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UPSC Prelims 2025 CSAT, question 77

Topic: Number system

Q77

Consider a set of 11 numbers :

Value−I=Minimumvalueoftheaverageofthenumbersofthesetwhentheyareconsecutiveintegers≥−5.Value-I=Minimum value of the average of the numbers of the set when they are consecutive integers \ge -5.

Value−II=Minimumvalueoftheproductofthenumbersofthesetwhentheyareconsecutivenon−negativeintegers.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 ?

  1. (a) Value−I<Value−IIValue-I<Value-II
  2. (b) Value−II<Value−IValue-II<Value-I
  3. (c) Value−I=Value−IIValue-I=Value-IICorrect answer
  4. (d) Cannot be determined due to insufficient data

Solution.

Answer: (c) Value−I=Value−IIValue-I=Value-II

  1. For Value-I\text{Value-I}, the 1111 consecutive integers ≥−5\ge -5 with the minimum average are −5,−4,−3,−2,−1,0,1,2,3,4,5-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, whose average is 00.
  2. For Value-II\text{Value-II}, the 1111 consecutive non-negative integers with the minimum product are 0,1,2,…,100, 1, 2, \dots, 10, whose product is 00 (and no product of non-negative integers can be negative).
  3. Therefore, Value-I=0=Value-II\text{Value-I} = 0 = \text{Value-II}.