CAT 1999 — QA Question 32
Directions: Answer the questions based on the following information.
There are 50 integers a1, a2 … a50, not all of them necessarily different. Let the greatest integer of these 50 integers be referred to as G, and the smallest integer be referred to as L. The integers a1 through a24 form sequence S1, and the rest form sequence S2. Each member of S1 is less than or equal to each member of S2.
All values in S1 are changed in sign, while those in S2 remain unchanged. Which of the following statements is true?
Answer & solution
- A
Every member of S1 is greater than or equal to every member of S2.
- B
G is in S1.
- C
If all numbers originally in S1 and S2 had the same sign, then after the change of sign, the largest number of S1 and S2 is in S1.
None of the above
The ideal approach is to pick up the options one by one.
Option (a) – Let S1 and S2 be two sequences of positive numbers. After change of sign, S1 will consist of negative numbers while S2 remains unchanged.
Clearly, the members of S1 would be less than that of S2.
Hence, option (a) is not correct.
Option (b) - Let S1 and S2 be two sequences of positive numbers. After change of sign, S1 will consist of negative numbers while S2 remains unchanged.
Clearly, G would remain in S2 itself. Hence, option (b) is not correct.
Option (c) – If S1 and S2 had same sign, say positive initially, then the largest number of S1 and S2 would be in S2. Then after the change of sign, every member of S1 will be negative and therefore, less than every member of S2. This implies that the largest number would remain in S2.
Hence, option (c) is not correct.