# CAT 1999 Question Paper

Instructions

DIRECTIONS for the following questions: These questions are based on the situation given below: There are fifty integers $$a_1, a_2,...,a_{50}$$, not all of them necessarily different. Let the greatest integer of these fifty integers be referred to as $$G$$, and the smallest integer be referred to as $$L$$. The integers $$a_1$$ through $$a_{24}$$ form sequence $$S1$$, and the rest form sequence $$S2$$. Each member of $$S1$$ is less than or equal to each member of $$S2$$.

Question 41

Question 42

## Every element of S1 is made greater than or equal to every element of S2 by adding to each element of S1 an integer x. Then x cannot be less than:

Instructions

DIRECTIONS for the following questions: These questions are based on the situation given below: Let x and y be real numbers

f(x, y) = | x + y |

F(f(x, y)) = -f(x, y)

G(f(x, y)) = -F(f(x, y))

Question 43

Question 44

Question 45

## Which of the following expressions yields $$x^2$$ as its result?

Instructions

DIRECTIONS for the following questions:

These questions are based on the situation given below: A robot moves on a graph sheet with x and y-axes. The robot is moved by feeding it with a sequence of instructions. The different instructions that can be used in moving it, and their meanings are: Instruction Meaning GOTO(x,y) move to point with coordinates (x, y) no matter where you are currently WALKX(P) Move parallel to the x-axis through a distance of p, in the positive direction if p is positive, and in the negative direction if p is negative WALKY(P) Move parallel to the y-axis through a distance of p, in the positive direction if p is positive, and in the negative direction if p is negative.

Question 46

Question 47

## The robot is initially at (x, y), x > 0 and y < 0. The minimum number of instructions needed to be executed to bring it to the origin (0,0) if you are prohibited from using the GOTO instruction is:

Instructions

DIRECTIONS for the following three questions

These questions are based on the situation given below:

A road network (shown in the figure below) connects cities A, B, C and D. All road segments are straight lines. D is the midpoint on the road connecting A and C. Roads AB and BC are at right angles to each other with BC shorter than AB. The segment AB is 100 km long. Ms. X and Mr. Y leave A at 8:00 am, take different routes to city C and reach at the same time. X takes the highway from A to B to C and travels at an average speed of 61.875 km per hour. Y takes the direct route AC and travels at 45 km per hour on segment AD. Y's speed on segment DC is 55 km per hour.

Question 48

Question 49

Question 50