Numerical: averages MCQ — 3 Practice Questions with Answers

Explanation

Let the six numbers in decreasing order be a, b, c, d, e and f. The average of the first five is 40, so their sum is 200. The average of the last five is 30, so their sum is 150. Subtracting the second sum from the first cancels b, c, d and e, leaving a minus f equal to 50. Therefore 50 is correct. The values 25, 75 and 90 do not follow from the two average equations.

Explanation

From the averages, A + B = ₹ 12,000, B + C = ₹ 11,000, and A + C = ₹ 10,500. Adding these three equations gives 2(A + B + C) = ₹ 33,500, so A + B + C = ₹ 16,750. To find A, subtract B + C from this total: ₹ 16,750 - ₹ 11,000 = ₹ 5,750. The amounts ₹ 6,250, ₹ 6,450 and ₹ 6,200 would make the pairwise averages inconsistent with the given three average values.

Explanation

The sum of all 11 observations is 11 x 50 = 550. The sum of the first six observations is 6 x 40 = 240, and the sum of the last six observations is 6 x 55 = 330. Adding these two sums counts the sixth observation twice, so 240 + 330 = 570 equals the total sum plus the sixth observation. Hence the sixth observation is 570 - 550 = 20. The values 30, 40 and 35 would make the combined counted sum too high or inconsistent.