CDS 2026 (I) Elementary Mathematics, question 37

Topic: Statistics

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Q37

All possible groups of 3 distinct numbers from among A, B, C, D and E are formed. If the aggregate of sums of numbers of each group is 120, then what is the arithmetic mean of A, B, C, D and E ?

  1. (a) 44Correct answer
  2. (b) 55
  3. (c) 1010
  4. (d) 2020

Solution.

Answer: (a) 44

  1. Each of the five numbers occurs in exactly C(4,2)=6C(4,2) = 6 of the three-number groups: choose its two companions from the remaining four.
  2. Thus 6(A+B+C+D+E)=1206(A + B + C + D + E) = 120.
  3. The sum is 20, and the mean is 20/5=420/5 = 4.