Multiple choice

The mean of the 8 smallest numbers in a group is 17, while taking together the mean of all the numbers in the group is 20. If the mean of the remaining numbers after leaving the smallest eight numbers is 22, then how many numbers are there in the group?

  1. 18

  2. 20

  3. 22

  4. 19
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let there be n numbers total. Sum of 8 smallest = 8 × 17 = 136. Sum of all numbers = n × 20. Sum of remaining (n-8) numbers = (n-8) × 22. Total sum = 136 + (n-8) × 22 = 20n. Solving: 136 + 22n - 176 = 20n, giving 2n = 40, so n = 20. Option B is correct. Option A (18) and D (19) don't satisfy the equation.

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