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PS - Mean

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Senior Manager
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Joined: 30 Nov 2008
Posts: 485

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Schools: Fuqua
PS - Mean [#permalink]

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New post 16 Dec 2008, 22:48
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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

Kudos [?]: 348 [0], given: 15

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Joined: 29 Aug 2007
Posts: 2473

Kudos [?]: 832 [0], given: 19

Re: PS - Mean [#permalink]

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New post 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
_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

Kudos [?]: 832 [0], given: 19

Senior Manager
Senior Manager
avatar
Joined: 30 Nov 2008
Posts: 485

Kudos [?]: 348 [0], given: 15

Schools: Fuqua
Re: PS - Mean [#permalink]

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New post 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. :-D

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Re: PS - Mean [#permalink]

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New post 17 Dec 2008, 03:58
1
This post received
KUDOS
(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

Answer is E.

Kudos [?]: 1 [1], given: 0

Senior Manager
Senior Manager
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Joined: 30 Nov 2008
Posts: 485

Kudos [?]: 348 [0], given: 15

Schools: Fuqua
Re: PS - Mean [#permalink]

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


My mistake - OA is E which is 400.

"perfect example of speed killls" :cry:

Kudos [?]: 348 [0], given: 15

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Joined: 29 Aug 2007
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Kudos [?]: 832 [0], given: 19

Re: PS - Mean [#permalink]

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

athathathathathathathatha .............. silly mistake. :oops:

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

_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

Kudos [?]: 832 [0], given: 19

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