# GMAT® Practice Question - Statistics

Concept: Average after new elements are added to a set of numbers.

This GMAT quant practice question is a problem solving question from statistics and averages. Concept: Computing arithmetic mean of new elements added to a set of data.

#### Question: The average age of a group of 10 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?

1. 22 years
2. 30 years
3. 44 years
4. 32 years
5. None of these

#### Video Explanation

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Standard Framework
Description Number Average Sum
Initially 10 20 200
After 2 students join 12 22 264
Weight of 2 new students     264 - 200 = 64 kg

The average age of a group of 10 students is 20.
Therefore, the sum of the ages of all 10 of them = 10 * 20 = 200

When two new students join the group, the average age increases by 2. New average = 22.
Now, there are 12 students.
Therefore, the sum of the ages of all 12 of them = 12 * 22 = 264

Therefore, the sum of the ages of the two new students who joined = 264 - 200 = 64

And the average age of each of the two new students = $\frac{64}{2}\\$ = 32 years.

Choice D is the correct answer.

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