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

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BTGmoderatorAT: Moderator; Posts: 426; Joined: Tue Aug 22, 2017 8:48 pmFollowed by: 1 member

by BTGmoderatorAT » Tue Feb 20, 2018 7:40 pm

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?

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Source: Beat The GMAT — Problem Solving | Tue Feb 20, 2018 7:40 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

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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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

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
Head of GMAT Instruction
[email protected]

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