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# If x and y are positive integers and 18 is a multiple of x*y^2, what

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Math Expert
Joined: 02 Sep 2009
Posts: 49968
If x and y are positive integers and 18 is a multiple of x*y^2, what  [#permalink]

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01 Oct 2018, 04:35
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Difficulty:

75% (hard)

Question Stats:

37% (01:40) correct 63% (02:22) wrong based on 19 sessions

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If x and y are positive integers and 18 is a multiple of x*y^2, what is the value of y?

(1) x is a factor of 54 and is less than half of 54.
(2) y is a multiple of 3

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Re: If x and y are positive integers and 18 is a multiple of x*y^2, what  [#permalink]

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01 Oct 2018, 04:39
Bunuel wrote:
If x and y are positive integers and 18 is a multiple of x*y^2, what is the value of y?

(1) x is a factor of 54 and is less than half of 54.
(2) y is a multiple of 3

Question: what is the value of y?

Given: $$18=2*3^2$$ is a multiple of $$x*y^2$$
i.e. Case1: x may be 2 and y may be 3 OR
Case2: x may be 18 and y may be 1

Statement 1: x is a factor of 54 and is less than half of 54.
i.e. x ≤27 and factor of 54
but as per cases mentioned above x may be 2 or 18 hence y may be 3 or 1 hence
NOT SUFFICIENT

Statement 2: y is a multiple of 3
i.e. y must be 3 (as per case 2)
SUFFICIENT

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Re: If x and y are positive integers and 18 is a multiple of x*y^2, what &nbs [#permalink] 01 Oct 2018, 04:39
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