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If m, n and p are positive integers such that (p^m)^n=256
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08 Jan 2018, 01:28
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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
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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
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Re: If m, n and p are positive integers such that (p^m)^n=256
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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.
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Re: If m, n and p are positive integers such that (p^m)^n=256
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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
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Re: If m, n and p are positive integers such that (p^m)^n=256
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10 Jan 2018, 01:15
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
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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
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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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