# CAT 1990

Instructions

For the following questions answer them individually

Question 1

If R is an integer between 1 & 9, P - R = 2370, what is the value of R?
I. P is divisible by 4.
II. P is divisible by 9.

Question 2

A man distributed 43 chocolates to his children. How many of his children are more than five years old?
I. A child older than five years gets 5 chocolates.
II. A child 5 years or younger in age gets 6 chocolates.

Question 3

Ramu went by car from Calcutta to Trivandrum via Madras, without any stoppages. The average speeds for the entire journey was 40 kmph. What was the average speed from Madras to Trivandrum?
I. The distance from Madras to Trivandrum is 0.30 times the distance from Calcutta to Madras.
II. The average speed from Madras to Trivandrum was twice that of the average speed from Calcutta to Madras.

Question 4

x, y, and z are three positive odd integers, Is x+z divisible by 4?
I. y - x = 2
II. z - y = 2

Question 5

The unit price of product P1 is non-increasing and that of product P2 is decreasing. Which product will be costlier 5 years hence?
I. Current unit price of P1 is twice that of P2.
II. 5 years ago, unit price of P2 was twice that of P1.

Question 6

X is older than Y, Z is younger than W and V is as old as Y. Is Z younger than X?
I. W may not be older than V
II. W is not older than V

Question 7

How long did Mr. X take to cover 5000 km. journey with 10 stopovers?
I. The $$i^{th}$$ stopover lasted $$i^2$$ minutes.
II. The average speed between any two stopovers was 66 kmph.

Question 8

Is $$[(x^{-1} - y^{-1} )/(x^{-2} -y^{-2}]>1$$?
I. x + y > 0
II. x and y are positive integers and each is greater than 2.

Instructions

In a game played by two people there were initially N match sticks kept on the table. A move in the game consists of a player removing either one or two matchsticks from the table. The one who takes the last matchstick loses. Players make moves alternately. The player who will make the first move is A. The other player is B.

Question 9

The smallest value of N (greater than 5) that ensures a win for B is

Question 10

The largest of N (less than 50) that ensures a win for B is

OR