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Thursday, November 13, 2008

Right Preparation for CAT Exams






   One of the things that has amazed experts and academicians about the CAT for a long time now, is that the exam continues to retain it’s aura of invincibility. This, in spite of the fact that most questions, which appear in the exam, are elementary class ten questions. Presented below is the quantitative aptitude (QA) section of the CAT 2007 paper along with the methodical approach that should be adopted to get the right answers. 

1) How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an odd integer less than 60? 

(a) 7 (b) 5 (c)
(d) 6 (e)

Thought process: 

Deduction 1: Since two positive fractions on the LHS equals 1/12 on the right hand side, the value of both these fractions must be less than 1/12. Hence, n can only take the values 49,51,53,55,57 and 59. 


Deduction 2: After this, students need to check which of the possible values of n would give an integral value of m. 
The equation can be transformed to 1/12 - 4/n = 1/m à (n - 48)/12n = 1/m. On reading this equation one should realise that for m to be an integer, the LHS must be able to yield a ratio in the form of 1/x. It can be easily seen that this occurs for n = 49, n = 51 and n = 57. Hence, there are only three pairs. 


Maximum solution time: 90 seconds 
2) Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos? (a) 18 (b) 15 (c) 19 (d) 17 (e) 16 

Thought process: 

Deduction 1: If you were to use two 50 miso notes, you would only pay the remaining 7 misos through one miso notes.


Deduction 2: If you were to use only one 50 miso note, you could use 10 miso notes in 6 different ways (from zero to five).


Deduction 3: If you were not to use any 50 miso notes, you could use 10 miso notes in 11 different ways (from zero to 10). Hence, the required answer is 1+ 6+ 11=18. 


Maximum solution time: 45 seconds 
3) In a tournament, there are n teams T1, T2, …, Tn, with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common: T1 and T2, T2 and T3, …, Tn -1 and Tn, and Tn and T1. No other pair of teams has any player in common. How many players are participating in the tournament, considering all the h teams are together? (a) n (k - 2) (b) k (n - 2) (c) (n - 1) (k - 1) (d) n (k - 1) (e) k (n -1) 

Thought process: 

If one considers six teams and four players per team, one would get four players in T 1 (each one of them unique), three more players in T 2 (since one player of T 2 would be shared with T 1 ), three more players in T 3 (since one player of T 3 would be shared with T 2 ), three more players in T 4 (since one player of T 4 would be shared with T 3 ), three more players in T 5 (since one player of T 5 would be shared with T 4 ) and two more players in T 6 (since one player of T 6 would be shared with T 5 and one with T 1 ). Hence, there would be a total of 18 (4+ 3+ 3+ 3+ 3+ 2) players with n = 6 and k = 4. Only option four would provide 18 as the solution. 
Maximum solution time: 60 seconds. 


4) Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares? 
(a) 4 (b) 0 (c)
(d) 3 (e)

Thought process: 

A number of students got stuck on this question for over five to seven minutes in the exam, since they tried to find out the squares of all two-digit numbers starting from 32. However, if one is well of the logic of finding squares of two digit numbers, one would realise that only three two-digit numbers after 32 have the last two digits in their squares equal (38, 62 and 88). Hence, there is no need to check any other numbers apart from these three. After checking these one would get the square of 88 as 7744. And hence, there is only one such number. 
Maximum solution time: 60 seconds 

About the QA section of CAT 2007 


Test takers who were able to attempt seven to eight questions out of the 25 questions in the paper received an excess of 95 percentile (for this section). Students were given 50 minutes to complete each section in the exam 


At zero marks in this paper, students reported a 20 percentile score. This in effect means that one in five test takers scored negative marks 


Sunil Sharma


Dil Se Desi Group


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