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# Is x^2 * y^2 an integer divisible by 9? 1) x is an integer

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Intern
Joined: 14 Jul 2006
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Is x^2 * y^2 an integer divisible by 9? 1) x is an integer [#permalink]

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09 Aug 2007, 17:22
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Is x^2 * y^2 an integer divisible by 9?

1) x is an integer divisible by 3
2) x*y is an integer divisible by 9

Could someone please explain the fastest way to solve this problem?

I appreciate the help!

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VP
Joined: 10 Jun 2007
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09 Aug 2007, 17:32
MooseDrool wrote:
Is x^2 * y^2 an integer divisible by 9?

1) x is an integer divisible by 3
2) x*y is an integer divisible by 9

Could someone please explain the fastest way to solve this problem?

I appreciate the help!

You get something like this: x^2 * y^2 = 3^2 * integer
Then you get: [(x*y) / 3]^2 = integer
This can only be true if x*y is divisible by 3.

1) INSUFFICIENT since y can be fraction
2) SUFFICIENT.

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Intern
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09 Aug 2007, 17:43

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Director
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10 Aug 2007, 01:39
MooseDrool wrote:
Is x^2 * y^2 an integer divisible by 9?

1) x is an integer divisible by 3
2) x*y is an integer divisible by 9

Could someone please explain the fastest way to solve this problem?

I appreciate the help!

One more for B.

x^2*y^2= (xy)^2
Therefore, if xy is divisible by 9 then (xy)^2 has to be divisible by 9

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SVP
Joined: 01 May 2006
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10 Aug 2007, 02:33
(B) for me

x^2 * y^2 = 9 * k ?

Stat 1
x = 3*j

2 cases:
o If y = 1/2 and x=3, then x^2 * y^2 = 9/4, which is not divisible by 9
o If y = 1 and x=3, then x^2 * y^2 = 9, which is divisible by 9

INSUFF.

Stat 2
x * y = 9 * v.....with v an integer
=> (x*y)^2 = 9 * 9 * v^2
<=> x^2 * y^2 = 9 * w....with w an integer such that w = 9 * v^2

SUFF.

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Director
Joined: 31 Mar 2007
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10 Aug 2007, 05:40
Straight B. They say nothing about Y being an integer in A.

OA is B, not E.

A lot of those test writers know 0 about math, =P

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Senior Manager
Joined: 14 Jun 2007
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10 Aug 2007, 14:10
MooseDrool wrote:
Is x^2 * y^2 an integer divisible by 9?

1) x is an integer divisible by 3
2) x*y is an integer divisible by 9

Could someone please explain the fastest way to solve this problem?

I appreciate the help!

i am not looking at others explanations, i want to reason this on my own... so i might repeat others, i could be wrong.

I:

gut instinct is to pick A and move on... but we still need to know what Y is. y could be a fraction and then the answer could be no.

II: xy = 9*integer
theres lots of combinations that could yield a true statement here.

1*9
sqrt9*sqrt9
27* 1/3

all divisible by 9. I say B.

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Senior Manager
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10 Aug 2007, 14:12
MooseDrool wrote:

???

how did they explain E as the answer, i am dying to know!

this is precisely why i asked for a refund for the challenges

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10 Aug 2007, 14:12
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# Is x^2 * y^2 an integer divisible by 9? 1) x is an integer

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