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# If m, x, and y are positive integers, what is the value of x

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Manager
Joined: 12 Jan 2013
Posts: 216
If m, x, and y are positive integers, what is the value of x [#permalink]

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12 Jan 2014, 03:27
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If m, x, and y are positive integers, what is the value of x - y?

1) $$2^x = m(2^y)$$

2) m is a multiple of 4

[Reveal] Spoiler:
Aren't questions like these fairly straightforward? Im asking because Im not sure my approach is correct, correct me if Im wrong:

1) gives us three unknowns and one equation, but since we need to solve for two "unknowns" (m and [x - y]), then 1) clearly is insufficient.

2) This only tells us that m =4n, that doesn't make anything easier for us, we know nothing about the relationship between m, x and y. Insufficient

1 + 2) We now have the equation $$2^x = 4n(2^y)$$, this has made nothing easier for us since m has now been converted to another unknown. Sure, its possible values have been restricted, but that's still clearly insufficient since we have 3 unknowns and one equation. So answer is E.

Is this - non calculations-based approach viable?
[Reveal] Spoiler: OA
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Joined: 02 Sep 2009
Posts: 43804
Re: If m, x, and y are positive integers, what is the value of x [#permalink]

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12 Jan 2014, 04:03
aeglorre wrote:
If m, x, and y are positive integers, what is the value of x - y?

1) $$2^x = m(2^y)$$

2) m is a multiple of 4

[Reveal] Spoiler:
Aren't questions like these fairly straightforward? Im asking because Im not sure my approach is correct, correct me if Im wrong:

1) gives us three unknowns and one equation, but since we need to solve for two "unknowns" (m and [x - y]), then 1) clearly is insufficient.

2) This only tells us that m =4n, that doesn't make anything easier for us, we know nothing about the relationship between m, x and y. Insufficient

1 + 2) We now have the equation $$2^x = 4n(2^y)$$, this has made nothing easier for us since m has now been converted to another unknown. Sure, its possible values have been restricted, but that's still clearly insufficient since we have 3 unknowns and one equation. So answer is E.

Is this - non calculations-based approach viable?

If m, x, and y are positive integers, what is the value of x - y?

(1) $$2^x = m(2^y)$$ --> divide both sides by 2^y: $$2^{x-y}=m$$. We need the value of m to get the value of x-y. Not sufficient.

(2) m is a multiple of 4. Clearly insufficient.

(1)+(2) We still don't know the value of m: if $$m=4$$, then $$2^{x-y}=2^2$$ and in this case $$x-y=2$$ but if $$m=8$$, then $$2^{x-y}=2^3$$ and in this case $$x-y=3$$. Not sufficient.

Hope it's clear.
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Re: If m, x, and y are positive integers, what is the value of x [#permalink]

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31 Oct 2017, 15:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If m, x, and y are positive integers, what is the value of x   [#permalink] 31 Oct 2017, 15:13
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