Average Question. Really need Help..

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younas: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Thu Feb 25, 2010 6:06 am

by younas » Tue Apr 06, 2010 1:09 pm

If the average of 27-x, x-8, and 3x-11 is y, what is the average of 2y and 2y/3?

a. 4x+40
b. x+10
c. (8x+80)/3
d. (4x+40)/3
e. (2x+20)/3

Answer is D, But i am having hard time getting to the answer.
Thank you very much for your time and help.

Source: Beat The GMAT — Problem Solving | Tue Apr 06, 2010 1:09 pm

student22: Master | Next Rank: 500 Posts; Posts: 216; Joined: Mon Dec 21, 2009 10:26 am; Thanked: 16 times

by student22 » Tue Apr 06, 2010 2:02 pm

Ok, I'll do my best to make this legible.

(27 - x) + (x - 8) + (3x + 11) = 3y --> 3x + 30 = 3y --> y = x + 10

2(x + 10) + 2/3(x + 10) = --> 2x + 20 + 2/3x + 20/3 = --> 8x/3 + 80/3 = --> (8x + 80)/3.

Now you take that last number and divide it by 2 since you are taking the average of 2 numbers:

(8x + 80)/3 * 1/2 = (4x + 40)/3

Last suggestion, if you encounter a problem like this and see that you'll have trouble solving it, pick numbers.

treker: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Fri Aug 22, 2008 9:32 pm; Thanked: 1 times

by treker » Tue Apr 06, 2010 4:43 pm

student22 wrote:Ok, I'll do my best to make this legible.

(27 - x) + (x - 8) + (3x + 11) = 3y --> 3x + 30 = 3y --> y = x + 10

2(x + 10) + 2/3(x + 10) = --> 2x + 20 + 2/3x + 20/3 = --> 8x/3 + 80/3 = --> (8x + 80)/3.

Now you take that last number and divide it by 2 since you are taking the average of 2 numbers:

(8x + 80)/3 * 1/2 = (4x + 40)/3

Last suggestion, if you encounter a problem like this and see that you'll have trouble solving it, pick numbers.

The last term is (3x - 11) or (3x + 11)?

student22: Master | Next Rank: 500 Posts; Posts: 216; Joined: Mon Dec 21, 2009 10:26 am; Thanked: 16 times

by student22 » Tue Apr 06, 2010 6:56 pm

I'm not sure what you mean?

The last term is (8x + 80)/3 / 2 --> (4x + 40)/3.

eaakbari: Master | Next Rank: 500 Posts; Posts: 435; Joined: Mon Mar 15, 2010 6:15 amFollowed by: 1 member; Thanked: 32 times

by eaakbari » Tue Apr 06, 2010 9:33 pm

You have stated the question wrong younas. Please do edit it. It is 3x+11 not -

To take average of three numbers, sum them and divide by three

(27-x +x-8+3x+11)/3 = y = 3x+10

Now to take average of 2y and 2y/3

(2y+2y/3)2
Solving
=4/3y
We know y = 3x+30
Hence we get 4x+40/3 = average
Answer D

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