in which Gyani alone is involved?
1.      
0
2.      
1.
3.      
4.
4.      
cannot be determined

What is the number of projects in which Medha alone is involved?
1.      
0
2.      
1.
3.      
4.
4.      
cannot be determined

Answer: The Venn diagram for the three consultants is shown below:

cat mba

Total Number of projects = 2 x number of projects in which more than one consultant is involved - 1 = 2 x 19 - 1 = 37.
Therefore, X + 8 + 6 + 3 + Y + 2 + X + Y
- 16 = 37 Þ X + Y = 17. The values of X or Y cannot be uniquely determined. Medha alone is involved in X + Y - 16 = 17 - 16 = 1 project.

Concept of Maxima and Minima:

1. When the total number of elements is fixed

Let's have a look at the Venn diagram of two sets again:

                                                                        cat mba

Imagine that in the beginning, the number of elements in all the areas is zero, as shown above. All the sets are empty right now.

Let's see what happens if I insert one element inside A∩B:

                                                                        cat mba

We can see that adding 1 element to A∩B increases the number of elements in both A and B by 1. The total number of elements in all areas combined is 1 only (0 + 1 + 0) but if you add the number of elements in A and B (A + B), the addition will come up to 2. Therefore, adding 1 element to A∩B gives an extra 1 element. Hence, for every surplus of 1 element we can add 1 element to A∩B.

Let’s see the Venn diagram for 3 sets:

                                                cat mba

In diagram 1, we have added 1 element to intersection of only two sets (A and B but not C). We can see that A and B both increase by 1 and therefore we get a surplus of 1 element.

In diagram 2, we have added 1 element to intersection of all the three sets (A and B and C). We can see that A, B and C all three increase by 1 element each and therefore we get a surplus of 2 elements.

Therefore, in case of three sets, we can accommodate the surplus by

·          adding elements to intersection of only two sets in which case a surplus of 1 element can be accommodated by increase of 1 element in the intersection of only two sets.

·          adding elements to intersection of three sets in which case a surplus of 2 elements can be accommodated by increase of 1 element in the intersection of three sets.

How is this related to maxima and minima?

Let's see:

According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?

Answer: Let's first calculate the surplus:

percentage of people who like apples + percentage of people who like bananas + percentage of people who like cherries = 70% + 75% + 80% = 225% Þ a surplus of 125%.

Now this surplus can be accommodated by adding elements to either intersection of only two sets or to intersection of only three sets. As the intersection of only two sets can accommodate only a surplus of 100%, the surplus of 25% will still be left. This surplus of 25% can be accommodated by adding elements to intersection of three sets. For that we have to take 25% out of the intersection of only two sets and add it to intersection of three sets. Therefore, the minimum percentage of people who like all three = 25%

The question can be solved mathematically also. Let the elements added to intersection of only two sets and intersection of three sets be x and y, respectively. These elements will have to cover the surplus.

-->x + 2y = 125%, where x + y £ 100%. For minimum value of y, we need maximum value of x.
--> x = 75%, y = 25%.

In a college, where every student follows at least one of the three activities- drama, sports, or arts- 65% follow drama, 86% follow sports, and 57% follow arts. What can be the maximum and minimum percentage of students who follow
·          all three activities
·          exactly two activities

Answer: Let us again see the surplus:

Percentage of students who follow drama + Percentage of students who follow sports + Percentage of students who follow arts = 65% + 86% + 57% = 208% Þ surplus = 108%. This surplus can be accommodated through adding elements either to intersection of only two sets or to intersection of only three sets. As the intersection of only two sets can accommodate only a surplus of 100%, the surplus of 8% will still be left. This surplus of 8% can be accommodated by adding elements to intersection of three sets. For that we have to take 8% out of the intersection of only two sets and add it to intersection of three sets. Therefore, the minimum percentage of people who like all three = 8%. In this case the percentage of students who follow exactly two activities will be maximum = 92%.

The surplus of 108% can also be accommodated through adding elements to only intersection of three sets. As adding 1 element to intersection of three sets give a surplus of 2 sets, adding 54% to intersection of three sets will give a surplus of 108%. Therefore, the maximum value of students who follow all three activities is 54%. In this case the percentage of students who follow exactly two activities will be minimum = 0%.

We can also solve it mathematically Þ x + 2y = 108%, where x + y £ 100%. The maximum value of x will give minimum value of y, whereas minimum value of x will give maximum value of y.

2. When the total number of elements is NOT fixed

In this case we assign the variables to every area of the Venn diagram and form the conditions keeping two things in mind:
·          try to express the areas in the Venn diagram through least number of variables.
·          all the numbers will be zero or positive. No number can be negative.

Out of 210 interviews of IIM- Ahmedabad, 105 CAT crackers were offered tea by the interview panel, 50 were offered biscuits, and 56 were offered toffees. 32 CAT crackers were offered tea and biscuits, 30 were offered biscuits and toffees, and 45 were offered toffees and tea. What is the
·          maximum and minimum number of CAT crackers who were offered all three snacks?
·          maximum and minimum number of CAT crackers who were offered at least one snack?

Answer: Let’s make the Venn diagram for this question. Since we want to assume least number of variables, we can see that assuming a variable for the number of students who were offered all three snacks will help us express all the other areas. Let the number of students who were offered all three snacks = x.

                                                            cat mba

In the above diagram, we have expressed all the areas in terms of x. To decide maximum value of x, we note that 32 - x, 45 - x and 30 - x will be zero or positive. Therefore, the maximum value of x will be 30. (30 is the lowest among 30, 32 and 45). To decide minimum value of x, we note than x - 19 and x – 12 will be zero or positive. Therefore, x cannot be less than 19 (19 is the higher number between 19 and 12).

Therefore, maximum and minimum number of CAT crackers who were offered all three snacks = 30 and 19.


The number of CAT crackers who were offered at least one snack = Total number of CAT crackers in the Venn diagram = x + 28 + 32
- x + x + 45 - x + x - 19 + 30 - x + x - 12 = 104 + x.
As the maximum and minimum values of x are 30 and 19, respectively, the maximum and minimum value of 104 + x will be 134 and 123, respectively.

Maximum and minimum number of CAT crackers who were offered at least one snack = 134 and 123.

I am afraid I shall have to end here and leave the rest of it for my CBT Club students. I shall cover some problems based on this in the CBT Club this week.

 

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Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Small Wonder - Tuesday, 18 September 2007, 05:02 PM
 
TG Sir ki jai ho big grin
Thanks a ton. God Bless You!
Small Wonder!
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Vaidyanathan Ganesan - Tuesday, 18 September 2007, 05:11 PM
 

TG,

I was always on the look for your articles on the homepage and this time i was not disappointed.. smile.  A new article!!!!

 

Keep up your good work.

 

 

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Gul Gul - Tuesday, 18 September 2007, 05:11 PM
  YAhooooooooo!!!!! Thnx TG Muahhhhhhhhh.......
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by kishore ayyadevara - Tuesday, 18 September 2007, 05:24 PM
  Thanks a lot TG
i could not get the following point..

Percentage of students who follow drama + Percentage of students who follow sports + Percentage of students who follow arts = 65% + 86% + 57% = 208% Þ surplus = 108%. This surplus can be accommodated through adding elements either to intersection of only two sets or to intersection of only three sets. As the intersection of only two sets can accommodate only a surplus of 100%, the surplus of 8% will still be left. This surplus of 8% can be accommodated by adding elements to intersection of three sets. For that we have to take 8% out of the intersection of only two sets and add it to intersection of three sets

but here we are considering 3 sets...so how come u took only 2?
the other 2 intersection are 0 then?

Regards,
Kishore.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Sri KLR - Tuesday, 18 September 2007, 05:36 PM
 

TG,

Good method to solve max and min.....

x+2y and x+y is too good...I like equations....no thinking needed from now on..smile

So far I used hit and trial.....but NO more smile...feel relieved now....

Please give us some problems on four dimensionals also....

Also give some more prob on venns.. as exercise on Quant-DI forum...

I have kinda premonition that CAT might rear it's ugly head again....CAT(We ) is (are) going thru Testing times...big grin

I have seen one prob in cat 2 years back....one tough venn prob..don remember...will get back with it..

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Software Engineer - Tuesday, 18 September 2007, 06:31 PM
  Here, the quality of content is best, relally ! Thank You.

Software Engineer
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by King Kong - Tuesday, 18 September 2007, 07:01 PM
  TG == Too Good !!?? [smile] Awesome stuff... 
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Total Gadha - Tuesday, 18 September 2007, 07:09 PM
  Hi Kishore,

"intersection of only two sets" means area containing intersection of two sets but not the third set. In the figure given below, the area in red is the intersection of only two sets.
cat mba
Total Gadha
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by padmaselvan lakshman - Tuesday, 18 September 2007, 07:38 PM
 

hi TG,

Thanx a lot for such a wonderful article.. U have made maxima and minima look a lot more easier through this article..

as suggested earlier, pls give us a quiz on Venn Diag for practice..

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by kishore ayyadevara - Tuesday, 18 September 2007, 08:05 PM
  hi TG,
the thing is...u said that the intersection can take a maximum surplus of 100%
but, why isnt it more than 100?

if the 3 shaded portions are a,b,c . then what if a+b = 100%(i.e., all the contents of the first circle are in the shaded part) and c>0?

Regards,
Kishore.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by the underdog - Tuesday, 18 September 2007, 08:12 PM
  "we are not worthy" "we are not worthy"*

* from the movie "Wayne's World"

hehe.. thanks TG!
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Akon Convict - Tuesday, 18 September 2007, 08:32 PM
 

Thank U very much TG.....

God Bless You

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Total Gadha - Tuesday, 18 September 2007, 08:34 PM
  Hi Kishore,

How can something be more than 100%? If I have given you 10 boys at most can you have more than 10 boys combining all the areas? smile


Total Gadha
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Crazy CAT - Tuesday, 18 September 2007, 08:49 PM
 

Thanx a tonne Tg ,

It was worth waiting for such a long time for this article.

one request Sir ,plz give some tips like this on  functions and graph article also.

Regards

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Gul Gul - Tuesday, 18 September 2007, 09:18 PM
 

a topic on cubes also please.....

