CAT 1999 | Question: 97

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.

Every element of S1 is made greater than or equal to every element of S2 by adding to each element of S1 an integer x. Then x cannot be less than

• A. $2^{10}$
• B. the smallest value of S2
• C. the largest value of S2
• D. (G – L)

 

Answer 1

I think option D
x = G - L

For eg.

As shown in fig G>= 56 and L <= 2 so x >= (G - L )= 56-2 = 54
Each element of S1 + x is greater than or equal to each element of S2.
S1  2+x=2+54 = 56 (greater than oe equal of each element of S2)

S1  9+x=9+54 = 63 (greater than oe equal of each element of S2)

After these additions G and L would be changed as well.