# GMAT Quant | Averages Question 2

#### GMAT Sample Questions | Average | Arithmetic Mean | GMAT Questionbank

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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#### 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

#### 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

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