Comprehension
There are 50 integers a1, a2, a3...a50, not all are necessarily different. The greatest of the integers is called G and the smallest L. The first 24 of the set, a1 to a24 are part of a sequence S1 and the rest make sequence S2. Each member of S1 is less than or equal to each member of S2
Question: 1

If all the signs of \( S1 \) are reversed and of \( S2 \) are kept the same, then which is true?

Show Hint

Always check the conditions of sign reversal carefully, as it affects the relative ordering of the numbers.
Updated On: Aug 5, 2025
  • Every member of \( S1 \geq \) every member of \( S2 \)
  • \( G \) is in \( S1 \)
  • 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
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is C

Solution and Explanation

Since the numbers of \( S1 \) and \( S2 \) originally had the same sign and the signs of \( S1 \) are reversed, the largest number of \( S1 \) and \( S2 \) will be in \( S1 \) after the sign change.
Was this answer helpful?
0
0
Question: 2

Elements of \( S1 \) are in ascending order and those of \( S2 \) are in descending order, \( a_{24} \) and \( a_{25} \) are interchanged. Then which of the following statements is true?

Show Hint

Always check how swapping elements affects the order of sequences, especially when dealing with ordered sets.
Updated On: Aug 5, 2025
  • \( S1 \) continues to be in ascending order.
  • \( S2 \) continues to be in descending order.
  • \( S1 \) continues to be in ascending order and \( S2 \) in descending order.
  • None of the above
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is D

Solution and Explanation

After interchanging \( a_{24} \) and \( a_{25} \), both sequences will not maintain their original orders. Hence, none of the options hold true.
Was this answer helpful?
0
0
Question: 3

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:

Show Hint

When comparing sets and manipulating their elements, focus on ensuring the required condition holds for the extreme elements of each set.
Updated On: Aug 5, 2025
  • \( 2^{10} \)
  • The smallest value of \( S2 \).
  • The largest value of \( S2 \).
  • \( (G - L) \)
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is C

Solution and Explanation

To ensure every element of \( S1 \) is greater than or equal to every element of \( S2 \), we need \( x \) to be at least the largest value of \( S2 \). This guarantees that the smallest element of \( S1 \) exceeds or equals the largest element of \( S2 \).
Was this answer helpful?
0
0

Top Questions on Data Sufficiency

View More Questions

Questions Asked in CAT exam

View More Questions