Consider a set of 11 numbers : Value-I = Minimum value of the average of the numbers of the set when they are consecutive integers ≥ -5. Value-II = Minimum value of the product of the numbers of the set when they are consecutive non-negative integers. Which one of the following is correct ?
- (a) Value-I < Value-II
- (b) Value-II < Value-I
- (c) Value-I = Value-II ✓ UPSC's answer
- (d) Cannot be determined due to insufficient data
Why the answer is (c)
• Value-I requires finding the minimum average of 11 consecutive integers that are all greater than or equal to -5.
• The smallest possible set of 11 consecutive integers satisfying the condition is {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}.
• The average of this arithmetic progression is the middle term, which is 0. Thus, Value-I = 0.
• Value-II requires finding the minimum product of 11 consecutive non-negative integers.
• The smallest possible set of 11 consecutive non-negative integers is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
• The product of this set is 0 because it includes the number 0. Thus, Value-II = 0.
• Since Value-I (0) is equal to Value-II (0), option (c) is correct.
Why the other options are wrong
- (a) Value-I < Value-II
- Value-I is 0 and Value-II is 0, so Value-I is not less than Value-II.
- (b) Value-II < Value-I
- Value-II is 0 and Value-I is 0, so Value-II is not less than Value-I.
- (d) Cannot be determined due to insufficient data
- The conditions for both values are fully specified, allowing for a definitive calculation of both values.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.