CAT 1999

Instructions

For the following questions answer them individually

Question 1

The number of positive integer valued pairs (x, y), satisfying 4x - 17 y = 1 and x < 1000 is:

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Question 2

Let a, b, c be distinct digits. Consider a two digit number $$'ab'$$ and a three digit number $$'ccb'$$, both defined under the usual decimal number system. If ($$ab^{2} = ccb$$) and $$ccb > 300$$ then the value of b is

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Question 3

The remainder when $$7^{84}$$ is divided by $$342$$ is :

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Question 4

Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?

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Question 5

For a scholarship, at most n candidates out of 2n + 1 can be selected. If the number of different ways of selection of at least one candidate is 63, the maximum number of candidates that can be selected for the scholarship is:

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Question 6

The speed of a railway engine is 42 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:

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Question 7

Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is Rs. 700 when there are 25 boarders and Rs. 600 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders?

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Question 8

Forty percent of the employees of a certain company are men, and 75 percent of the men earn more than Rs. 25,000 per year. If 45 percent of the company's employees earn more than Rs. 25,000 per year, what fraction of the women employed by the company earn Rs. 25,000 year or less'?

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Question 9

If | r - 6 | = 11 and | 2q - 12 | = 8, what is the minimum possible value of q / r?

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Question 10

If n = 1 + x, where x is the product of four consecutive positive integers, then which of the following is/are true?

A. n is odd

B. n is prime

C. n is a perfect square

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