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What is the remainder when P128 is divided by x, given that (127)x end

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What is the remainder when P128 is divided by x, given that (127)x end  [#permalink]

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New post 22 Jul 2017, 13:03
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  35% (medium)

Question Stats:

83% (00:41) correct 17% (02:06) wrong based on 12 sessions

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What is the remainder when P128 is divided by x, given that \((127)^x\) ends with 1? Both x and p are single digit positive integers.
(A) 2
(B) 1
(C) 0
(D) 3
(E) 4

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Re: What is the remainder when P128 is divided by x, given that (127)x end  [#permalink]

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New post 22 Jul 2017, 22:48
Gnpth wrote:
What is the remainder when P128 is divided by x, given that \((127)^x\) ends with 1? Both x and p are single digit positive integers.
(A) 2
(B) 1
(C) 0
(D) 3
(E) 4


\(127^{x}\) ends with \(1\): since the units digit is \(7\), possible units digits are \(7, 9, 3, 1\) so, \(x\) must be a multiple of \(4\). Since \(x\) is a single digit number, \(x\) can be \(4\) or \(8\).

\(\frac{128}{4}\) gives \(0\) as remainder

\(\frac{128}{8}\) gives \(0\) as remainder

So, for any single digit number \(P > 0\), \(P128\) when divided by \(4\) or \(8\) leaves a remainder of \(0\). Ans - C.

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This discussion does not meet community quality standards. It has been retired.


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Re: What is the remainder when P128 is divided by x, given that (127)x end   [#permalink] 22 Jul 2017, 22:48
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