Arithmetic Mean of an AP

Concept: Average of an arithmetic progression,

The GMAT Math practice question given below is a sequences and series question. The concept tested is that of finding the Arithmetic Mean of an AP.

Question: The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 9 consecutive integers that start with (m + 2)?

  1. m + 4
  2. n + 6
  3. n + 3
  4. m + 5
  5. n + 4

Explanatory Answer

Video explanation coming soon.
Approach: Work with a numerical example

The fastest way to solve problems of this kind is to take numerical examples.

Let the 5 consecutive integers be 1, 2, 3, 4, and 5.
The average of 5 consecutive integers from 1 to 5 is 3.
Therefore, the value of m is 1 and the value of n is 3.

9 consecutive integers starting from m + 2 will be 3, 4, ... , 11
The average of positive integers from 3 to 11 is 7.
We know n = 3. So, 7 has to be (n + 4)

Choice E is the correct answer.

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