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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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22 Jul 2017, 13:03
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Difficulty:

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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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.

--== Message from the GMAT Club Team ==--

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

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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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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