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# If x , p and q are positive integers , then

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Manager
Joined: 03 Oct 2016
Posts: 84

Kudos [?]: 89 [1], given: 6

Concentration: Technology, General Management
WE: Information Technology (Computer Software)
If x , p and q are positive integers , then [#permalink]

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08 Oct 2016, 06:34
1
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9
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Difficulty:

95% (hard)

Question Stats:

34% (01:18) correct 66% (01:02) wrong based on 218 sessions

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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

Keep the Kudos coming in and let the Questions coming out
[Reveal] Spoiler: OA

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Last edited by idontknowwhy94 on 08 Oct 2016, 09:07, edited 1 time in total.

Kudos [?]: 89 [1], given: 6

SVP
Joined: 11 Sep 2015
Posts: 1999

Kudos [?]: 2876 [2], given: 364

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

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08 Oct 2016, 08:30
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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

[Reveal] Spoiler:
E

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Brent Hanneson – Founder of gmatprepnow.com

Last edited by GMATPrepNow on 08 Oct 2016, 11:38, edited 1 time in total.

Kudos [?]: 2876 [2], given: 364

Manager
Joined: 03 Oct 2016
Posts: 84

Kudos [?]: 89 [0], given: 6

Concentration: Technology, General Management
WE: Information Technology (Computer Software)
Re: If x , p and q are positive integers , then [#permalink]

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08 Oct 2016, 09:09
Peeps my mistake edited the question - this makes sense now.
Thanks GMATPrepNow
_________________

KINDLY KUDOS IF YOU LIKE THE POST

Kudos [?]: 89 [0], given: 6

SVP
Joined: 11 Sep 2015
Posts: 1999

Kudos [?]: 2876 [0], given: 364

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

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08 Oct 2016, 11:38
Expert's post
Top Contributor
idontknowwhy94 wrote:
Peeps my mistake edited the question - this makes sense now.
Thanks GMATPrepNow

I've edited my response accordingly.

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Kudos [?]: 2876 [0], given: 364

Senior Manager
Joined: 15 Jan 2017
Posts: 360

Kudos [?]: 8 [0], given: 830

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

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07 Sep 2017, 02:27
Oh didnt think of 32^1 -->
Yes E makes sense over C.

Thank you GMATPrepNow

Kudos [?]: 8 [0], given: 830

Re: If x , p and q are positive integers , then   [#permalink] 07 Sep 2017, 02:27
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