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

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

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New post 12 Jan 2014, 04:27
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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



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?
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Re: If m, x, and y are positive integers, what is the value of x  [#permalink]

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New post 12 Jan 2014, 05:03
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



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.

Answer: E.

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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New post 31 Oct 2017, 16:13
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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 &nbs [#permalink] 31 Oct 2017, 16:13
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