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# Is x^2y^4 an integer divisible by 9 ? (1) x is an integer

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Is x^2y^4 an integer divisible by 9 ? (1) x is an integer [#permalink]

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11 Mar 2009, 18:45
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Is x^2y^4 an integer divisible by 9 ?

(1) x is an integer divisible by 3
(2) xy is an integer divisible by 9

Kudos [?]: 303 [0], given: 5

Senior Manager
Joined: 08 Jan 2009
Posts: 325

Kudos [?]: 180 [0], given: 5

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11 Mar 2009, 19:56
Given:

Is x^2 * y^4 divisible by 9?

1. x = 3k x^2 = 9k^2 therefore sufficient

2. xy = 9K.

x is a mutiple of 9 or y is a multiple of 9 or x and y( x =3a, y=3b) will contain factors of 9.

On all cases it is divisible. Sufficient.

Ans: D

Kudos [?]: 180 [0], given: 5

Intern
Joined: 28 Feb 2009
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12 Mar 2009, 00:38
I would say D since:

(1) x being divisible by 3 and then being squared will ensure that there are two factors of three, which means x the any expression including x^2 will be divisible by 9

(2) if xy is divisible by 9, then raising it to the fourth will ensure that there are factors to make it divisible 4 times...

Is this a reasonable explanation?

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12 Mar 2009, 01:15
Is x^2y^4 an integer divisible by 9 ?

(1) x is an integer divisible by 3
(2) xy is an integer divisible by 9

E

1. says nothing about y, Not suff
1.1 x=3, y=1, OK x^2y^4 is an INTEGER divisible by 9
1.2 x=3, but y= 1/2 so y=1/2^4 --> x^2y^4 can not be an integer divisible by 9

2. Again, xy is an integer and x^2y^2 can be an integer but y^2 alone can not necessarily be integer, so x^y^4 are not necessarily be an integer divisible by 9! not suff

1 and 2 combine, not suff too
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Senior Manager
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12 Mar 2009, 05:25
Trap - qts force us to think Y as interger ..
What if Y is 1.5 or .5 ??

Agree with E .
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Kudos [?]: 245 [0], given: 7

Retired Moderator
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12 Mar 2009, 06:22
The OA is E. good explanation guys.

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Senior Manager
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13 Mar 2009, 09:06
Thank you Guys.

i got my mistake.

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Re: DS: Divisibility   [#permalink] 13 Mar 2009, 09:06
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