### CAT 1999 Question Paper Question 40

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

# All values in S1 are changed in sign, while those in S2 remain unchanged. Which of the following statements is true?

Solution

We will give an example to disprove each of the three options A, B and C and hence, the correct answer will be option D.

Initially, if the least integer in S1 is -20 and the greatest integer in S2 is 50, then after the doing the operations mentioned in the question, the greatest integer in S1 is not greater than 50. Hence option A is false.

G is in S2 as per the given information => Option B is false.

If S1 contains numbers from 1 to 24 and S2 contains numbers from 25 to 50. Then G = 50 and L = 1. If all the numbers of S1 change in sign, G will remain 50 and will be in S2 while L will be -24 and will be in S1.

Hence, none of the statements is true always.