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Learning Quant through problem solving
by Total Gadha - Monday, 27 April 2009, 04:37 AM
 

CAT 2009 quant problems CAT 2010Year after year, the only burning question which nags my mind is “how do I prepare students better for CAT quant?” Many of the answers have started coming. For example, after two years of TathaGat, we have realized that making our classroom teaching heavy with quality questions yields better results than having mere practice questions in the classroom content and having tests and mocks full of quality material. For one thing, many students don’t solve the mocks completely. For another, by the time mocks have arrived, they don’t have enough time to deliberate and develop the fundamentals behind good problems. Second thing which we have seen is that exposing students to a vast variety of questions on different fundas is better than giving repeated questions on the same funda. Although collecting problems of different flavors and colours is not easy, it is better than having repeated problems. Still, we have not worked everything out. There are questions which are unanswered. And all of them boil down to the same problem- how to make quant more easily understandable to students? Is quant really difficult to master for students who did not pursue it after school?

My vehement answer is no. It is not difficult to master. It takes only as much pain as it takes to master any other subject. And like any other subject, it becomes more and more understandable as you spend more and more time on it. But learning does not happen in classrooms. It happens when you look for new problems, try and discover new things, think deeply about some topics, experiment on your own, test your own theories, and so many other things. The key is to get totally involved. In this article, maybe my CAT aspirants will get some feel about how an aptitude for quant is slowly developed through different adventures.

I was recently having a look at a problem that I had posted in the Quant-DI forum long time back. The problem can be found in TG Special- 1 thread, a collection of my problems that I keep posting in the forum. The problem, shown in the figure below is extremely short:


cat 2009 quant problems cat 2010


cat problems

cat problems

Re: Learning Quant through problem solving
by sudip saha - Monday, 27 April 2009, 04:15 PM
  Is it 10 pisoners ???
Re: Learning Quant through problem solving
by Total Gadha - Monday, 27 April 2009, 07:14 PM
  yep. smile
Re: Learning Quant through problem solving
by nikhil chaturvedi - Wednesday, 29 April 2009, 02:29 AM
  A knowledge laden ,nicely written article
sir.........I am gonna fan of you.Please post some more of similar kind so that we can have a very comprehensive preparation to tame this year's wild CAT
Re: Learning Quant through problem solving
by ramya rao - Wednesday, 29 April 2009, 07:52 PM
  can u pl explain how it is 10
Re: Learning Quant through problem solving
by akash gupta - Wednesday, 29 April 2009, 10:00 PM
 

hey cant guess afetr readin the answer to earlier question

guess how much is 2^10

its 1024 and the no of bottles presnt are 1000..which is less than 1024..thus using binary theoram its 10

Re: Learning Quant through problem solving
by alsadra @TG - Friday, 1 May 2009, 10:49 AM
  Hi Ramya

let us consider there are 16 bottles.
we divide the bottles into two groups of 8 each, take a part of the wine from each bottle and make two cups of wine( each comprising of wine from its own group).
Tn= thief no 'n'

T1 will determine whether the poisoned bottle is in the 1st 8 or 2nd 8.
T2 will determine in which four it is
T3.....................which 2
T4.....................which 1.

so if there are 2^n bottles we need n thiefs.
if the no is between 2^n and 2^(n-1), again we need 'n' thiefs only.

as in our qn 2^9< 1000< 2^10.

we need 10 thiefs.

with regards
Alsadra



Re: Learning Quant through problem solving
by ramya rao - Friday, 1 May 2009, 08:17 PM
  hey thanks a lot.
Re: Learning Quant through problem solving
by himanshu mishra - Wednesday, 13 May 2009, 09:20 AM
 

Tg,

    You have amazing power of lucid explanation. 

Re: Learning Quant through problem solving
by rohin ji - Thursday, 14 May 2009, 07:57 AM
  TG, m an engineer but ironically im not so good at problem solving...and its precisely coz of the fact that i havnt solved a lot of quesns on maths earlier in my studies...and now, with two other sections to prepare for CAT, i dont find unlimited time to make up for the lack of practice....
can u suggest what i can do to enhance my problem solving skills in the least possible time??
Re: Learning Quant through problem solving
by Atul Mittal - Monday, 18 May 2009, 04:10 PM
  hi TG,

In case of finding the polynomial. what if it contains negative coefficients?

second thing for the second polynomial when we get 22507 how can we predict that for power of x the coefficient is 25 and not 22 for x^2?

For the king's problem...
I think only one person is needed to find the poisoned bottle because no other constraints like time, least wine consumption (coz expensive) etc are not given in the problem.

Please help me in clarifying the doubts.

Regards,
Atul
Re: Learning Quant through problem solving
by SUPER gadhi.. :P - Monday, 18 May 2009, 04:46 PM
  this last 1 was a stoner mannn..!
awesome..n yeah... eye opener
                                            
Re: Learning Quant through problem solving
by Total Gadha - Friday, 22 May 2009, 02:42 AM
  Hi Atul,

When we are taking x = 100, x2 term will have 4 zeros at the end. That is why the coefficient is 2 and not 22 for x2 because I have to account for 4 zeros also.

Total Gadha
Re: Learning Quant through problem solving
by Ankita Chowdhury - Sunday, 24 May 2009, 07:46 PM
 

TG Sir,

Can ou please let me knw how to take the TG CopyCAt online.

I eagery want to taje up the tests.

I have got ur ebooks of NS n Gemometry they r really very helpful.