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by the underdog - Tuesday, 18 September 2007, 09:25 PM
  +1 Gullz Golu 
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Gul Gul - Tuesday, 18 September 2007, 09:34 PM
 

Help me in the following problem TG

All students in a class of 100 attended a summer camp. Each student had the option of enrolling for coaching in atmost 3 namely Football, Cricket and hockey.

a students had enrolled for hockey

b for football

c for cricket

Also d students had enrolled for eactly 1 sport, e for exactly 2, f for exactly 3 and g students had not enrolled for any of the three sports.

Q1 If d>e>f and c is less than a as well as b, what is the maximum possible value of c?

Q2 If a,b,c,d,e,f and g are all distinct the minimum possible no. of students who enrolled for atleast 1 sport is ?

Q2 If a is less than b as well as c, the no. of students who enrolled only for hockey is ?

Please Help....

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by kishore ayyadevara - Tuesday, 18 September 2007, 09:35 PM
  smile TG

seems i made some horrible interpretations then
thought A ,B,C are 100% each

what i find is the thrice intersected part(part common to all the circles) is counted thrice and (AnB) (BnC)(CnA)
are counted twice

coming to the problem,

so the surplus 108% should be distributed in the following way

x+2y = 108% ( where x is the intersection of 2 circles n y is common to three)

my problem is , i could not get how x+y = 100%...do u mean to say that the elements belonging to ONLY A, B,C are all zero and every element lies in the intersection parts?

Regards,
Kishore.

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Gul Gul - Tuesday, 18 September 2007, 10:01 PM
 

Kishore,

See if this is clear:

Say all students = 100 % in terms of equation a1+a2+a3=100 and we have a1+2a2+3a3=208. Subtract the above 2 equations we haave a2+2a3=108 now a3 should be minimum 8 and a2 maximum 92 i.e. 92+2*8=108 see now a1+a2+a3 = 100 is maintained. Also a3 max= 54 in this case a2=0 and a1 will take 46. Is it a bit clear now?

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Top CAT - Tuesday, 18 September 2007, 11:09 PM
  Exhaustive yet Simple
that,s ur trademark.....smile
that's what we all like about this site...
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Abhi S - Wednesday, 19 September 2007, 02:21 AM
  nw iv gone mad...i thot u r lost somewhere...bt u...bt u came wid a bang....
thnx TG sir.....
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Abhi S - Wednesday, 19 September 2007, 02:23 AM
  nw plz...u may hav a rest....let us hav a sip f d same caffiene....take care TG sir...
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by anand pani - Wednesday, 19 September 2007, 08:17 AM
 

great

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by kishore ayyadevara - Wednesday, 19 September 2007, 10:40 AM
  Thank You Gullz
it's clear now...i was having problems with interpreting the assumptionssad

and thanks TG for this useful article
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Gul Gul - Wednesday, 19 September 2007, 10:46 AM
  Thanks to TG....smile
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by dinesh munna - Wednesday, 19 September 2007, 12:41 PM
  Sir...I am sorry but this article was not exactly what i expected.I was expecting you to put sum fundaes on solving problems like the one just posted here by sum guy.Pls luk into it and fit ur solution into that.thanq
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Total Gadha - Wednesday, 19 September 2007, 01:22 PM
  Hi Dinesh,

Unfortunately, I am not preparing you for a Math Olympiad but CAT only. Have a look at the Venn diagram problem that came in CAT 2006:

A survey was conducted of 100 people to find out whether they had read recent issues of Golmal, a monthly magazine. The summarized information regarding readership in 3 months is given below: Only September: 18, September but not August: 23, September and July: 28, September: 28, July: 48, July and August: 10, None of the three months: 24.

What is the number of surveyed people who have read exactly two consecutive issues (out of the three)?
(1) 7 (2) 9 (3) 12 (4) 14 (5) 17

The article already has question that came in previous CAT papers. There has been no mention of even maxima or minima in CAT.

I sincerely believe that this is all that you need to know to tackle Venn diagram problems in CAT.

As for the fundas for solving problems like the one posted here, I can solve it through the fundas mentioned in the article only. smile

Total Gadha
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Tom Goel - Wednesday, 19 September 2007, 01:30 PM
 

I know what we can say in respect of TG falls very short of what he deserves...a word of thanks for TG not from the keyboard but from heart.

Thanks a lot and keep the good work going.......

+1 regrading article on cubes ;)

 

Amit Goel

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Total Gadha - Wednesday, 19 September 2007, 01:46 PM
  Hi Tom,

Let me try. smile I can certainly imagine the hours on 'paint' I will have to spend to draw images of cubes dead

Total Gadha

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Gul Gul - Wednesday, 19 September 2007, 02:06 PM
 

TG

PLZ help out in the question posted i was able to crack half questions in that set but the rest half posted is posing some problem. Plz help so that i can be completely confident in this topic..

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by ravi kumar - Wednesday, 19 September 2007, 03:06 PM
  TG

I feel ashamed to learn so much from you for free. Give me your address I want to send you some gurudakshina. Also feel sorry for ppl who are not gadhas yetsmile

best regards

Ravi Kumar
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by jitendra havaldar - Wednesday, 19 September 2007, 04:37 PM
 

Hi TG,

In the problem of cars having ACs,power windows(PW),radio(R) i didn't understand the way you have splitted the radio and the power windows part by taking (4-3) = 1 in the area common to both R & PW ...thoughtful

It would really be great if you take some time to explain this ..any help from anyone is also welcome on this....

 

Thanks.

Jitendra

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Abhishek Deb - Wednesday, 19 September 2007, 04:49 PM
 

Hi TG,

I wanted to know one thing that u said that "minimum values of the students following three activities will be 54% max in drama, arts ques.. I wanted to know then what will be the min of all the ppl having two activities interest.... will it be 54%....?If not then how to solve it......

Abhishek.

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Nitin Jain - Wednesday, 19 September 2007, 05:14 PM
 

Hello TG

Please clarify my doubt. You said that there are two cases for solving maxima and minima problems. In the former the total no of elements are fixed and in the latter the total no of elements are not fixed. I guess total no of elements imply AUBUC? Because in the last question of CAT interviewers , total no of elements are fixed i.e 210.Then how can we classify the question to fall under fixed elements or not?

 

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by sun is here - Wednesday, 19 September 2007, 09:04 PM
  HI TG ,
               A survey was conducted of 100 people to find out whether they had read recent issues of Golmal, a monthly magazine. The summarized information regarding readership in 3 months is given below: Only September: 18, September but not August: 23, September and July: 28, September: 28, July: 48, July and August: 10, None of the three months: 24.

What is the number of surveyed people who have read exactly two consecutive issues (out of the three)?
(1) 7 (2) 9 (3) 12 (4) 14 (5) 17
 



              iam not able to solve this problem please throw some light on it

Thanks
Sun
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Total Gadha - Thursday, 20 September 2007, 01:02 AM
  Hi Gullz,

lease give me the options. I calculated highest value of c as 48% assuming some values but I do not know if you need answer in terms of a, b, d, e, f or otherwise.

Total Gadha
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Mou Sukoshi - Thursday, 20 September 2007, 01:07 AM
 

A survey was conducted of 100 people to find out whether they had read recent issues of Golmal, a monthly magazine. The summarized information regarding readership in 3 months is given below: Only September: 18, September but not August: 23, September and July: 28, September: 28, July: 48, July and August: 10, None of the three months: 24.

What is the number of surveyed people who have read exactly two consecutive issues (out of the three)?
(1) 7 (2) 9 (3) 12 (4) 14 (5) 17

are these figures correct?? sad

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by R V - Thursday, 20 September 2007, 07:47 AM
 

Hi Gullz how did you get the equation a1+2a2+3a3=108?? Could you please explain.

Thank you

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Gul Gul - Thursday, 20 September 2007, 09:37 AM
 

TG m so sorry i didnt write the options....I m in office and i forgot 2 bring the paper in which the question was given i will definitely post it in the evening... But i remember the options for following question

Q2 If a,b,c,d,e,f and g are all distinct the minimum possible no. of students who enrolled for atleast 1 sport is ? a) 9 b)12 c) 15 d) none

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Gul Gul - Thursday, 20 September 2007, 09:41 AM
 

R V

a1 only 1

a2 exactly 2

a3 exactly 3

when you add all a2 is added twice and a3 thrice see a venn diagram for 3 circles u will get it..

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Total Gadha - Thursday, 20 September 2007, 10:17 AM
  Hi Sun is here,

The options to this CAT 2006 question are NOT correct. This was one of the two questions in CAT 2006 that was wrong.

Total Gadha
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Mohit Goyal - Thursday, 20 September 2007, 10:31 AM
  Hi TG.

Wonderful Attempt to unearth the Concepts of venn Dig !! I have some very interesting sets on Venn dig and will shortly post them but only if you promise to reply me after solving cause i have posted 2 queries earlier n dint get ne reply....I am not a regular user of TG.com but i really believe that you are doing a Noble Job Sir....Hats Off ...

Mohit
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by SS VV - Thursday, 20 September 2007, 10:57 AM
 

knew you were taking a while since u had to write it up to your standard which is excellent :>:>

you rock!!

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by gourav kalra - Thursday, 20 September 2007, 01:24 PM
 

Hey..lovely article...any word of praise wud be less...

u really rock...am impressed...smile)

god bless u!!

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Total Gadha - Thursday, 20 September 2007, 02:43 PM
  Hi Mohit,

I will certainly reply to you. Do post your problems. smile

Total Gadha
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Nitin Jain - Thursday, 20 September 2007, 03:12 PM
 

Hi TG

Pls reply to my post also given above.

Thanks

 

 

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Arun Prasad G - Thursday, 20 September 2007, 03:18 PM
 

TG, it is regarding this problem of apples, bananas and cherries.

x + 2y = 125%, where x + y £ 100%. For minimum value of y, we need maximum value of x.
--> x = 75%, y = 25%.

I understand this. But after solving this, I wanted to fit this back into the venn diagrams and I am totally confused. For example,

I wrote AnBnC as 25, and AnB excluding C as 75, BnC excluding A as 75 and so on. Now I am trying to find only apples, only banana's and only cherries. I am not able to get it fully as I am not getting 100% after writing individual percentages. Please explain this to me.

Also I have posted a query on your "How to find the Units Digit of a Number?" . Please respond tp that also.

THANK YOU VERY MUCH FOR YOUR WONDERFUL CONTRIBUTION TO ALL ASPIRANTS. ITS FANTASTIC TO READ EACH AND EVERY ARTICLE OF YOURS.

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by rishi sawla - Thursday, 20 September 2007, 03:41 PM
 

Hey Arun,

I think Sum of  AnB excluding C , BnC excluding A and AnC excluding B is 75.

