GMAT Challenging Question 13 | Statistics PS

GMAT Sample Questions | Mean and Median

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?

  1. 23
  2. 21
  3. 25
  4. 26
  5. 24

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Explanatory Answer | Statistics - Mean, Median

Key Data from the Question Stem

  1. a ≤ b ≤ c
  2. a, b, and c are positive integers.
  3. Average of the three integers = 20
  4. Sum of all the three integers = 60
  5. Median = b = a + 11

Check for the possible values of c

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.

Choice C is the correct answer.

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