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If x , p and q are positive integers , then

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If x , p and q are positive integers , then [#permalink]

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New post Updated on: 08 Oct 2016, 10:07
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If x , p and q are positive integers , then \(x^{p} / x ^ {q}\) = ?

1. p = q + 5

2. \(x^{q}\) = 32


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Originally posted by idontknowwhy94 on 08 Oct 2016, 07:34.
Last edited by idontknowwhy94 on 08 Oct 2016, 10:07, edited 1 time in total.
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If x , p and q are positive integers , then [#permalink]

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New post Updated on: 08 Oct 2016, 12:38
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idontknowwhy94 wrote:
If x , p and q are positive integers , then \(x^{p} / x ^ {q}\) = ?

1. p = q + 5

2. \(x^{q}\) = 32


NOTE: I have edited my response to reflect the new wording of the question

Target question: What is the value of \(x^{p} / x ^ {q}\)?
This is a good candidate for rephrasing the target question.
Since the base is x in both the numerator and denominator, we can apply the Quotient Law to get: x^(p-q).
So, we can REPHRASE the target question....
REPHRASED target question: What is the value of x^(p-q)?

Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Given: x , p and q are positive integers

Statement 1: p = q + 5
Rearrange to get: p - q = 5
Great! So, the exponent in x^(p-q) must equal 5.
However, we don't know the value of x, so there's no way to determine the value of x^(p-q)
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x^q = 32
Since there's no information about q, there's no way to determine the value of x^(p-q)
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that p = q + 5
Statement 2 tells us that x^q = 32. Since we're told that x and p are positive integers, there are only 2 possible cases to consider: x = 2, q = 5 AND x = 32 and q = 1
Case a: If x = 2, q = 5, then (from statement 1), we know that p = 10. In this case, x^(p-q) = 2^(10-5) = 32
Case b: If x = 32, q = 1, then (from statement 1), we know that p = 6. In this case, x^(p-q) = 32^(6-1) = some BIG number
Since we cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT

Answer:
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Originally posted by GMATPrepNow on 08 Oct 2016, 09:30.
Last edited by GMATPrepNow on 08 Oct 2016, 12:38, edited 1 time in total.
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Re: If x , p and q are positive integers , then [#permalink]

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New post 08 Oct 2016, 10:09
Peeps my mistake edited the question - this makes sense now.
Thanks GMATPrepNow
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Re: If x , p and q are positive integers , then [#permalink]

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New post 08 Oct 2016, 12:38
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idontknowwhy94 wrote:
Peeps my mistake edited the question - this makes sense now.
Thanks GMATPrepNow


I've edited my response accordingly.

Cheers,
Brent
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Re: If x , p and q are positive integers , then [#permalink]

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New post 07 Sep 2017, 03:27
Oh didnt think of 32^1 --> :(
Yes E makes sense over C.

Thank you GMATPrepNow
Re: If x , p and q are positive integers , then   [#permalink] 07 Sep 2017, 03:27
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