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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
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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, 00:28
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Difficulty:

15% (low)

Question Stats:

76% (00:47) correct 24% (00:56) wrong based on 55 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
[Reveal] Spoiler: OA

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Re: If m, n and p are positive integers such that (p^m)^n=256 [#permalink]

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08 Jan 2018, 00:32
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

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Re: If m, n and p are positive integers such that (p^m)^n=256 [#permalink]

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08 Jan 2018, 00:55
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.
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Posts: 4896
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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, 00:03
=>

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.
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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, 00:15
1
KUDOS
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, 07:58
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, 08:21
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, 08:21
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# If m, n and p are positive integers such that (p^m)^n=256

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