Venn Diagrams Basics, Problems, Maxima and Minima  
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.
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: Â·
Intersection (Aâˆ©B)
Denotes the set of elements that are shared by two or more given sets. In the
figure
A âˆ© B = {6,
12, 18, 24} Â· ˜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:
Only A =
{2, 4, 8, 10, 14, 16, 20, 22, 26, 28}, only B = {3, 9, 15, 21} Â· Union (AUB) Denotes all the elements of the given sets taken once.
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 The venn diagram for three sets is shown below:
It can be shown that Problemsolving through Venn diagrams: I use the following method to solve problems through Venn diagrams: Solved Examples: Of all the users on Totalgadha.com, 80% spend time in CAT QuantDI 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 Â·
will crack CAT? Answer: n(AUB) = n(A) + n(B)  n(Aâˆ©B) Ãž 100% =
80% + 60%  n(Aâˆ©B) Ãž n(Aâˆ©B) = 40% 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
â€” air conditioning, radio and power windows â€” were already installed. The
survey found: 15 had air
conditioning What is the number of cars that had none of the
options? (CAT 2003) Answer: We make the Venn diagram and start filling the areas as shown:
Total Number of cars according to the diagram = 2 + 6 + 3
+ 1 + 5 + 2 + 4 = 23. 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? What is the number of projects in which Medha
alone is involved? Answer: The Venn diagram for the three consultants is shown below:
Total Number of projects = 2 x number
of projects in which more than one consultant is involved  1 = 2 x 19  1 = 37. 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:
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 Aâˆ©B:
We can see that adding 1 element to Aâˆ©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 Aâˆ©B gives an extra 1 element.
Hence, for every surplus of 1 element we can add 1 element to Aâˆ©B. Letâ€™s see the Venn diagram for 3 sets:
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 Â· 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. Â·
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% Ãž 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 Â£ 100%. For minimum value of y, we need maximum value of x. 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 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% Ãž 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 Ãž x + 2y = 108%, where x + y Â£ 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: 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 Answer: Letâ€™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 â€“ 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.
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.

Re: Venn Diagrams Basics, Problems, Maxima and Minima  
TG Sir ki jai ho Thanks a ton. God Bless You! Small Wonder! 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
YAhooooooooo!!!!! Thnx TG Muahhhhhhhhh....... 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Here, the quality of content is best, relally ! Thank You. Software Engineer 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
TG == Too Good !!?? [] Awesome stuff... 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
"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  
Thank U very much TG..... God Bless You 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
a topic on cubes also please..... 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
+1 Gullz Golu 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Exhaustive yet Simple that,s ur trademark..... that's what we all like about this site... 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
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  
great 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Thank You Gullz it's clear now...i was having problems with interpreting the assumptions and thanks TG for this useful article 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Thanks to TG.... 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Hi Tom, Let me try. I can certainly imagine the hours on 'paint' I will have to spend to draw images of cubes Total Gadha 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
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  
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  
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  
Hey..lovely article...any word of praise wud be less... u really rock...am impressed...) god bless u!! 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Hi Mohit, I will certainly reply to you. Do post your problems. Total Gadha 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Hi TG Pls reply to my post also given above. Thanks

Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
hi Gullz, thanks for the explanation. i understood it. RV

Re: Venn Diagrams Basics, Problems, Maxima and Minima  
TG options r given now......... 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Hi Gullz, Have taken the printout of your question. Let me have a go at it. Total Gadha 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
A too good article........ Thanks a lot TG 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
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  
This is a cool stuff dear TG. 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
hi tg.pls post some text on functions,maxima and minima 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Hey Alpha, U got it right how did u solve the second one (37) 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Kudos Sir............. 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
fantastic... mindblowing... superb.... thanks TG.... Total Genius..... 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
A very good explanation. Thanks a lot!! 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
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  
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  
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  
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...thanku 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
Hi, Could you please guide me to solve this problem of Chinese checkers. Regards, Mohan 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
thank you TG sir.......... the concepts are of great help..... u rock sir!!!!!!! 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
Sorry, TG.I found the fallacy in my argument. The total percentage doesn't add up to 100 in the case proposed by me. 
4 Set or Greater Venn diagrams  
Hi TG plz give some easier ways to solve 4 set or 6 set venn diagrams 
Re: 4 Set or Greater Venn diagrams  
hi devi da... please post your 4 set or 6 set venn diagrams problem... 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Hi Amit, Thank you. Total Gadha 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Hey TG, Amazin article... Jus one doubt.. wats ur real name??? 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
a very good article indeed.....but i need more problems & examples like these.... thanx 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
a very good article indeed.....but i need more problems & examples like these.... thanx 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
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  
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  
supercool 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Thanks Vikas 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
The OA is 25. 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
I think answer should be option e) 15. 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
thanks Rohit. you are right bro. 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Hi sir .. its really helped me much sir 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
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  
@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  
ans is 70.. 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
15percent 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
hey ashwin can u plz explain it in detail. 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
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  
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  
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  
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  
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.. 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Amazing Article ..I always had a problem solving these questions..but not anymore Thank you indeed. 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
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  
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  
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  
Hey i know thogh the post is very old , but if anyone is watching 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  
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  
In this case we assign the variables to every area of the Venn diagram and form the conditions keeping two things in mind: Â· try to express the areas in the Venn diagram through least number of variables. Â· 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 Â· maximum and minimum number of CAT crackers who were offered all three snacks? Â· maximum and minimum number of CAT crackers who were offered at least one snack? Answer: Letâ€™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 â€“ 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  
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  
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 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
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  
Nishit Vora, Is the answer 1500 for this question. 16%(10,000)100 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
one thing got wrong in the (2.), that in the below part there is the value is x29, instead of the x19. Thanking you sir for the above article. 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
Hi n k 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. Kamal Lohia 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
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  
Hi Neha 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. Kamal Lohia 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Hmmmmmm. I got it... Thanks Sir 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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 Â· all three activities Â· exactly two activities We can also solve it mathematically Ãž x + 2y = 108%, where x + y Â£ 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  
The maximum surplus it can accommodate is 2 Ã— 100% = 200%. How it is calculated....please explain 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
Hi Prerna 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 reread the article again. Kamal Lohia 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
I am unable to understand x+2y 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
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  
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  
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  
hello TG , can u plz help me solve d problem given in the attachment???? 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
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  
Hi TG, AWESOME PIECE OF WORK TG SIR!!!...UR SURPLUS concept simply roccksssss!!!!... 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
@Devishree Nath 6)d 7)e 8)e 9)c 10)e 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
What if surplus is 50%???????? 
Re: Venn Diagrams Basics, Problems, Maxima and Minima  
What if the question is........ What is the maximum possible number of men using only A??????? 