CAT 2006 Question Paper

Instructions

For the following questions answer them individually

CAT 2006 - 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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CAT 2006 - 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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CAT 2006 - 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;

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)?

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CAT 2006 - 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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CAT 2006 - 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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CAT 2006 - 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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CAT 2006 - Question 17


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

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CAT 2006 - 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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CAT 2006 - 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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CAT 2006 - 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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