Not individually.

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by ravi teja - Thursday, 20 September 2007, 05:03 PM
 

hai gulz,

i was not able to solve even a single question in the set u mentioned.can u pass the answer to me too if u get it please.if needed i can provide the options too. 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by neelakanta siva - Thursday, 20 September 2007, 05:20 PM
 

for GOLU'S  question ,

only hockey+only football+only cricket > both H & C and not F +both C & Fand not H+both F &

Hand not C  > ALL THREE

means H only + F only + C only > intersection of 2 only > intersection of 3

we can take intersection of 3 as 0

now intersection of 2 games only can take a max value of 49, then only the other remaining part can be 51 and be greater.

49 can be alloted to the intersection of H and C only as we have to max cricket (C)

then intersection of F&C Xonly= 0

intersection of F&H Xonly=0

the remaining part can take 51 which should be divided as 16+17+18 and the 16 should be alloted to cricket(C) and 17 and 18 can be alloted to only F and only H. This is becz of the condition (C has to be less than A and B)

SO 0+0+49+16 = 65 IS THE MAX VALUE CRICKET CAN TAKE

 

PART 2 &3 OF THE Q IS NOT COMPLETE

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Total Gadha - Thursday, 20 September 2007, 07:46 PM
  Hi Nitin,

In the previous sets, it has been mentioned that every student follows at least one activity. This kind of statement is critical to determine that AUBUC is fixed. Even if the total number of students/people etc. are given, if it is not given that every person belongs to at least one category, AUBUC is not fixed.

Total Gadha
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by R V - Friday, 21 September 2007, 08:09 AM
 

hi Gullz, thanks for the explanation. i understood it.smile

RV

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Gul Gul - Friday, 21 September 2007, 09:04 AM
 

TG so sorry yesterday net was nt working at my place...,here r d options

If d>e>f and c is less than a as well as b, what is the maximum possible value of c? Options a) 63 b)64 c)65 d)66 e) none

If a,b,c,d,e,f and g are all distinct the minimum possible no. of students who enrolled for atleast 1 sport is ? a)9 b)10 c)11 d) 13 e) none

If a is less than b as well as c, the no. of students who enrolled only for hockey is ? a) 32 b) 48 c) 49 d) 50 e) none

Answers are c, e, c respectively......I hav 2 go 4 a full day training sad

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by sonal singh - Friday, 21 September 2007, 11:21 AM
 

hello Tg

Thanks for such a wonderful article.

Please explain how did u get 4-3 =1 for the following.and 15 had air conditioning specify all the elements in B or Only B


 

 survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options — air conditioning, radio and power windows — were already installed. The survey found:

15 had air conditioning
2 had air conditioning and power windows but no radios
12 had radio
6 had air conditioning and radio but no power windows
11 had power windows
4 had radio and power windows
3 had all three options.

What is the number of cars that had none of the options? (CAT 2003)
1. 4                                           2. 3                                           3. 1                                           4. 2

Answer: We make the Venn diagram and start filling the areas as shown:

cat mba

Total Number of cars according to the diagram = 2 + 6 + 3 + 1 + 5 + 2 + 4 = 23.
Therefore, number of cars having none of the given options = 25
- 23 = 2.
thanks

sonal

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Sumit Singla - Friday, 21 September 2007, 09:04 PM
  Thanks for the brilliant article TG... Something that I solved mostly by hit and trial has been made simple enough to be solved verbally! YOU ROCK!!
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Saurabh Goyal - Friday, 21 September 2007, 11:46 PM
  Hi Tg,
Found ur Venn diagram topic very helpful, but still getting ques with more difficulty...
I  am facing problem in getting the logic of the question mentioned below..

Q. In a town 70% of the persons suffer from disease A, 80% from disease B, 75% from C and 85% from disease D and "P%" from all the four diseases. Find the minimum value of P.

i tried this ques by the above mentioned funda in your post, but not getting any where with the logic. will it be 200% of surplus now?as the common 1 between all four fields will be increased by 1 in comparison to 3 fields???


Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Total Gadha - Saturday, 22 September 2007, 11:50 AM
  Hi Saurabh,

A + B + C + D = 310%. Therefore, surplus = 210%. Now, the intersection of 4 sets can accommodate a surplus of 3 per element. The intersection of 3 sets can accommodate a surplus of 2 per element. The maximum surplus it can accommodate is 2 × 100% = 200%. The surplus of 10% would be left. Now you can decrease intersection of two sets and shift the decreased amount in the intersection of 3 sets. Going by this manner, you can quickly obtain that if you keep 90% in intersection of 2 sets and 10% in the intersection of 3 sets, the surplus accommodated = 90 × 2 + 10 × 3 = 210%.

Therefore, the minimum value of P = 10%. The maximum will be when P accommodates all the surplus. Therefore, maximum value = 210/3 = 70%
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by nitin verma - Monday, 24 September 2007, 03:39 PM
 

Hi TG,

I like this site very much. I thank you for entertaining my request of explaining my doubt. I am very much thankful to you. YOur explanation is fantastic and easy to grasp. You wont believe before i struggled hard to understand the concept but could not, but your docile explanation is so clear that any sane person can grasp it. Thank you very much. I will come back to you with more such request. You are helping cat aspirants in a big way.

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Gul Gul - Tuesday, 25 September 2007, 08:52 AM
  TG options r given now.........
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Total Gadha - Tuesday, 25 September 2007, 11:31 AM
  Hi Gullz,

Have taken the printout of your question. Let me have a go at it. smile

Total Gadha
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Abhra Chatterjee - Wednesday, 26 September 2007, 06:14 PM
  A too good article........

Thanks a lot TG
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by amit sharma - Thursday, 27 September 2007, 02:28 AM
 

Hi TG

It was a goog article but i have one query

In the above que we escape the intersection of 2 set which can accomodate 1 surplus per element and if we considder it then min value of  P=0 .

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by abc abc - Thursday, 27 September 2007, 01:56 PM
 

Thanks a ton for this one !!!!!!

This topic has not figured at length in most of the notes available to students !!!!

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by shinjini mondal - Saturday, 29 September 2007, 11:09 PM
  hi TG
nice article,esp liked maxima minima application in it.and please do add for combination of four sets.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by sweta x - Sunday, 30 September 2007, 08:42 PM
 

Hi TG ,
    I've been following your forum since long now ....And I must say thank you for all the sincere effort put into making MBA prep easier for all of us.

I have a doubt regarding the venn diagrams article .....
Had a problem on similar lines in Mock CAT 6 of time and tried using the funda ,( it was a problem with 5 sets of data overlapping) , so I think I might not have understood the problem properly.

Attached   is the problem and my approach ....

I'd be very gr8ful if u could tell me whats wrong with my approach !!!!!!!!!!!!

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by pranav tendolkar - Sunday, 30 September 2007, 11:13 PM
 

reeeeeeeeeeaaaallly very goood,

 

can u explain same things in case of 4 or 5 circle venn diagrams... is there any theoretical way other than drawing venn diagram as higher diagrams are complex

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Alpa dedhia - Monday, 1 October 2007, 10:23 AM
  Hi sweta,
for the first question i have simply taken the least number of people in each cities who can opt for all the qualities .
so the no is 26+25+26+18+15+29 = 139

for the second question .. is 37 the answer .. please let me knw..

regards
Alpa
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by ran for_cat - Tuesday, 2 October 2007, 12:35 PM
 

for the 1st one

a+b+c-e-2f+g=100

also d+e+f+g =100

now a+b+c = 100+e+2f-g

so e+2f+-g should be max...

now d+e+f+g =100 and d>e>f ==> for e and f to be as max as possible e should be 32 and f is 33...(g=0 and f=35)

so a+b+c =100+32+66=198

so for a>c and b>c c can have a max value of 65 here.

 

for the 2nd question:

a+b+c-e-2f+g=100

d+e+f+g =100

keep d=0 ==> we can check for any arbitary values of e f and g that the distinct values are possible

e+f+g =100 or g=1 e=50 f=49

a+b+c =100 -1 +50+49=198

a b c can have different values here as well.

 

for the 3rd question b>a and c>a

==> let say b and c constitutes the same elements in that case the max possible value of a is 49.where a contains all the elements distinct from b and c

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Uthay Mathi - Tuesday, 2 October 2007, 05:21 PM
  This is a cool stuff dear TG.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by lavika gupta - Wednesday, 3 October 2007, 04:26 PM
  hi tg.pls post some text on functions,maxima and minima
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by sweta x - Wednesday, 3 October 2007, 11:34 PM
  Hey Alpha,
          U got it right
how did u solve the second one (37)
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Kumar M - Wednesday, 3 October 2007, 11:51 PM
 

Hi TG

In the first exampe problem of maxima & minima u have mentioned "As the intersection of only two sets can accommodate only a surplus of 100%".How it can be only 100%

why cant we accommadate the suplus of 110% as follows?

       only Apple and Banana = 30%;only apple and cherry = 40%; only Banana and Cherry = 40% remaining 5 can be only Banana.

Can we minimise the only three part as i explained. Please help me....

Thanks & Regards,

CM

 

 

      

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Varun Choudhary - Thursday, 4 October 2007, 11:59 AM
  Kudos Sir.............smile
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by sgx100 Online - Saturday, 6 October 2007, 07:04 AM
  TG Sir

Mindblowing article smile
Absolutely terrific !!!

Thnx a lot

Sir
if u can help with one article on Graphs (linear,quadratic,modulus...)
it wud be really helpful to all of us

Thanking You
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by ashish tyagi - Saturday, 6 October 2007, 11:20 AM
  really a very gud article t g sir,
i have a problem pls solve it........

1   A survey was conducted on the eating habits of a group of 1000 people .results show that 92% of the people surveyed eat south Indian food, 91% eat north Indian food,82% eat American food , 78% eat Chinese food, 79% eat italin food and 80% eat continental food. What must be the minimum no. of people who eat all the 6 type of food, if 7 people do not eat any of the 6 types of food?

