CAT 1999 | Question: 95

Question

Answer the question based on the following information:

There are $50$ integers $a_1, a_2, \dots , a_{50}$, not all of then necessarily different. Let the greatest integer of these 50 integers be referred 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 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 statement 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

Lets take sequence 1111...... 24 times , 11111.......... 26times (here each element of s1 is less than or equal to s2)

reverse the sign of s1 then -1,-1,-1.,....... 24times . 11111.............26times

Statement 1 is false . because every member of s1 is greater than or equal to s2.

Statement 2 is false because max element 1 is not in s1.

Statement 3 is false beacause in given above example both s1 and s2 are having same signs but after inverting the sign of s1 . largest of s1 and s2 are not in s1 . so it is also false .

So correcct option is D