CAT 2006 Question Paper


For the following questions answer them individually

Question 11

What are the values of x and y that satisfy both the equations?

$$2^{0.7x} * 3^{-1.25y} = 8\sqrt{6}/27$$

$$4^{0.3x} * 9^{0.2y} = 8*81^{1/5}$$

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Question 12

The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x <= y is:

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Question 13

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: 8;


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)?

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Question 14

The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

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Question 15

The graph of y - x (on the y axis) against y + x (on the x axis) is as shown below. (All graphs in this question are drawn to scale and the same scale and the same scale has been used on each axis.)

Which of the following shows the graph of y against x?

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Question 16

Consider the set S = { 1, 2, 3, .., 1000 }. How many arithmetic progressions can be formed from the elements of S that start with l and end with 1000 and have at least 3 elements?

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Question 17

What values of x satisfy $$x^{2/3} + x^{1/3} - 2 <= 0$$?

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Question 18

Let f(x) = max (2x + 1, 3 - 4x), where x is any real number. Then the minimum possible value of f(x) is:

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Question 19

Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40 and 60 km per hour respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

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Question 20

When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?

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