# CAT 1999 Question Paper

Instructions

DIRECTIONS for the following two questions: These questions are based on the situation given below: Seven university cricket players are to be honored at a special luncheon. The players will be seated on the dais along one side of a single rectangular table. A and G have to leave the luncheon early and must be seated at the extreme right end of the table, which is closest to the exit. B will receive the Man of the Match award and must be in the center chair. C and D who are bitter rivals for the position of wicket keeper, dislike one another and should be seated as far apart as possible. E and F are best friends and want to sit together.

Question 31

## Which of the following pairs may not be seated together?

Instructions

DIRECTIONS for the following two questions: These questions are based on the situation given below:

A rectangle PRSU, is divided into two smaller rectangles PQTU, and QRST by the line TQ. PQ=10cm, QR = 5 cm and RS = 10 cm. Points A, B, F are within rectangle PQTU, and points C, D, E are within the rectangle QRST. The closest pair of points among the pairs (A, C), (A, D), (A, E), (F, C), (F, D), (F, E), (B, C), (B, D), (B, E) are $$10 \sqrt{3}$$ cm apart.

Question 32

Question 33

## AB > AF > BF; CD > DE > CE; and BF = $$6\sqrt{5}$$ cm. Which is the closest pair of points among all the six given points?

Instructions

DIRECTIONS for the following questions: These questions are based on the situation given below: In each of the questions a pair of graphs F(x) and F1(x) is given. These are composed of straight-line segments, shown as solid lines, in the domain $$x\epsilon (-2, 2)$$.

a. If F1(x) = - F(x)

b. if F1(x) = F(- x)

c. if F1(x) = - F(- x)

d. if none of the above is true

Instructions

DIRECTIONS for the following questions: These questions are based on the situation given below:

There are m blue vessels with known volumes $$V1, V2 , ...., V_m$$, arranged in ascending order of volume, where $$v_1 > 0.5$$ litre, and $$V_m < 1$$ litre. Each of these is full of water initially. The water from each of these is emptied into a minimum number of empty white vessels, each having volume 1 litre. The water from a blue vessel is not emptied into a white vessel unless the white vessel has enough empty volume to hold all the water of the blue vessel. The number of white vessels required to empty all the blue vessels according to the above rules was n.

Question 38

Question 39

## Let the number of white vessels needed be n1 for the emptying process described above, if the volume of each white vessel is 2 liters. Among the following values, which is the least upper bound on n1?

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 40