This GMAT Problem Solving practice question combines core concepts of statistics including mean and median. It is a typical example of a question which requires you to iterate to get to the correct answer.

Question 13: Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?

- 23
- 21
- 25
- 26
- 24

@ INR

- a ≤ b ≤ c
- a, b, and c are positive integers.
- Average of the three integers = 20
- Sum of all the three integers = 60
- Median = b = a + 11

Theoretically, the least value of c is when c = b.

Therefore, a + (a + 11) + (a + 11) = 60 (b and c are equal and b, the median, is a + 11)

Or 3a = 38 or a = 12.66

So, b = c = 12.66 + 11 = 23.66

However, we know that these numbers are all integers.

Therefore, a, b, and c cannot take these values.

So, the least value for c with this constraint is NOT likely to be when c = b.

Let us increment c by 1. Let c = (b + 1)

In this scenario, a + (a + 11) + (a + 12) = 60

Or 3a = 37. The value of the numbers is not an integer in this scenario as well.

Let us increment c again by 1. i.e., c = b + 2

Now, a + (a + 11) + (a + 13) = 60

Or 3a = 36 or a = 12.

If a = 12, b = 23 and c = 25.

**The least value for c that satisfies all these conditions is 25.**

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