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Alligation method

by Mo2men » Sat Nov 19, 2016 2:59 am
When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of n?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

Could we solve this question use alligation method??

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by GMATGuruNY » Sat Nov 19, 2016 3:18 am
I suggest two approaches here:
https://www.beatthegmat.com/ps-mean-t111153.html
The second approach involves alligation.
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by MartyMurray » Sat Nov 19, 2016 5:54 am
Here's another way to do it.

Adding a 39 increases the average by 2. So basically 39 adds to the average 2 for every member, including 39.

So 39 - Current Average = 2(n + 1)

Adding a 15 decreases the average by 1 by decreasing the average by 1 for every element including 15. So 15 must by n + 1 less than the current average.

Current average - n + 1 = 15

The average is between 15 and 39, and the difference between 39 and 15 is 3(n + 1).

39 - 15 = 3(n + 1) = 24

n + 1 = 8

Remember to choose answer n rather than n + 1.

n = 7

The correct answer is A.
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