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?
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: Mar 23, 2026
- 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
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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.
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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?
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: Mar 20, 2026
- \( S1 \) 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
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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.
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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:
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 \( S2 \).
- \( (G - L) \)
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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 \( S2 \).
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