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# PS - Mean

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Senior Manager
Joined: 30 Nov 2008
Posts: 479
Schools: Fuqua

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16 Dec 2008, 22:48
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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

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If the numbers x and y are added to set K {5, 1, 6, 4}, the mean will increase by 50%. What is the value of x ^2 + 2xy + y^2?
(A) 8
(B) 24
(C) 64
(D) 144
(E) 400

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SVP
Joined: 29 Aug 2007
Posts: 2420

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16 Dec 2008, 23:13
mrsmarthi wrote:
If the numbers x and y are added to set K {5, 1, 6, 4}, the mean will increase by 50%. What is the value of x^2 + 2xy + y^2?
(A) 8
(B) 24
(C) 64
(D) 144
(E) 400

k = 5+1+6+4 = 16
so k+x+y = 24
x+y = 8
x = 8 - y

= x^2 + 2xy + y^2
= (8-y)^2 + 2(8-y)y + y^2
= 64 - 16y +y^2 + 16y -2y^2 + y^2
= 64 - 16y + 16y +2y^2 - 2y^2
= 64

No matter the value of x and x^2 + 2xy + y^2 will be 64.

Good question
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Senior Manager
Joined: 30 Nov 2008
Posts: 479
Schools: Fuqua

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17 Dec 2008, 00:22
Yep OA is C.

But can we not solve in a simpler way?

GMAT TIGER wrote:
x+y = 8
x = 8 - y

= x^2 + 2xy + y^2
= (8-y)^2 + 2(8-y)y + y^2
= 64 - 16y +y^2 + 16y -2y^2 + y^2
= 64 - 16y + 16y +2y^2 - 2y^2
= 64

No matter the value of x and x^2 + 2xy + y^2 will be 64.

We already found that x + y = 8, the question being asked is nothing but (x+y) ^ 2 which should be 64.

Its a matter of reducing steps and gaining time.
Intern
Joined: 16 Dec 2008
Posts: 2

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17 Dec 2008, 03:58
1
(5+1+6+4)/4=4

=> (5+1+6+4+x+y)/6=6
which means that 16+x+y=36
x+y=20
x^2+2xy+y^2=(x+y)^2=20^2=400

Senior Manager
Joined: 30 Nov 2008
Posts: 479
Schools: Fuqua

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17 Dec 2008, 06:08
mrsmarthi wrote:
Yep OA is C.

My mistake - OA is E which is 400.

"perfect example of speed killls"
SVP
Joined: 29 Aug 2007
Posts: 2420

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17 Dec 2008, 08:52
Cannot digest it...

athathathathathathathatha .............. silly mistake.

GMAT TIGER wrote:
mrsmarthi wrote:
If the numbers x and y are added to set K {5, 1, 6, 4}, the mean will increase by 50%. What is the value of x^2 + 2xy + y^2?
(A) 8
(B) 24
(C) 64
(D) 144
(E) 400

k = 5+1+6+4 = 16
so k+x+y = 24
x+y = 8
x = 8 - y

= x^2 + 2xy + y^2
= (8-y)^2 + 2(8-y)y + y^2
= 64 - 16y +y^2 + 16y -2y^2 + y^2
= 64 - 16y + 16y +2y^2 - 2y^2
= 64

No matter the value of x and x^2 + 2xy + y^2 will be 64.

Good question

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Re: PS - Mean &nbs [#permalink] 17 Dec 2008, 08:52
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