GMAT Quant | Averages Question 2

This GMAT practice question is a problem solving question in statistics. Concept tested: Basics of computing arithmetic mean (average). An easy, GMAT 550 to 600 level, sample question.

Question 2: The arithmetic mean of the 5 consecutive integers starting with 's' is 'a'. What is the arithmetic mean of 9 consecutive integers that start with s + 2?

1. 2 + s + a
2. 22 + a
3. 2s
4. 2a + 2
5. 4 + a

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Video Explanation

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Explanatory Answer

Hints to solve this GMAT Statistics question

1. Consecutive integers are equally and symmetrically distributed with respect to the middle number.
2. i.e., the middle number is the average of a set of consecutive integers.
3. Determine which term is 'a' and then work out the average of the second set relative to that term.

Step 1 of solving this GMAT Statistics Question: Understanding the given data

The first sequence of 5 consecutive numbers starts with 's' and its mean is 'a'
The mean of 5 consecutive numbers is the 3rd term - the middle term.
Hence, 'a' the mean is the middle (3rd) term.

Step 2 of solving this GMAT Averages Question: Relating 'a' to 's'

The first sequence starts with 's'
Hence, the terms are s, s + 1, s + 2, s + 3, and s + 4
The middle term is s + 2
Therefore, a = s + 2

Step 3 of solving this GMAT Averages Question: The second series and its mean

The second series of 9 consecutive numbers starts from s + 2
The terms will therefore, be s + 2, s + 3, s + 4, s + 5, s + 6, s + 7, s + 8, s + 9, and s + 10
The average of these 9 numbers is the middle term of the second series. i.e., the 5th term = s + 6
If a = s + 2, then s + 6 will be a + 4
The average of the second sequence is a + 4

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Alternative Approach

The fastest way to solve such questions is to assume a value for 's'.

Let s be 1
Therefore, the 5 consecutive integers that start with 1 are 1, 2, 3, 4, and 5
The average of these 5 numbers is the middle term, which is 3. Hence, a = 3

9 consecutive integers that start with s + 2 will start from 1 + 2 = 3
The second sequence is therefore, 3, 4, 5, 6, 7, 8, 9, 10, and 11
The average of these 9 number is the middle term, which is 7

If the average of the first sequence 3 = a, the average of the second sequence 7 = 4 + a

Choice E is the correct answer.