Encountered this in a timed online test, only allowing 20 seconds per question:
The average (arithmetic mean) of 4 numbers is greater than 8 but less
than 14. Which of the following could not be the sum of these four
numbers?Answer choices: 44, 53, 38, 31, 48
8 x 4 is 32 and 14 x 4 is 56, so the sum should be somewhere between 32 and 56, NOT inclusive, is that correct (thus the answer being 31)
I've seen a variation of this question where one of the answers was 32 itself. If the average is greater than 8, wouldn't that mean it's >32 – not inclusive?
What is this question looking for?
Best Answer
You're correct. Since the average must be greater than $8$, it cannot include $8$. And since $8\cdot 4 = 32$, when adding all the terms, you can't have $32$. This also means you cannot have $56$; all numbers must be between $32$ and $56$ non-inclusive, so $$33, 34, \dots, 54, 55.$$