Question

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 is 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.
If all values in S1 are changed in sign, while those in S2 remain unchanged, which of the following statements is true?

• 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.
• D. None of the above

Answer 1

The correct option is D None of the above

None of the options (a), (b) and (c) is necessarily true. Hence, option (d) is the answer.

As this is a variable based question, the word "ANY" can be used.

Let the series of integers $a_1,a_2,.......,a_{50}$ be $1,2,3,4,5,.......,50.$

$S_1=1,2,3,4,.......24,S_2=25,26,\mathrm{27............50}$.