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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] New post 13 Jan 2012, 08:49
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

65% (01:46) correct 34% (01:04) wrong based on 107 sessions
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] New post 13 Jan 2012, 09:20
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.

Answer: D.
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Re: If x and y are nonzero integers [#permalink] New post 13 Jan 2012, 10:04
I considered y rather y^2
Thank u bunnuel
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Re: If x and y are nonzero integers [#permalink] New post 13 Jan 2012, 10:56
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

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Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink] New post 22 May 2013, 02:39
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Re: If x and y are nonzero integers, is 18 a factor of xy^2? [#permalink] New post 22 May 2013, 13:40
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] New post 14 Nov 2013, 09:58
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] New post 14 Nov 2013, 11:46
Expert's post
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] New post 14 Nov 2013, 11:57
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.
Re: If x and y are nonzero integers, is 18 a factor of xy^2?   [#permalink] 14 Nov 2013, 11:57
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