A:0 B:13 c:27 D:55
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by shriram samant - Saturday, 6 October 2007, 05:10 PM
 

fantastic...

mindblowing...

superb....

thanks TG.... Total Genius.....  smile

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Ankush Keshwani - Sunday, 7 October 2007, 05:52 PM
  A very good explanation.
Thanks a lot!!
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Abhra Chatterjee - Thursday, 11 October 2007, 10:19 AM
  Hi TG,

I am not able to solve this question properly:
A survey about Tv viewership was conducted on 100 respondents. The results are,
93 liked sony,89 liked Zee, 81 liked Stratv, 75 liked zee cinema, 78 like Mtv.
1 did not like any of the above.
Find the minimum number of people liking all the the 5 channels.
I will tell you the approach that I followed. Please correct me where I am going wrong.
The total number of people watching any of these channels = (100-1)=99(I don't watch any).
Now the surplus = [(93+89+81+75+78) - 99] = 317. Now for every increase in the number of viewers watching two channels, there is actually a 20% increase from the initial (I am not sure whether we have to consider all the 5 combinations or not). Then for every increase in the number of people watching 3 channels, there is a resultant increase of [8-5]/5 = 60% (Here also are we to consider the total number of combinations possible). Again for every increase in the number of people watching 4 channels, the resultant increase = [9-5]/5 = 80%.
Now here I consider the combinations of groups possible for each of these groups:
2 channel groups = 5.
3 channel groups = 3.
4 channel groups = 2.
So the surplus we have been able to cover till now = (100+180+160) = 340. So there need not be any people watching all the five channels.

I am not at all confident of the answer arrived at.
Somebody Please help !!!!
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Prasad L - Saturday, 13 October 2007, 12:01 PM
 

TG Sir,

I have no words to describe the amazing work you are doing ......

BTW, the TIME material also has some quick methods to crack the venn diagrams. Hope the TG users make use of that as well... ATB!

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Mou Sukoshi - Monday, 15 October 2007, 01:05 PM
 

hi ashish.....

A survey was conducted on the eating habits of a group of 1000 people .results show that 92% of the people surveyed eat south Indian food, 91% eat north Indian food,82% eat American food , 78% eat Chinese food, 79% eat italin food and 80% eat continental food. What must be the minimum no. of people who eat all the 6 type of food, if 7 people do not eat any of the 6 types of food?

A:0 B:13 c:27 D:55

ppl having south indian food = 920
ppl having north indian food = 910
ppl having American food = 820
ppl having Chinese food = 780
ppl having Italian food = 790
ppl having Continental food = 800
hence, total= 920 + 910 + 820 + 780 + 790 + 800 = 5020
 
Of the 1000 ppl, 7 dont like any of the 6 types.
Remaining = 1000 -7 = 993
 
Surplus = 5020 - 993 (Becoz 7 ppl dont like any of the 6 types of food)
            = 4027
 
Accomodating the surplus in the portions of 5 intersecting groups, we can have at most 993 * 4 = 3972 ppl surplus.
Remaining surplus to be accomodated in the portion where all 6 groups intersect = 4027 -3972 = 55
Hence, answer (D)55..........
 
Plz let me know if i am  correct.......
Thnx........
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Rishi Kapoor - Wednesday, 17 October 2007, 07:02 AM
 

Hi Abhra...

The answer is atleast 20 people watch all 5 channels...

For solutiuon, see the above post

...RK...

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by manjari malpani - Friday, 19 October 2007, 01:37 PM
  hi

the article is awesome !!!!! thanks ....n ashish is the answer to ur question 27 ?option c
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Ajay ..... - Thursday, 8 November 2007, 11:49 PM
  hi somporna
can u explain why did u accomadated persons in 5 intersecting group and why not in 1 2 3 4 one's means u r assuming those to be Zero ???

Plz do explain.otherwise u are absolutely correct..
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by the terminator - Monday, 12 November 2007, 05:57 PM
  @ dinesh munna
hey if u urself cant post somethg useful let others do it and by d way donno y u r so critical abt the article. and can u u plz explain wat u mean by ur so called "FUNDAS". think before u write. before this how many useful posts u hav put up???
nothing personal but be careful wat u write.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by the underdog - Tuesday, 13 November 2007, 10:56 AM
  Hi TG,

I don't think the CAT 2006 question (July-Sept-August) is wrong. Its asking for those who read consecutive issues: July-August and August-September

July-August: 7
August-September: 2

So answer is 9.

Or else I have misunderstood the question.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Bharat Suri - Tuesday, 13 November 2007, 09:38 PM
  sir shouldnt maximum value ,regarding the example given by u about the college students, be 57% and NOT 54% ie the maximum value for the students to take all the 3 fields as all the arts ppl can take the other two as well .  
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Mou Sukoshi - Friday, 16 November 2007, 12:13 PM
 

hi ajay

look closely thru TG's article......

we move to 2 intersecting grps only when we are unable to accomodate within non-intersecting portions......

similarly, we move to 3 intersecting grps only when we are unable to accomodate within 2 intersecting grps........

like in the prob, we move the surplus to gps where all intersect only when we cannot accomodate them within 5 intersecting grps........

so we have already considered smaller intersecting grps before moving on to the higher number of intersecting grps......

i suggest u draw a diag as it will help u to understand the accomodation of the surplus better........

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Mou Sukoshi - Friday, 16 November 2007, 12:15 PM
 

hi ajay

look closely thru TG's article......

we move to 2 intersecting grps only when we are unable to accomodate within non-intersecting portions......

similarly, we move to 3 intersecting grps only when we are unable to accomodate within 2 intersecting grps........

like in the prob, we move the surplus to gps where all intersect only when we cannot accomodate them within 5 intersecting grps........

so we have already considered smaller intersecting grps before moving on to the higher number of intersecting grps......

i suggest u draw a diag as it will help u to understand the accomodation of the surplus better........

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by yash modi - Wednesday, 4 June 2008, 10:57 PM
 

a big thank u to tg sir,

 

brilliantly explained concepts ...thanks a ton sir...better than any coaching you can get..thanks again;;

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Divyasha Ray - Tuesday, 24 June 2008, 05:26 PM
  Hi TG sir
Can u please help me with this particular question???
A survey was conducted in a community of 350 people regarding three games - Chess ,Carrom and Chinese Checkers. The Following information is obtained in the survey.
(i) Thrice the no. of people who play all  the three games is equal to the  no.  of  people who  Chinese  Checkers .

(ii) The no. of people who play Chinese Checkers and Carrom is equal to the no. of people who play Chess only

(iii) In every three people who play Chess and Chinese Checkers only, there are five people who play none of the three games.

(iv) In every seven people who play Chinese Checkers, four people play Carrom also.

(v) For every four people who play exactly two games,there is one person who plays Carrom and Chinese Checkers only and two persons who play none of the three games

Questions:
1. How many people play exactly two games?
2. How many people play Chess but not Carrom?
3. How many people do not play Chinese Checkers?
4.How many people play Chess or Carrom

Divyasha
Edit | De
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by abhinav tripathi - Thursday, 26 June 2008, 11:21 AM
  TG you rock man.....!!!!
   venn diagrams were always a matter of concern for me........you freed me ............!!!
thanks a lot....
waiting for an article on graphs.......
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by shubham singh - Thursday, 3 July 2008, 02:26 PM
 

tg u just great!!!

initially i was so scared of venn diagram n maxima n minima but now after going thru ur article ,m much relieved...thankusmile

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Mou Sukoshi - Friday, 4 July 2008, 11:13 AM
 

@ Divyasha

There shd be one more condition for the Carrom Only portion. All the other sections can be expressed in terms of a single variable. Plz check the prob.

Somparna

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by A S - Monday, 7 July 2008, 09:48 AM
 

hi tg,

This is the first time I am writing in this forum. And before everything else i want to say that you are simply great!! I got to find your website 2 months back, and you know what, within this short timespan my confidence and grip over quant. part have increased tremendously. I wrote CAT in 2006, and needless to say it was patheticsad. This year I am going to write it more confidently. And one day I'll join you to help students...at least thats what I dream today..
Anyway, lets come to the business!!! I understand the way you have presented the maxima and minima using Venn diagram..but I think it can be simplified to further extent. I discovered this when I was at Class 12 and used it confidently without any hiccup. Hope this will help others too. Please let me know your valuable input on the same.

Let X = Elements having only A or only B or only C
    Y = Elements having two elements exactly.
    Z = Elements common with all three elements (intersection of all three sets)

So, we'll always be given,
   (X + 2Y + 3Z)
   (X + Y + Z) = 100 %
    We generally have to find min or max of Z.
That can easily be done by adjusting X or Y.

Let's take this example:
"In a college, where every student follows at least one of the three activities- drama, sports, or arts- 65% follow drama, 86% follow sports, and 57% follow arts. What can be the maximum and minimum percentage of students who follow
·          all three activities
·          exactly two activities"

(X + 2Y + 3Z) = 208%
(X + Y + Z) = 100%

[If Z has to be fixed (be min or max) either X or Y has to be zero (they can not be negative, remember). Now who will correspond to max and who to min - only question. If X = 0, Y + Z will 'eat away' maximum Z, leaving small Z. So it will be used to calculate min Z. Vice-versa.]

In this case,
for min Z, X = 0%
=> Z = 8%, X = 0%, Y = 92%
for max Z, Y = 0%
=> Z = 54%, X = 46% and Y = 0%

It may seem to very lengthy process, but practically very small and easy to understand.
Sorry for posting such a long and boring mail. But I got the chance to communicate with you and could not resist myself...sorry again!!

Abhishek

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Total Gadha - Monday, 7 July 2008, 12:42 PM
  Hi Abhishek,

Welcome to the gadha gang. smile

Thank you for the method. I will try it out and check. And good luck to you or your CAT. As for helping students, you are more than welcome. We can certainly do with some more hands. smile

Total Gadha
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by dibyaranjan mallick - Tuesday, 8 July 2008, 01:08 AM
  416 will be the total...
416 - 99 = 317 be the surplus
3x + 4y = 317, x + y = 100% max i.e. 99
so, y = 317 - 99*3 = 20. (ans)
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by dibyaranjan mallick - Tuesday, 8 July 2008, 01:20 AM
  yaar it's the same thing as written in this article.

(X + 2Y + 3Z) = 208%
(X + Y + Z) = 100%
---------------------- deduct
y + z = 108%

and that's what this article explains smile
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Prashant Kumar - Tuesday, 8 July 2008, 08:36 AM
 

Hello TG,

It really very tailor made informaion for CAT.But tell me one thing

In the section "When the total number of elements is NOT fixed " .We have 210 interviews in IIM A.So cant we take this problem in the same way as calculating the surplus (105+56+50-210=1).But the solution comes out to be spurious using this.Please help me

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by A S - Tuesday, 8 July 2008, 10:59 AM
  Hey dibya, of course it will give the same answersmile and will eventually form same equations..what i mean to say that in stead of the process 'injecting' one element in common area, i find it easier to calculate them in this algebraic method..I am not giving a brand new theory..just another perspective of looking at this kind of problem.smile
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Rajat Vashishta - Sunday, 13 July 2008, 12:34 AM
  Thanks TG for a great article. it was really useful. smile
this is a question from one of the AIMCATs. I found it really tough to solve..please guide.

