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# If m, n and p are positive integers such that (p^m)^n=256

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If m, n and p are positive integers such that (p^m)^n=256  [#permalink]

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08 Jan 2018, 01:28
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:20) correct 18% (01:31) wrong based on 68 sessions

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[GMAT math practice question]

If $$m, n$$ and $$p$$ are positive integers such that $$(p^m)^n=256$$, which of the following could be the value of $$n$$?

I. 1
II. 2
III. 4

A. I and II
B. I and III
C. II and III
D. II only
E. I, II and III

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 17 Oct 2016 Posts: 313 Location: India Concentration: Operations, Strategy GPA: 3.73 WE: Design (Real Estate) Re: If m, n and p are positive integers such that (p^m)^n=256 [#permalink] ### Show Tags 08 Jan 2018, 01:32 Let p=16, m=2, n=1. Then (p^m)^n=256. n=1 Let p=4, m=2, n=2. Then (p^m)^n=256. n=2 Let p=2, m=2, n=4. Then (p^m)^n=256. n=4 Hence I, II, III are right. Option E Posted from my mobile device _________________ Help with kudos if u found the post useful. Thanks examPAL Representative Joined: 07 Dec 2017 Posts: 1153 Re: If m, n and p are positive integers such that (p^m)^n=256 [#permalink] ### Show Tags 08 Jan 2018, 01:55 MathRevolution wrote: [GMAT math practice question] If $$m, n$$ and $$p$$ are positive integers such that $$(p^m)^n=256$$, which of the following could be the value of $$n$$? I. 1 II. 2 III. 4 A. I and II B. I and III C. II and III D. II only E. I, II and III Since we're asked 'which of the following could be' we'll use the answers. This is an Alternative approach. If n = 1 then p^m = 256. This works with p=m=4. If n = 2 then p^m = 16. This works with p=4 and m=2 If n = 4 then p^m = 4. this works with p=m=2. Therefore (E) is correct. _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8024 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If m, n and p are positive integers such that (p^m)^n=256 [#permalink] ### Show Tags 10 Jan 2018, 01:03 => Since $$256 = 2^8$$, $$(p^m)^n = p^{mn} = 2^8.$$ So, $$p = 2$$and $$mn = 8$$. Since $$n$$ is a factor of $$8$$, $$n$$ could be any of the values $$1, 2, 4$$, and $$8$$. Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: If m, n and p are positive integers such that (p^m)^n=256  [#permalink]

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10 Jan 2018, 01:15
1
256=2^8
So mXn has following combination
8X1
4X2
2X4
1X8

So n can take the value 1, 2, 4, 8
So E
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Re: If m, n and p are positive integers such that (p^m)^n=256  [#permalink]

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10 Jan 2018, 08:58
MathRevolution wrote:
[GMAT math practice question]

If $$m, n$$ and $$p$$ are positive integers such that $$(p^m)^n=256$$, which of the following could be the value of $$n$$?

I. 1
II. 2
III. 4

A. I and II
B. I and III
C. II and III
D. II only
E. I, II and III

$$256^1 = 256$$

$$2^8 = 256$$

Or, $$4^4 = 256$$

Or, $$16^2 = 256$$

Thus, the possible values of n are all 1 , 2 and 4, answer will be (E)
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If m, n and p are positive integers such that (p^m)^n=256  [#permalink]

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10 Jan 2018, 09:21
MathRevolution wrote:
[GMAT math practice question]

If $$m, n$$ and $$p$$ are positive integers such that $$(p^m)^n=256$$, which of the following could be the value of $$n$$?

I. 1
II. 2
III. 4

A. I and II
B. I and III
C. II and III
D. II only
E. I, II and III

$$(256^1)^1$$ = 256 ; Eliminate (C) and (D)

$$(4^2)^2$$ = 256 ; Eliminate (B)

$$(4^1)^4$$ = 256 ; Eliminate (A)

So (E)
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If m, n and p are positive integers such that (p^m)^n=256   [#permalink] 10 Jan 2018, 09:21
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