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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.

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

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

D _________________

I am the master of my fate. I am the captain of my soul. Please consider giving +1 Kudos if deserved!

DS - If negative answer only, still sufficient. No need to find exact solution. PS - Always look at the answers first CR - Read the question stem first, hunt for conclusion SC - Meaning first, Grammar second RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

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 ?

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.

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.

gmatclubot

Re: If x and y are nonzero integers, is 18 a factor of xy^2?
[#permalink]
14 Nov 2013, 11:57