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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8024
GMAT 1: 760 Q51 V42 GPA: 3.82
If m, n and p are positive integers such that (p^m)^n=256  [#permalink]

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

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

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=>

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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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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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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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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"Do not watch clock; Do what it does. KEEP GOING." If m, n and p are positive integers such that (p^m)^n=256   [#permalink] 10 Jan 2018, 09:21
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