Q. In a group of 100 students, each student has to opt for one or more of the 3 subjects among Physics, Chem and Maths. The number of students opting for maths is more than that of physics which in turn is more than that of chem, which in turn, is more than the no of students opting for exactly 2 of the 3 subjects, which in turn, is more than the no of students opting for all the 3 subjects. It is also said that at least one student opted for all the 3 subjects.

1. Max no of students opting for chem:?
a)72 b)79 c)80 d)81 e)None of these

2. Min no of students opting for maths:?
a)38 b)37 c)36 d)35 e)34

3. If exactly half the students opted for maths, what is the max no of students who opted for all the three subjects?
a)15 b)16 c)17 d)18 e)19

4. Max no of students who opted for only physics:?
a)33 b)50 c)49 d)48 e)52

5. Max no of students who opted for physics and chem but not maths:?
a)47 b)48 c)49 d)50 e)51
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Rajat Vashishta - Sunday, 13 July 2008, 12:43 AM
  "49 can be alloted to the intersection of H and C only as we have to max cricket (C)"..how?
if we do that won't c become greater than b? the q says c
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by mohan chandra - Wednesday, 16 July 2008, 12:07 AM
  Hi,

Could you please guide me to solve this problem of Chinese checkers.

Regards,
Mohan
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Amey Panke - Wednesday, 16 July 2008, 01:49 AM
  thank you TG sir..........
the concepts are of great help.....
u rock sir!!!!!!!
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by ashish jain - Thursday, 17 July 2008, 03:09 AM
  Hello TG sir,

Following the same question which Nitin Jain has asked above, I still have doubt regarding the classification of problems into Fixed and Non-Fixed category.

In your answer above, did you mean that if it is not given that every person belongs to at least one category , then there may be some persons who doesn't belong to any category and hence AUBUC is not fixed ?

Can you explain this classification in detail please ?

Thanks and Regards,
Ashish
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by inderpreet makkar - Thursday, 17 July 2008, 03:11 AM
 

Hello TG Sir

I dint get the concept of x+y and x+2y clearly...can u pls help me wit hthe same...

Regards

Inder

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by inderpreet makkar - Thursday, 17 July 2008, 03:29 AM
 

Hi

Understood the logic u gave to Kishore...thnx for the same..dint get the last part though, how could u say that the maximum could be 92 abd minm beibg 8...its beyond my comprehension presently..would appreciate if u can help me wid that..

Rgds

Inder

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Riyaz Iqbal - Tuesday, 22 July 2008, 09:30 AM
  Hi TG,
         I'm impressed ! Again !! Thanks for your quality conceptual lesssons. I've a question about the Drama,Arts,Sports question. Since the least percentage given is 57% why can't we just include 57 to the intersection of all three areas and adjust the remaining values? Leave the areas of intersection of exactly two sets empty(which gives the minima of zero for that area,as you've already proved) and put 57 in the intersection of all three areas.Again zero for 'only arts', 8 for 'only drama' and 29 for 'only sports'. It seems this satisfies all the conditions(Am I missing something?). So, shouldn't the max value be 57 instead of 54? Please clarify.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Riyaz Iqbal - Tuesday, 22 July 2008, 05:46 PM
  Sorry, TG.I found the fallacy in my argument. The total percentage doesn't add up to 100 in the case proposed by me.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Adithya G - Wednesday, 23 July 2008, 09:03 AM
  Hi TG, Nice stuff..very much impressed with the quality and simplicity.
I would like add one more technique about minima when total number is fixed or when total number can be
found out.. I ll explain throughthe same examples illustrated above.

1.According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries.
What is the minimum percentage of people who like all three?

Ans: for min of all three= 100-((100-70)+(100-75)+(100-80))
              =>100-(30+25+20)=100-75=25
2.In a college, where every student follows at least one of the three activities- drama, sports, or arts-
65% follow drama, 86% follow sports, and 57% follow arts. What can be the maximum and minimum percentage of students who follow
·        all three activities
·          exactly two activities

Ans:min For all three activities= 100-((100-65)+(100-86)+(100-57))
                 =>100-(35+14+43)=100-92=8%

max For exactly two=100-8=92%(since x+2y=100 and min of all three can be used)

Regards
Adi
4 Set or Greater Venn diagrams
by devi prakash - Tuesday, 5 August 2008, 03:30 AM
  Hi TG plz give some easier ways to solve 4 set or 6 set venn diagrams
Re: 4 Set or Greater Venn diagrams
by Junglee Gadha - Friday, 12 September 2008, 05:34 PM
 

hi devi da...

please post your 4 set or 6 set venn diagrams problem...

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by amit amit - Wednesday, 17 September 2008, 08:34 PM
  I am a avid reader of TG site. An I have to admit that the quality of stuff on this site is simply great. In today's world where everything is commercialized, the way u r spreading knowledge is simply unheard of. I work on Linux and cant help noticing the similarity between the underlying theme of Linux and your endeavor. Knowledge is free and should be shared. You are on something great TG. Keep up the good work. God Bless.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Total Gadha - Friday, 19 September 2008, 07:58 PM
  Hi Amit,

Thank you. smile

Total Gadha
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Saurabh Mishra - Saturday, 20 September 2008, 11:54 AM
  Venn diagrams involving maxima and minima have always been my nemesis.
This post really helped a lot.
Would be really gre8 if we could get some more practice questions or samples.
Nevertheless, a great post smile
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by srini vaas - Saturday, 20 September 2008, 04:47 PM
 

Hey TG,

Amazin article...

Jus one doubt..

wats ur real name???

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by sathyan sadagopan - Monday, 22 September 2008, 04:34 AM
  hi TG,
A small clarification,
in d above explanation,

Going by this manner, you can quickly obtain that if you keep 90% in intersection of 2 sets and 10% in the intersection of 3 sets, the surplus accommodated = 90 × 2 + 10 × 3 = 210%.

shouldn this be

Going by this manner, you can quickly obtain that if you keep 90% in intersection of 3 sets and 10% in the intersection of 4 sets, the surplus accommodated = 90 × 2 + 10 × 3 = 210%.


Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by karan sobti - Tuesday, 23 September 2008, 10:56 PM
  a very good article indeed.....but i need more problems & examples like these....

thanx smile
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by karan sobti - Tuesday, 23 September 2008, 10:57 PM
  a very good article indeed.....but i need more problems & examples like these....

thanx smile
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by SHRESHTH ANAND - Wednesday, 24 September 2008, 02:13 AM
  Hi TG,
Indeed it's a very nice article but I have some problems in handling Maxima and Minima problems.
Say, If i have to find out the following things :

In a town people read five kinds of newspapers say A, B ,C,Dand E.
Say, 90% read paper A , 74% paper B , 80% paper C,65% paper D and 40% paper E.
Now if I have to find at most how many read exactly four out of five papers and exactly 3 out of five.

And

at least how many read exactly four out of five papers and exactly 3 out of five.

How should I go about it?????

Kindly help

Regards
Shreshth Anand
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Sreedevi PV - Wednesday, 24 September 2008, 06:58 PM
 

Hi TG,

Again Kudoooos. U rock.

Max&min funda was a bit confusing when i first read it. smile. Now its clear....and seems like a real gem.

Question:According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?

To get the answer, I use a ‘one-liner’ funda.Seems it works everytime. Hope its useful.

Minimum Percentage of people who like all three= 80 – (100-75)-(100-70) =25

Cheers!!

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Rohit Pathak - Thursday, 25 September 2008, 10:54 AM
 

Hi Shreshth,

For at most how many read exactly 4 out of 5 papers the answer that i am getting is 83% and for at least how many read exactly 4 out of 5 i am getting 49% please let me know if these are correct.

Thanks

Rohit

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Aastha Chalana - Thursday, 25 September 2008, 03:20 PM
 

Hi,

This lesson was of great help, though small but important fundas.

In all i throughly enjoyed working on it!

Thanks.

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Kosher InBlues - Thursday, 25 September 2008, 09:58 PM
  HI TG
  I am  a new fan  of yours , and i really like the  way  you present a topic
"to the point ",,,,,,
Thanks

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by LALIT MALIK - Wednesday, 8 October 2008, 05:36 AM
 

Hi

Can you tell why before adding the surplus to the intersection of the three sets we are subracting the same amount from the intersection of only two sets like if the surplus is 108% then can't we represent the surplus in this manner - 100% is from intersection of two sets only and 4% (which means surplus of 8%) from the intersection of three sets. why we have take 8% out from the intersection of 2 sets and then add 8%  to intersection of three sets.

Kindly do reply

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Neelesh Sethi - Monday, 27 October 2008, 12:58 AM
 
thnx sir for great topic,intersection of only two sets can accommodate only a surplus of 100%,is it because intersection of 2 eta gives surplus of 1 element.So by that logic is it tht intersection of 3 sets can accomodate 200%.by that logic intersection of n sets can accomodate n-1 % surplus.and also if any 1 knows line technique for such problems, plz explain.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by shantanu rangaswami - Monday, 10 November 2008, 11:08 AM
 

hey ,,,,wass up,,,can u check sixth line from top of ur reply

.......d>e>f,,,nd g is 0shouldn't d=35 e=33 &f=32

 

 

....if m not wrong...

 

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Sukanya Chowdhury - Friday, 19 December 2008, 12:32 AM
 

Hi Shreshth,

I'v also got the same answer..

At least  49% and at most 83% for those who read exactly four out of 5 papers .

@TG ,

Can yu please check whether it's right .n solve the other part of the qsn.

THanks .

Sukanya.