Re: Learning Quant through problem solving
by lalita chauhan - Wednesday, 27 May 2009, 05:34 PM
 

Hi all..

can anyone explain the logic of the coprime numbers and the equation related to it..

thanks & regards

lalita

Re: Learning Quant through problem solving
by nidhi soni - Wednesday, 27 May 2009, 10:35 PM
 

hi TG

i dint get prb 5th the plynomial one...could u explain it in different way

Re: Learning Quant through problem solving
by Eternal Flame - Thursday, 28 May 2009, 11:08 PM
 

Thanks TG !!! Add more problems please smile

Re: Learning Quant through problem solving
by Atul Mittal - Tuesday, 2 June 2009, 05:59 PM
  Thanks TG..
Sorry, I cd not reply earlier because i was busy in my project work...smile
Re: Learning Quant through problem solving
by anirban bhar - Saturday, 6 June 2009, 04:06 PM
  wat if the coefficients r negative as atul asked..........
plzz xplain
Re: Learning Quant through problem solving
by Total Gadha - Saturday, 6 June 2009, 04:43 PM
  Hi Anirban,

Question to padh lo. sad whole number coefficients negative kaise ho sakte hain.

Total Gadha
Re: Learning Quant through problem solving
by divya francis - Monday, 8 June 2009, 10:26 PM
  Hey TG, Just a small doubt.. if the question is to find the minimum number of prisoners, would not one prisoner do the job by drinking wine from bottles one by one, till he finds the poisoned bottle??
Re: Learning Quant through problem solving
by Total Gadha - Monday, 8 June 2009, 11:47 PM
  Hi Divya,

True. Actually, when I give the question in class I tell the students that the poison takes effect in one month and that the wedding, in which the king is going to use the wine bottles, is in one month only.

Total Gadha
Re: Learning Quant through problem solving
by rohin ji - Tuesday, 9 June 2009, 07:44 PM
  TG, m an engineer but ironically im not so good at problem solving...and its precisely coz of the fact that i havnt solved a lot of quesns on maths earlier in my studies...and now, with two other sections to prepare for CAT, i dont find unlimited time to make up for the lack of practice....
can u suggest what i can do to enhance my problem solving skills in the least possible time??

(u did not reply to this earlier...i request u to please suggest something to save my CAT!!!)
Re: Learning Quant through problem solving
by anirban bhar - Wednesday, 10 June 2009, 03:43 PM
  tg sir,


oops..srry sir ji.....

Re: Learning Quant through problem solving
by Namit Midha - Tuesday, 7 July 2009, 12:27 AM
 

can you pls answer this 1

magacian during one of his shows calls a volunteer and asks him to think of three three-digit numbers, say m, n, p. Then magician gives the volunteer another set of three distinct numbers X, Y, Z and asks him to give the magician the final value of Xm + Yn +Zp using which magician claims he can figure out each of the three numbers m, n, p that the volunteer had thought

Ques.volunteer gives the final value as 123456789 following which magician gives him the sum of his three numbers, what is the value of m+ n+ p.

a)1368     b)1248   c)1182        d)1089       e)1024

 

 

 

Re: Still wondering
by divya francis - Wednesday, 8 July 2009, 05:26 PM
 

Dear TG,

I do get the method which is being conveyed. But, the answer will be 999 if the poison takes effect in 1 month.. Or, am i missing something???

Any way nice question and a great article too.

Regards.

Re: Still wondering
by Brat 4 Cat - Tuesday, 14 July 2009, 05:30 PM
  Hi divya ,
Let me explain how ans is 10 .

King called 10 thieves (T1 to T10)
 
He gave a drop of wine bottle number -W1,W3,W5,W7....W999 to thief 1 (see w1,w3,w5...all have their LSB=1(least significant bit(sorry for being technocrat) .

T2 gets a drop of wine from - W2,W3  , W6,W7 and so on ( having second bit = 1 )

T3 gets a drop from W4,5,6,7 ...12,13,14,15...and so on ( 3rd bit - 1)

This will happen upto T10.


Now lets say , bottle 10 was poisoned.

this means -> 10 = 0000 00 1010  --->>Thief 2 and Thief 4 should die .



So after checking that which thieves died, King can easily get to know which bottle is poisoned !!




Taking this in other way , say thief 5 and thief 3 and thief 1 died.
This implies = 0000 0 10101  ==> Bottle number 21 is poisoned.(16+4+1)


Regards
Brat4Cat  !!smile


Re: Still wondering
by DAKSH anand - Wednesday, 15 July 2009, 02:58 PM
  u r gr8......Brat4Cat

thx for this gr8 solution!!!!!
Re: Still wondering
by Ayshwar Pandey - Thursday, 21 October 2010, 04:44 AM
  The question asks for minimum prisoners.
I don't understand y only 1 can't do.
We can ask him to drink from each bottle till he dies...Plz help!
No of Primes
by Sandipan Sarkar - Wednesday, 10 November 2010, 07:08 AM
 

Hi

I am not getting one thing....does phai(N) give the no of primes less than N????

if so....then phai(102)=102(1-1/2)(1-1/3)(1-1/17)=32 which is not true....

Re: No of Primes
by TG Team - Wednesday, 10 November 2010, 12:46 PM
  Hi Sandipansmile
It gives number of numbers which are co-prime to N and less than N.smile
Re: Learning Quant through problem solving
by amit kumar - Saturday, 13 November 2010, 10:39 PM
  hey credos to tg for writing a fab article...the last problem in particular can jst grab you.

please note it here the reason to choose power of 10 greater than p(1) is to make sure the greatest co-efficient in polynomial is not greater than the 10's power,so that coefficients dont mingle once added and the sum contains all the co-efficient cleanly.
Re: Learning Quant through problem solving
by vaibhav matle - Monday, 19 May 2014, 10:53 AM
  using binary logic we get 10. But how logically min 10 are required to test 1000 bottles?