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# Is x^2 - y^2 divisible by 8? 1. x and y are even integers 2.

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Manager
Joined: 22 May 2007
Posts: 213
Is x^2 - y^2 divisible by 8? 1. x and y are even integers 2. [#permalink]

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28 Jul 2008, 20:39
Is $$x^2 - y^2$$ divisible by 8?

1. x and y are even integers
2. x + y is divisible by 8

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Director
Joined: 27 May 2008
Posts: 539

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28 Jul 2008, 20:43
aaron22197 wrote:
Is $$x^2 - y^2$$ divisible by 8?

1. x and y are even integers
2. x + y is divisible by 8

statement 1 : not suff

statement 2 : looks suff but wait... what if x = 5.25 and y = 2.75, (x+y) = 8 and (x-y) = 2.5
so x^2 - y^2 is not divisible by 8, even though x+y is..... not suff

combine both ... suff Option C
Manager
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Posts: 131
Schools: ISB, Tuck, Michigan (Ross), Darden, MBS

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28 Jul 2008, 20:45
Statement 1 not sufficient

Statement 2: Divisible by 8 since (x+y)(x-y)
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29 Jul 2008, 12:21
GMBA85 wrote:
Statement 1 not sufficient

Statement 2: Divisible by 8 since (x+y)(x-y)

Agree with durgesh unless question says x,y are integers...

(5.25+2.75) (5.25-2.75) = 8* 2.50 = not divisible.
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Joined: 28 Dec 2004
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29 Jul 2008, 14:54
aaron22197 wrote:
Is $$x^2 - y^2$$ divisible by 8?

1. x and y are even integers
2. x + y is divisible by 8

I get B..

x^2 - y^2 = (x+y)(x-y) regardless if x or y are integers..

(x-y)(x+y) where (x+y)=8*M then i think x^2 - y^2 is divisble by 8..
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Joined: 28 Dec 2004
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Location: New York City
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29 Jul 2008, 18:25
durgesh79 wrote:
aaron22197 wrote:
Is $$x^2 - y^2$$ divisible by 8?

1. x and y are even integers
2. x + y is divisible by 8

statement 1 : not suff

statement 2 : looks suff but wait... what if x = 5.25 and y = 2.75, (x+y) = 8 and (x-y) = 2.5
so x^2 - y^2 is not divisible by 8, even though x+y is..... not suff

combine both ... suff Option C

wow..totally agree..great work...
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Joined: 17 Jun 2008
Posts: 1325

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03 Aug 2008, 11:17
aaron22197 wrote:
Is $$x^2 - y^2$$ divisible by 8?

1. x and y are even integers
2. x + y is divisible by 8

Clearly (1) is not sufficient since when x=4,y=2 the logic fails
(2)since x^2-y^2=x-y * x+y hence (2) is SUFFI

IMO B
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Manager
Joined: 22 May 2007
Posts: 213

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04 Aug 2008, 05:55
OA is C. Good discussion
Retired Moderator
Joined: 18 Jul 2008
Posts: 920

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04 Aug 2008, 07:22
Yes, I came to the same conclusion, algebraically. But it seems wrong when plugged in numbers as above.

But why is our approach wrong?

spriya wrote:
aaron22197 wrote:
Is $$x^2 - y^2$$ divisible by 8?

1. x and y are even integers
2. x + y is divisible by 8

Clearly (1) is not sufficient since when x=4,y=2 the logic fails
(2)since x^2-y^2=x-y * x+y hence (2) is SUFFI

IMO B
VP
Joined: 17 Jun 2008
Posts: 1325

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04 Aug 2008, 10:18
Yes, I came to the same conclusion, algebraically. But it seems wrong when plugged in numbers as above.

But why is our approach wrong?

spriya wrote:
aaron22197 wrote:
Is $$x^2 - y^2$$ divisible by 8?

1. x and y are even integers
2. x + y is divisible by 8

Clearly (1) is not sufficient since when x=4,y=2 the logic fails
(2)since x^2-y^2=x-y * x+y hence (2) is SUFFI

IMO B

Thats because we want integers for divisibility and we dont have one
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Senior Manager
Joined: 06 Apr 2008
Posts: 401

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05 Aug 2008, 03:01
aaron22197 wrote:
Is $$x^2 - y^2$$ divisible by 8?

1. x and y are even integers
2. x + y is divisible by 8

$$x^2 - y^2$$ = (x +y)(x - y)

So if x + y is divisible by 8 then $$x^2 - y^2$$ should be divisible as well but only when x,y are integers.

Therefore C)
Retired Moderator
Joined: 18 Jul 2008
Posts: 920

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05 Aug 2008, 16:32
Thanks. That makes sense now. I never knew that to be true. Always thought X,Y could be all numbers.

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Re: x2   [#permalink] 05 Aug 2008, 16:32
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# Is x^2 - y^2 divisible by 8? 1. x and y are even integers 2.

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