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by vikas sharma - Saturday, 21 February 2009, 11:35 AM
 

In a college, where every student follows at least one of the three activities- drama, sports, or arts- 65% follow drama, 86% follow sports, and 57% follow arts. What can be the maximum and minimum percentage of students who follow
·          all three activities
·          exactly two activities

Answer: Let us again see the surplus:

Percentage of students who follow drama + Percentage of students who follow sports + Percentage of students who follow arts = 65% + 86% + 57% = 208% Þ surplus = 108%. This surplus can be accommodated through adding elements either to intersection of only two sets or to intersection of only three sets. As the intersection of only two sets can accommodate only a surplus of 100%, the surplus of 8% will still be left. This surplus of 8% can be accommodated by adding elements to intersection of three sets. For that we have to take 8% out of the intersection of only two sets and add it to intersection of three sets. Therefore, the minimum percentage of people who like all three = 8%. In this case the percentage of students who follow exactly two activities will be maximum = 92%.

The surplus of 108% can also be accommodated through adding elements to only intersection of three sets. As adding 1 element to intersection of three sets give a surplus of 2 sets, adding 54% to intersection of three sets will give a surplus of 108%. Therefore, the maximum value of students who follow all three activities is 54%. In this case the percentage of students who follow exactly two activities will be minimum = 0%.

We can also solve it mathematically Þ x + 2y = 108%, where x + y £ 100%. The maximum value of x will give minimum value of y, whereas minimum value of x will give maximum value of y.

 

HI  SRI KLR CAN U PLEASE EXPLAIN ME THIS AGAIN I DIDNT GET WHY 54% AND HOW ADDING IN ONE ADD IN ALL .WAITING FOR REPLY

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by vikas sharma - Saturday, 21 February 2009, 11:46 AM
 

hi TG SIR

CAN U ELABORATE BELOW GIVEN AGAIN

 

In diagram 1, we have added 1 element to intersection of only two sets (A and B but not C). We can see that A and B both increase by 1 and therefore we get a surplus of 1 element.

In diagram 2, we have added 1 element to intersection of all the three sets (A and B and C). We can see that A, B and C all three increase by 1 element each and therefore we get a surplus of 2 elements.

Therefore, in case of three sets, we can accommodate the surplus by

·          adding elements to intersection of only two sets in which case a surplus of 1 element can be accommodated by increase of 1 element in the intersection of only two sets.

·          adding elements to intersection of three sets in which case a surplus of 2 elements can be accommodated by increase of 1 element in the intersection of three sets.

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Ashish Sharma - Saturday, 25 April 2009, 09:26 AM
  supercool
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by vakati babu - Sunday, 31 May 2009, 11:19 PM
 

There are 10 people learning A, 11 people learning B and 14 people learning C. The number of people learning just one is 20. The number of people learning all three is 3. How many people only learn two of three?


how to answer this /

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by William Wallace - Wednesday, 3 June 2009, 05:52 PM
  Hi TG,

Kudos to u as it's really a wonderful article but i have some doubts related to that.

in 1st problem "According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?" u said surplus is 125 % and hence the minimum% of people who like all three is 25%

But in second problem "
In a college, where every student follows at least one of the three activities- drama, sports, or arts- 65% follow drama, 86% follow sports, and 57% follow arts. What can be the maximum and minimum percentage of students who follow
·          all three activities
·          exactly two activities"

The surplus of 108% can also be accommodated through adding elements to only intersection of three sets. As adding 1 element to intersection of three sets give a surplus of 2 sets, adding 54% to intersection of three sets will give a surplus of 108%. Therefore, the maximum value of students who follow all three activities is 54%

My question is that shouldn't the answer in the 1st problem be 12.5 % rather 25% as is the case in the second question?? I hope u get my doubt smile

Please answer this and clear this doubt. 
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by William Wallace - Wednesday, 3 June 2009, 06:05 PM
  Hi Vakati,

draw diagram , formulate equations and done smile...Is ans 3???

a+d+f=7
b+d+e=8
f+e+c=11
a+b+c=20

to find d+f+c=(26-20)/2=3.

Sorry could't draw the diagram.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by vikas yadav - Friday, 19 June 2009, 03:18 PM
 

@TargetIIM

Hi dude,

Please read the statements below carefully as mentioned by TG sir while explaining the same problem.

This surplus of 25% can be accommodated by adding elements to intersection of three sets. For that we have to take 25% out of the intersection of only two sets and add it to intersection of three sets. Therefore, the minimum percentage of people who like all three = 25%.

So,actually v are taking out the elements from the intersections of two sets and putting them in all the 3 sets intersection space.This would mean covering a surplus of 1 per element taken out from the sets of twin intersection.Hence,it would be 25% and not 12.5% dear.

I hope you got my explaination well.

Thanks

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by William Wallace - Friday, 3 July 2009, 02:28 PM
  Thanks Vikas smile
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Pragya dasgupta - Sunday, 12 July 2009, 07:30 PM
 

HEllo

Can Anyone help me ith this problem

Is there any Fixed process to solve this ype of problems.

in a job fair among 100 participants who attended the interview,the number of participants who attended for company A is more than that of co. B is more than that of C.The no of participants who attended interview of exactly one co. is more than that of 2,which in turn is more than that of 3.Among these 100 participants at least one person attended the interview of all the 3 companies.
Q:What is the minimun possible no. of participants who attended the interview of co. A?
a.36 b.38 c.37 d.40 e.48
Q.What is the max possible no of participants who attended the interview of co. C?
a.56 b.45 c.65 d.67 e.64

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by vivek ghiria - Sunday, 26 July 2009, 06:25 PM
  Hi TG

I am going through lessons in this forum one by one.
I have one concern.
After going through a particular lesson, If few problems pertaining to that chapter will be available, then it will help us a lot.
As of now, I have to search the problems related to that chapter in Quant-DI forum which take bit extra time.

Thanks a lot for the lessons -
Vivek
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Nitin Kumar - Thursday, 13 August 2009, 11:08 PM
 

Hi TG,

Que: In a class of 120 students, each student studies at least one of the subjects from H, E and M. 59 study H, 67 study E and 73 study M. 34 study M+H, 26 study E+M and 33 study H+E. Then find the max and min number of students who study all the three subjects? 

 If I solve the question by drawing the venn diagram the max value I am getting as 26.

While if I solve this question in this way then I m getting rt ans.

total students - 120

surplus = 59+67+73-120=79

Total number of students study more than one sub = 34+33+26=93

b'coz surplus is 79 but being accomodated is 93, that's why max no. of students study more than 3 subjects is 93-79=14

Please let me know is this correct way of sloving this que.

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by ashu jain - Thursday, 17 September 2009, 01:04 PM
  The problem that I am facing is that the lesson is given on solving the question based on percentage but most of the time the question does not contain percentage but real numbers where converting into percentage can be cumbersome.
Like this question given below:

Q)In a survey report, which was conducted in a club of 300 men, it was found that 100 men use a products of brand A, 75 use the same products of brand B and 175 use the same products of brand C. What is the maximum possible number of men using all the three brands?

Here x+2y = 50.
What now???

I am not getting the hang of this thing!!!!!!!!!!!!!!!!!!!!!!
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by ROHIT K - Thursday, 17 September 2009, 03:05 PM
  Hi ashu,

Q)In a survey report, which was conducted in a club of 300 men, it was found that 100 men use a products of brand A, 75 use the same products of brand B and 175 use the same products of brand C. What is the maximum possible number of men using all the three brands?

is the answer 200..?

Please check and revert back..

Rohit
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Pallav Jain - Thursday, 17 September 2009, 05:08 PM
 

Hi All,

Can anyone please explain me how to approach this kind of questions?

In a class of 30 students, there are 2 categories of students:
Liars: who always lie.
Truth Tellers: who always speak the truth.
These students make three different statements as follows :
Statement I :Seven of them say “ There are exactly 7 Liars in this class”
Statement II :Eight of them say “ There are exactly 8 Liars in this class”
Statement III :The rest of them say “ There are exactly 15 Liars in this class”.
How many Liars are there in the class ?

Options :-

a) 7      b) 8     c) 23     d) 22     e)  15    

Thanks

Pallav

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by ashu jain - Thursday, 17 September 2009, 08:06 PM
  The OA is 25.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by ashu jain - Thursday, 17 September 2009, 08:11 PM
  I think answer should be option e) 15.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by ROHIT K - Thursday, 17 September 2009, 11:33 PM
  Hi Ashu,

Sorry mate i made a big goof up ..

Anyways coming back to your question,

Q)In a survey report, which was conducted in a club of 300 men, it was found that 100 men use a products of brand A, 75 use the same products of brand B and 175 use the same products of brand C. What is the maximum possible number of men using all the three brands?

Ans:

Total Men=300
A=100, B=75, C=175

A+B+C=350

Surplus=350-300=50

Now how do we allocate this surplus 50 to maximize A^B^C..?

For each men allocated to A^B^C, we get surplus of 2.

Therefore for surplus of 50 we allocate 50/2=25 men to A^B^C.

Hence 25 is the Answer..

Please check if I am going wrong anywhere..

Hope this helps..smile
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by ashu jain - Saturday, 19 September 2009, 02:06 PM
  thanks Rohit. you are right bro.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Suresh S - Monday, 21 September 2009, 12:04 PM
  Hi sir .. its really helped me much sir
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Rajat Vashishta - Tuesday, 20 October 2009, 11:02 AM
  In the problem
"According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three? "

why do we have to include 25% in the intersection of 3 sets? Cant this no be 12.5%?? In that case too, the intersection of 3 sets would consume a surplus of 25%, while the intersection of 2 would consume 100%. So the whole surplus of 125% would be accommodated.
Please tell me where i am wrong?
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Rajat Vashishta - Tuesday, 20 October 2009, 03:05 PM
  and vikas's explaination is not sufficient. why we are taking 25% from the twin set intersection is because putting 25% in 3 set intersection would give us a surplus of 150% so we need to lessen it from the 2 set intersection!
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Total Gadha - Wednesday, 21 October 2009, 09:47 PM
  Rajat,

100% se jyada quantity kahan se laoge? Agar number 100 hi honge to 100 se jaayada kaise allocate karoge?

Total Gadha
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Rajat Vashishta - Friday, 23 October 2009, 01:47 AM
  extremely sorry for the silly doubt..
atleast it got cleared..
Sir,
can we have some questions on maxima n minima..a small set maybe? seems everytime i think i've got this concept right, a new question pops up and baffles me!
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Jayant Choudhary - Friday, 30 October 2009, 02:30 PM
  TG sir,,

Here is a problem on Venn diagrams which is solvable using equations but when i apply ur concept i get stuck.. can u please provide the explaination using ur method of surpluses!!!!

