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# If x and y are nonzero integers, is 18 a factor of xy^2?

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If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

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13 Jan 2012, 09:49
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59% (00:57) correct 41% (00:56) wrong based on 286 sessions

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If x and y are nonzero integers, is 18 a factor of xy^2?

(1) x is a multiple of 54.
(2) y is a multiple of 6.

[Reveal] Spoiler:
I did A.
In case of option 2 y is a multiple of 6.
So y = 6, 12, 18 .......if y = 6, then the factors of 6 could is 2 & 3 but factors of 18 are 2, 3 & 3. Thus 18 Could be not a factor of xy^2.

What is the wrong with me?
[Reveal] Spoiler: OA

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Re: If x and y are nonzero integers [#permalink]

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13 Jan 2012, 10:20
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Expert's post
Baten80 wrote:
If x and y are nonzero integers, is 18 a factor of xy^2?
(1) x is a multiple of 54.
(2) y is a multiple of 6.

I did A.
In case of option 2 y is a multiple of 6.
So y = 6, 12, 18 .......if y = 6, then the factors of 6 could is 2 & 3 but factors of 18 are 2, 3 & 3. Thus 18 Could be not a factor of xy^2.

What is the wrong with me?

If x and y are nonzero integers, is 18 a factor of xy^2?

(1) x is a multiple of 54 --> x is a multiple of 18 as well (54=18*3) --> xy^2 is also a multiple of 18. Sufficient.

(2) y is a multiple of 6 --> y^2 is a multiple of 6^2=36 --> y^2 is a multiple of 18 as well (36=18*2) --> the same here: as y^2 is a multiple of 18 then xy^2 is also a multiple of 18. Sufficient.

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Re: If x and y are nonzero integers [#permalink]

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13 Jan 2012, 11:04

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Re: If x and y are nonzero integers [#permalink]

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13 Jan 2012, 11:56
1. x=54 = 18 x 3. So, 18 is a factor of x -> 18 is a factor of xy^2. Suff
2. y=6 -> y^2 = 36 = 18x2 -> 18 is a factor of y^2 -> 18 is a factor of xy^2. Suff

D
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Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

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22 May 2013, 03:39
Bumping for review and further discussion.
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Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

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22 May 2013, 14:40
I was actually thinking C cause they both can be used but wasnt sure if they could be used alone

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Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

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14 Nov 2013, 10:58
Baten80 wrote:
If x and y are nonzero integers, is 18 a factor of xy^2?

(1) x is a multiple of 54.
(2) y is a multiple of 6.

[Reveal] Spoiler:
I did A.
In case of option 2 y is a multiple of 6.
So y = 6, 12, 18 .......if y = 6, then the factors of 6 could is 2 & 3 but factors of 18 are 2, 3 & 3. Thus 18 Could be not a factor of xy^2.

What is the wrong with me?

Is it safe to rephrase as:
Does any of x or y^2 divide 18 ?

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Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

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14 Nov 2013, 12:46
Skag55 wrote:
Baten80 wrote:
If x and y are nonzero integers, is 18 a factor of xy^2?

(1) x is a multiple of 54.
(2) y is a multiple of 6.

[Reveal] Spoiler:
I did A.
In case of option 2 y is a multiple of 6.
So y = 6, 12, 18 .......if y = 6, then the factors of 6 could is 2 & 3 but factors of 18 are 2, 3 & 3. Thus 18 Could be not a factor of xy^2.

What is the wrong with me?

Is it safe to rephrase as:
Does any of x or y^2 divide 18 ?

No, xy^2 can be a multiple of 18 even if neither x nor y is a multiple of 18. For example: x=2 and y=3 --> xy^2=18.

Hope it's clear.
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Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

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14 Nov 2013, 12:57
Bunuel wrote:
Skag55 wrote:
Baten80 wrote:
If x and y are nonzero integers, is 18 a factor of xy^2?

(1) x is a multiple of 54.
(2) y is a multiple of 6.

[Reveal] Spoiler:
I did A.
In case of option 2 y is a multiple of 6.
So y = 6, 12, 18 .......if y = 6, then the factors of 6 could is 2 & 3 but factors of 18 are 2, 3 & 3. Thus 18 Could be not a factor of xy^2.

What is the wrong with me?

Is it safe to rephrase as:
Does any of x or y^2 divide 18 ?

No, xy^2 can be a multiple of 18 even when neither x nor y is a multiple of 18. For example: x=2 and y=3 --> xy^2=18.

Hope it's clear.

Yes, you're right. Thanks.

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GMAT 1: 670 Q48 V34
Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

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19 Feb 2015, 15:42
Q) Is 18 a factor of x*y^2??

1) x is a multiple of 54... Means x=54q.
(54q)*y^2/18... =(3q)*y^2 = Integer... So, 18 is a factor. Sufficient.

2) y is a multiple of 6... Means y=6q.
x*(6q)^2/18 = (36x)*q^2/18 = (2x)*q^2 = Integer... So, 18 is a factor. Sufficient.

(D)

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Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

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14 May 2016, 08:56
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Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink]

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24 Aug 2016, 02:41
Ecelelnt Question
Here is what i did
We need to check whether XY^2/18 =integer or not
Statement 1 => X=54*I for some integer I
Hence XY^2=54*I*Y^2=> 18*x where x=3*I*Y^2
hence Suff
Statement 2 =>
Y=6*I
Y^2=36*I
hence XY^2=X*36*I^2=> 18*x for x=X*2*I^2
hence Suff
SMASH THAT D
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Re: If x and y are nonzero integers, is 18 a factor of xy^2?   [#permalink] 24 Aug 2016, 02:41
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