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If the average (arithmetic mean) of 3, 6, 10, m and n is 9,

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by Jay@ManhattanReview » Fri Mar 09, 2018 1:25 am
ardz24 wrote:If the average (arithmetic mean) of 3, 6, 10, m and n is 9, then what is the average of m + 4 and n - 2 ?

(A) 9
(B) 13
(C) 14
(D) 18
(E) 26

I'm confused how to set up the formulas here. Can any experts help?
The average (arithmetic mean) of 3, 6, 10, m and n = (3 + 6 + 10 + m + n)/5 = 9

=> m + n = 26

The average of m + 4 and n - 2 = (m + 4 + n - 2)/2 = (m + n + 2)/2; replaing the value of m + n, we get (m + n +2)/2 = (26 + 2)/2 = 14

The correct answer: C

Hope this helps!

-Jay
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by Brent@GMATPrepNow » Fri Mar 09, 2018 7:31 am
ardz24 wrote:If the average (arithmetic mean) of 3, 6, 10, m and n is 9, then what is the average of m + 4 and n - 2 ?

(A) 9
(B) 13
(C) 14
(D) 18
(E) 26
The average (arithmetic mean) of 3, 6, 10, m and n is 9
So, (3 + 6 + 10 + m + n)/5 = 9
Multiply both sides by 5 to get: 3 + 6 + 10 + m + n = 45
Simplify: 19 + m + n = 45
Subtract 19 from both sides to get: m + n = 26

What is the average of m + 4 and n - 2 ?
We get: average = [(m + 4) + (n - 2)]/2
Simplify: average = (m + n + 2)/2
Replace m + n to get: average = (26 + 2)/2
Simplify: average = (28)/2 = 14

Answer: C

Cheers,
Brent
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by Vincen » Fri Mar 09, 2018 7:39 am
Hello ardz24.

Look, we have that the average of 3, 6, 10, m and n is equal to 9, that is to say: $$\frac{3+6+10+m+n}{5}=9\ \Leftrightarrow\ \ 19+m+n=45\ \Leftrightarrow\ \ m+n=26.$$ Now, we want to find the average of m+4 and n-2, that is to say $$\frac{m+4+n-2}{2}=\frac{m+n+2}{2}=\frac{26+2}{2}=\frac{28}{2}=14.$$ Therefore, the correct answer is the option C.
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by Jeff@TargetTestPrep » Mon Mar 12, 2018 3:50 pm
ardz24 wrote:If the average (arithmetic mean) of 3, 6, 10, m and n is 9, then what is the average of m + 4 and n - 2 ?

(A) 9
(B) 13
(C) 14
(D) 18
(E) 26
We can use the formula for the arithmetic mean to create the equation:

(3 + 6 + 10 + m + n)/5 = 9

19 + m + n = 45

m + n = 26

We need to determine the average of m + 4 and n - 2; thus:

(m + 4 + n - 2)/2 = (m + n + 4 - 2)/2 = (26 + 4 - 2)/2 = 28/2 = 14

Answer: C

Jeffrey Miller
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