Half of a class of 200 students enrolled for exactly one of the three activities swimming, skating and dancing. Total enrollments were 80 in swimming, 75 in skating and 60 in dancing from the class. Number of students who enrolled for skating and swimming only was 10 more than the number of students who enrolled for skating and dancing only.
Q 1 Find the maximum possible number of students who enrolled for exactly 2 activities?
Q 2 Find the minimum possible number of students who enrolled for at least one of the three activities.

Please help me out!!!
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Saravanar B - Sunday, 1 November 2009, 02:35 AM
 

Hi Jayant,

Total students enrolling for the classes = 200/2 = 100

Swimming+skating+dancing = 80 + 75 + 60 = 215

Surplus = 215 - 100 = 115

This 115 has to be accomodated in the "exactly two" and "exactly three" region..

As far as ques 1 is concerned the max for exactly 2 activities : it can accomodate 100 students ( as the total students we've is only 100 )

remaining 15 (i.e., 115-100 ) has to be accomodated in the exactly three region.... this 15 is taken from exactly two region ( i.e., 100 - 15 = 85 ) and placed it in exactly three region.. so the ans is 85...

pls let me know whether u hav understood or not ???

Cheers.........................

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by mayuri joshi - Sunday, 1 November 2009, 12:38 PM
 

Hi Jayant this is related to your problem. Also Saravanar,

I think you have misunderstood the problem. The total number of people attending the classes is NOT 100. The total number of people attending exactly one of the classes is 100. Hence what you are doing is wrong -- since you are assuming a surplus over the value of 100 but the total value is NOT 100 in the first place.

This is how I think u do this -

Assume a, b, c to be the three sets. Assume m, n, p to be the number of people attending exactly one of the 3 classes. Assume x, y, z to be the intersection of a and b, b and c, c and a. Let l be the intersection of all three.

then we have 2 equations -

m + n + p + 2(x + y + z) + 3l = 80 + 75 + 60 = 215

but m + n + p = 100

so, 2(x + y + z) + 3l = 115 -----eqn 1.

also

m + n + p + x + y + z + l = total number of students.

100 + x + y + z + l cannot be more that 157. ( from eqn 1)

so x + y + z + l <= 57 ----- eqn 2. (and required value of x + y + z is max when value of eqn 57.)

solving 1 & 2 we get l = 1; x + y + z = 56

hence the maximum value of students attending exactly two classes is 56.  

 

 

 

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by mayuri joshi - Sunday, 1 November 2009, 12:36 PM
 

For the next problem,

using both above eqns -

2 (x + y + z) + 3l = 115

subs in this eqn y = x + 10 as per given data. For obtaining minimum values, if we consider x as 0 then y = 10. We can consider z as 0 for minimum value but the eqn doesnt have + integer values upon solving. Hence we consider z = 1.

so l = 31.

now 100 + x + y + z + a = total number of students.

so total number of students (min) = 100 + 0 + 1 + 10 + 31 = 142.

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by amit amit - Monday, 2 November 2009, 01:31 AM
  First one's answer is 56
2nd
question's answer is 142
Given is "who enrolled for skating and swimming only was 10 more than the
number of students who enrolled for skating and dancing only

let

the number of students who enrolled for skating and dancing Xonly= e
=>no of students enrolled for skating and swimming Xonly=e+10=f


Surplus is 115.
Suppose there r only 100 students now in ven diagram and 100 r outside it.
our job is to accommodate surplus of 115 using at most remaining 100 students.

Let e=0  => f=10 , let g be the no. of students common in all 3 sets.

When from 100(students) outside Venn diagram we take one in the area common to two only,  surplus reduced by 2.
explaination=> new total=101 surplus =215 => 215-101=114, plus one student is in the area common to two, it consumes one more surplus.

When one student is taken from outside venn diagram into area common to all 3,  surplus is reduced by 3.

thus,
let x= no. of students enrolled in exactly 2 activities(each consumes 2 surpluses)
 y= no of students enrolled in exactly 3 activities.(each consumes 3 surpluses)
==> total surplus is 115.
 hence,  2x+3y=115
      solving the equation, max value of x is 56.

For minimum possible number of students who enrolled for at least one of the three activities , make y maximum
but minimum value of x is 10 when e=0
      which consumes 20 surpluses.
 remaining surplus = 95.
when 
let  d be the no. of students enrolled for  swimming and dancing only
now,a=x-10, as we hv counted 10 students before
2(a)+3y=95
        2a+3y=95
        maximum value of y=31 ==>a=1 in above equation.
==>  x=e+ (e+10)+d,
e=0, f=10, d=1
 ==> x=11. y=31 and initial 100 students.
so, 100+11+31=  142

here f=e+10, condition satisfied






Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by amit amit - Monday, 2 November 2009, 01:04 AM
  Can anyone help me with binary logic problem, problem of truth teller, liar, alternator with an example??? 
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Jayant Choudhary - Monday, 2 November 2009, 07:08 AM
  @saravanar...mayuri is right we cant take total value of students as 100.. mayuri and amit thanks for the lucid explaination!!!
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by rohit dwivedi - Tuesday, 10 November 2009, 10:41 PM
  Hi TG and family,
would need ur help in solving following problem according to above concept.

In a survey conducted, it was found that, of the 150 people who were surveyed, 90 read sports magazines, 80 read business magazines and 70 read political magazines. Each of the surveyed persons reads at least one of these three magazines.

What is the maximum possible number of people who read sports magazines only?
90

a) 60 b) 70 c)80 d)
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by akash gupta - Thursday, 12 November 2009, 01:38 PM
  ans is 70..
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by amit amit - Saturday, 14 November 2009, 11:48 AM
  ans is 70
total surplus= 90
50 in business and politics only will contribute 50 surplus.
20 common all the three magazines will contribute 40 surplus
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by sammy badyal - Sunday, 15 November 2009, 06:49 PM
  answer is 70 keep 20 in intersection of three and 50 in intersection of business and political sets, this will absorb surplus of 90 with sports magazine max
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Pallav Jain - Wednesday, 18 November 2009, 01:21 AM
   Question :--
In a survey it was found that 80% of viewers watches DD, 60% watches BBC and 75% watches Star Plus.

What is the minimum percentage of the viewers watching all the three channels?

  a60%
  b45%
  c15%
  d20%

  e10%
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Ashwin A - Wednesday, 18 November 2009, 10:56 AM
  15percent
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Pallav Jain - Wednesday, 18 November 2009, 12:53 PM
  hey ashwin can u plz explain it in detail.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by amar goswami - Thursday, 19 November 2009, 02:16 AM
  hi pallav,

  Surlus = 80% + 75% + 60% -100% = 115%

to find out minimum value for all three channels we need to accommodate maximum value of surplus in two channels. Max value it can take is 100% but still we are left with 15% hence this needs to be put in all three channels. 
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Pallav Jain - Thursday, 19 November 2009, 03:55 AM
  Hey Amar, can you please explain it ?

A REAL test contains 3 sections: QA, VA and DI. A student taking the test has to attempt at least one section. When the data of test takers was assimilated, it showed that 74% of students attempted QA, 91% attempted VA and 77% attempted DI section.

If the percentage of students who attempted all the three sections is found to be 71%, then find the possible percentage of students who attempted only two sections.

58 %
21 %
0
37 %
Can not be Determined

Cheers !!!
Pallav
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by amar goswami - Thursday, 19 November 2009, 11:28 AM
  Hi Pallav,

   Total surplus = 142 %
suppose only two sections =x %
and only three = y % = 71 % given
hence x + 2y = 142%

x + 142 =142
x= 0

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Pallav Jain - Thursday, 19 November 2009, 02:18 PM
  thanx Amar but I cud'nt get this step...... why u have taken 2y

hence x + 2y = 142%

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by amar goswami - Thursday, 19 November 2009, 07:27 PM
  if u draw venn diagram then y belongs to the area which is being shared by 3 circles, say a, b and c. Hence anything you put in this area will be counted 3 times in the the sum of a+b+c and 2 times in the surplus.
coz surplus = a+b+c -100%
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by abhishek rai - Saturday, 8 May 2010, 06:19 PM
  Great one sir, but maybe the CBT club members can have some more of this stuff and a full fledged chapter on set theory?

Waiting for the Reply.. thoughtful
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by deepika guliani - Friday, 6 August 2010, 09:57 PM
  Amazing Article ..I always had a problem solving these questions..but not anymore smile
Thank you indeed.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by vivek bajaj - Saturday, 21 August 2010, 12:26 PM
  Hi TG,

I might be wrong, but can u check upon:

In a college, where every student follows at least one of the three activities- drama, sports, or arts- 65% follow drama, 86% follow sports, and 57% follow arts. What can be the MAXIMUM % OF STUDENTS WHO FOLLOW ALL 3 ACTIVITIES?


It seems to me (maybe wrong), the maximum % of students who follow all 3 activities can be 57% (by common sense; since these same 57% students who follow arts can follow sports as well as drama) as opposed to the 54% explained by you.

If I am wrong, please can u explain the 54% concept more elaborately.

Thankyou.

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by ritika bhalla - Monday, 23 August 2010, 06:16 PM
  dear TG sir..

i have a doubt that is bothering me..

i just am not able to understand how x+y=100%

i noe u have replied to this in earlier posts but its not clear

kindly help sir..waiting for your reply.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Nishit Vora - Tuesday, 21 September 2010, 05:06 PM
  Hi TG,

I just loved your concept
But the following problem from latest Time Mock is bothering me. could you please help me out

A survey about prefered TV channels amongst 10,000 people
93%liked sony
89% Zee
81% Star plus
75% Zee cinema
78% Mtv

100 did not like any channels

Find Minimum Number of people who liked all 5.

So according to your concept adding 93 , 89 , 81 , 75, 78
gives 416%

So now excess is 316%
So what to do after this?
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Rebeck Carvalho - Saturday, 25 September 2010, 07:16 PM
  Superb Article TG,hats off!!!
Can u please also include about 4x4 Venn Diagrams .Then it would be a complete article
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by ankur kejriwal - Tuesday, 12 October 2010, 03:25 PM
 

Hey i know thogh the post is very old , but if anyone is watching smilesmile then

How the minimum value of P is 10 % .

If surplus is 210 then a + 2b + 3c = 210 , c being intersection of 4 diseases .

Pls help ......

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by albus dumbeldore - Saturday, 9 July 2011, 01:23 AM
  hii...
i still cudn't get the maxima /minima concept
anybody can clear it for me ....
the adjusting the surplus part and
how do we get the equation x + 2y =0

thanks
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Dang Dong - Monday, 11 July 2011, 06:51 PM
  In this case we assign the variables to every area of the Venn diagram and form the conditions keeping two things in mind:
· try to express the areas in the Venn diagram through least number of variables.
· all the numbers will be zero or positive. No number can be negative.

