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# If x and y are positive integers, is x a multiple of y?

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Re: If x and y are positive integers, is x a multiple of y? [#permalink]
Bunuel wrote:
If x and y are positive integers, is x a multiple of y?

(1) $$2y^2 + 5y = 3x$$
(2) y is not a multiple of 3.

Project DS Butler Data Sufficiency (DS3)

This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
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Re: If x and y are positive integers, is x a multiple of y? [#permalink]
Bunuel wrote:
If x and y are positive integers, is x a multiple of y?

(1) $$2y^2 + 5y = 3x$$
(2) y is not a multiple of 3.

Rephrase the question:

Is $$x = i * y$$, where $$i$$ is an integer?

Statement 1 Alone:

We have $$x = \frac{2y^2 + 5y}{3} = \frac{2y + 5}{3}*y$$. We are concerned if $$\frac{2y + 5}{3}$$ is an integer. If it is not, then y must be a multiple of 3 as we already know the result $$x$$ is an integer. Currently we do not have enough information so this is insufficient.

Statement 2 Alone:

Insufficient.

Both Statements Combined:

Since y is not a multiple of 3, we need $$\frac{2y + 5}{3}$$ to be an integer. Thus $$x = i*y$$ is a multiple of 3.

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Re: If x and y are positive integers, is x a multiple of y? [#permalink]
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I still get confused with this exercise.

The answer is supposed to be C (Both statements). However I have the following scenarios:
If Y = 5 (not a multiple of 3), then X = 25 and X is in fact a multiple of Y,
If Y = 7 (not a multiple of 3), then X = 133/3 and obviously X is not a multiple of Y.

That's why I chose answer E (not sufficient together).

Hope you could check my racionale.
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Re: If x and y are positive integers, is x a multiple of y? [#permalink]
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Re: If x and y are positive integers, is x a multiple of y? [#permalink]
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