Out of 210 interviews of IIM- Ahmedabad, 105 CAT crackers were offered tea by the interview panel, 50 were offered biscuits, and 56 were offered toffees. 32 CAT crackers were offered tea and biscuits, 30 were offered biscuits and toffees, and 45 were offered toffees and tea. What is the
· maximum and minimum number of CAT crackers who were offered all three snacks?
· maximum and minimum number of CAT crackers who were offered at least one snack?

Answer: Let’s make the Venn diagram for this question. Since we want to assume least number of variables, we can see that assuming a variable for the number of students who were offered all three snacks will help us express all the other areas. Let the number of students who were offered all three snacks = x.



In the above diagram, we have expressed all the areas in terms of x. To decide maximum value of x, we note that 32 - x, 45 - x and 30 - x will be zero or positive. Therefore, the maximum value of x will be 30. (30 is the lowest among 30, 32 and 45). To decide minimum value of x, we note than x - 19 and x – 12 will be zero or positive. Therefore, x cannot be less than 19 (19 is the higher number between 19 and 12).

Therefore, maximum and minimum number of CAT crackers who were offered all three snacks = 30 and 19.


The number of CAT crackers who were offered at least one snack = Total number of CAT crackers in the Venn diagram = x + 28 + 32 - x + x + 45 - x + x - 19 + 30 - x + x - 12 = 104 + x.
As the maximum and minimum values of x are 30 and 19, respectively, the maximum and minimum value of 104 + x will be 134 and 123, respectively.

Maximum and minimum number of CAT crackers who were offered at least one snack = 134 and 123.
ANY WAY TO SOLVE FOR THE VALUE OF X?
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by k m - Sunday, 17 July 2011, 12:20 AM
  can sum1 pll help me out and explain this problem to me??

Q.A survey was conducted among 500 ppl each of whom likes at least one of apple, orange , banana.The number of ppl who like apple is 240, those who like orange are 250 and those who like banana are 290.

Q1. If 60 ppl like only apple and banana, then what is the maximum possible number of ppl who like only orange?

1)120   2) 130  3)140(ans)

Q2. If 120 ppl like only apple, then what is the maximum possible number of ppl who like only orange and banana?

1)170  2)160(ans)   3)180

Q3. What is the maximum possible number of ppl who like all the 3 fruits?

1)110   2)120   3)150    4)130   5)140(ans)
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Rajasekaran Rajaram - Sunday, 24 July 2011, 12:18 AM
 
A+B+C+D+E+F+G = 500
A+B+C+2(D+E+F)+3G=780
D+E+F+2G=280
Apples =A+D+G+E=240
Banana=C+E+F+G=250
Orange=B+D+F+G=290

1) Given e =60,

From equation D+E+F+2G=280,
                      D+F+2G=220

In order to maximize B in equation B+D+F+G=290 put D and F = 60 and hence B will be 140

3) In equation D+E+F+2G=280 put D, E, F = 0 to maximize G which will be 140 smile
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by soumyarup banerjee - Friday, 19 August 2011, 06:09 PM
  I have a question :

When say we have 83 persons liking soccer , 88 persons liking cricket and 51 persons liking chess. Total number of people surveyed is 100.

Here when we calculate the surplus it is : (83+88+51)-100 = 122

Now , the maximum number of persons who can like all the 3 games can be = 122/2 = 61 , but that is not possible bcoz only 51 likes chess !!

Kindly clarify this for me
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by gaggi d - Monday, 12 September 2011, 08:17 PM
  Hi TG,
CAn you explain why in the question where u have calculated the maximum no of people doing all three activities is 54 % instead of 57% as it is visible directly..
Because let the the 57% to be part of other percentages as well..
Correct me if i am wrong
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Rajasekaran Rajaram - Monday, 12 September 2011, 10:31 PM
  Nishit Vora,

Is the answer 1500 for this question.

16%(10,000)-100
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Gaurav Tomar - Sunday, 9 October 2011, 08:23 PM
  one thing got wrong in the (2.), that in the below part there is the value is x-29, instead of the x-19. Thanking you sir for the above article.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by n k - Sunday, 30 October 2011, 12:33 PM
  Hi Everyone,

Can you please help me in solving

Let A denote the set of integers between 1 and 1000 which are divisible by 12. Let B denote the set of integers between 1 and 1000 which are divisible by 18. How many elements are in the set A∪B?
(A) 108
(B) 109
(C) 110
(D) 111
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by TG Team - Monday, 31 October 2011, 12:28 PM
 

Hi n k smile

Number of elements in set A = n(A) = [1000/12] = 83

and number of elements in B = n(B) = [1000/18] = 55

Number of elements common in both A and B = n(A∩B) = [1000/LCM(12,18)] = [1000/36] = 27.

So n(AUB) = n(A) + n(B) - n(A∩B) = 83 + 55 - 27 = 111. smile

Kamal Lohia

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Sreedipto Bhattacharyya - Friday, 3 February 2012, 12:38 AM
  Hi cud anyone help me with this problem please. Cannot understand how to approach. plz help.


Q. In a group of 100 students, each student has to opt for one or more of the 3 subjects among Physics, Chem and Maths. The number of students opting for maths is more than that of physics which in turn is more than that of chem, which in turn, is more than the no of students opting for exactly 2 of the 3 subjects, which in turn, is more than the no of students opting for all the 3 subjects. It is also said that at least one student opted for all the 3 subjects.

1. Max no of students opting for chem:?
a)72 b)79 c)80 d)81 e)None of these

2. Min no of students opting for maths:?
a)38 b)37 c)36 d)35 e)34

3. If exactly half the students opted for maths, what is the max no of students who

opted for all the three subjects?
a)15 b)16 c)17 d)18 e)19

4. Max no of students who opted for only physics:?
a)33 b)50 c)49 d)48 e)52

5. Max no of students who opted for physics and chem but not maths:?
a)47 b)48 c)49 d)50 e)51
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by neha aggarwal - Thursday, 22 March 2012, 08:05 AM
  Hi TG sir.. Great Article..
I am just unable to understand that how are you adjusting the surplus to intersection of two circles...

For minimum case:
Like if we have a surplus of 108% how do we conclude that a surplus of 100% is adjusted to intersection of two circles...
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by TG Team - Thursday, 22 March 2012, 01:04 PM
 

Hi Neha smile

100% means all persons. So no set can have more than 100% i.e. all of persons. So if we want that there should be least number of persons who fall in all three category, we should allot maximum number to intersection of two which is 100%.

See, if it helps. smile

Kamal Lohia

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by neha aggarwal - Saturday, 24 March 2012, 10:01 PM
  Hmmmmmm. I got it...

Thanks Sir
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Prerna Golani - Monday, 14 May 2012, 11:28 PM
  Hi TG
In a college, where every student follows at least one of the three activities- drama, sports, or arts- 65% follow drama, 86% follow sports, and 57% follow arts. What can be the maximum and minimum percentage of students who follow
· all three activities
· exactly two activities
We can also solve it mathematically Þ x + 2y = 108%, where x + y £ 100%. The maximum value of x will give minimum value of y, whereas minimum value of x will give maximum value of y.

I am unable to understand how x+2y =108%.Please explain this part.....plz
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Prerna Golani - Monday, 14 May 2012, 11:30 PM
  The maximum surplus it can accommodate is 2 × 100% = 200%. How it is calculated....please explain
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by TG Team - Tuesday, 15 May 2012, 06:51 PM
 

Hi Prerna smile

If you understand what are x and y then it's easy to get that x + 2y is the surplus i.e. what is extra than 100%.

I'd suggest you to re-read the article again.

Kamal Lohia

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Prerna Golani - Sunday, 20 May 2012, 07:12 PM
  I am unable to understand x+2y
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by bamlesh kumar - Wednesday, 23 May 2012, 12:58 PM
  plz tell me whether videos lesson be provided to the cbt member...will I be able to download videos lessons on each topic by paying 1000 rs
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by bamlesh kumar - Wednesday, 23 May 2012, 12:59 PM
  plz tell me whether videos lesson be provided to the cbt member...will I be able to download videos lessons on each topic by paying 1000 rs
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by kshitij sharma - Saturday, 22 September 2012, 05:06 PM
  TG Sir, ur help required in this question..
There is a group of 200 students, where each student studies one or more of the three subjects among X, Y and Z . The no. of students studying Z is more than no. students studying X, which in turn, is more than the number of students who study Y, which, in turn, is more than the no. of students who study exactly 2 subjects, which in turn is more than the no. of students who study all the subjects. It is known that atleast 1 student studies all the subjects.

Q.1) Max no of students who study Y ? (148 ; 149 ; 150 ; 147 ; None)
Q.2) Min no. of students who study Y ? (67 ; 68 ; 69 ; 70 ; None)
Q.3) Max no of students who study only X ? (100 ; 99 ; 98 ; 97 ; none)
Q.4) If it's known that exactly half the students study Z, what is the max no. of students who study all the three ??(30 ; 31 ; 32 ; 33 ; none)
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Ankur Jain - Thursday, 4 October 2012, 07:01 PM
  I am too confused on this. The question says there are 4 cars with radio and power windows (off course without AC). So , what are we subtracting 3 (all 3 features) from this ? Doesn't seem to me correct !
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Devishree Nath - Monday, 15 October 2012, 01:18 PM
  hello TG , can u plz help me solve d problem given in the attachment????
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Rupert Martin - Tuesday, 16 October 2012, 02:50 PM
  Sorry my friend i have tried to solve the problem but i damn confuse with sum if you get any solution then fwd to me.Thanks.
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by arsh arora - Saturday, 20 October 2012, 03:32 PM
 

Hi TG,

  AWESOME PIECE OF WORK TG SIR!!!...UR SURPLUS concept simply roccksssss!!!!...

Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by ishant goel - Sunday, 21 October 2012, 12:33 PM
  @Devishree Nath

6)d
7)e
8)e
9)c
10)e
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Jagroop Singh - Friday, 14 August 2015, 02:35 PM
  What if surplus is 50%????????
Re: Venn Diagrams- Basics, Problems, Maxima and Minima
by Jagroop Singh - Friday, 14 August 2015, 03:02 PM
  What if the question is........ What is the maximum possible number of men using only A???????