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# What is the value of the positive integer n? What is the va

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What is the value of the positive integer n? What is the va [#permalink]

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18 Feb 2012, 01:55
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Question Stats:

81% (02:09) correct 19% (01:28) wrong based on 109 sessions

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What is the value of the positive integer n?

1) If 31, 32, and 33 are each divided by n, the reminders are 7, 0, and 1, respectively.

2) n is an even number.
[Reveal] Spoiler: OA
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Re: PT #2 DS 12 [#permalink]

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18 Feb 2012, 02:24
Ok. Finally a simple question.

What is the value of the positive integer $$n$$?

Statement A: If $$31$$, $$32$$, and $$33$$ are each divided by $$n$$, the reminders are $$7$$, $$0$$, and $$1$$, respectively.

Let's check $$31$$ . Since remainder is $$7$$, the number has to be bigger than $$7$$.

Hence for $$31$$ the positive integer could be $$8$$, $$12$$, or $$24$$. So three possibilities so far.

Let's check $$32$$ . Since remainder is $$0$$, the number can be any fraction of $$32$$ .

Let's check $$33$$ . Since remainder is $$1$$, the number can be 2, 4, 8, or any factor of $$32$$ for that matter .

The only overlap is the number $$8$$ so $$n$$ must be $$8$$ or to see it in a different light (and that is why i mentioned factors of 32 in the first instance), the only factor of $$32$$ that fits the bill for $$31$$ is $$8$$. Hence Sufficient.

Statement 2: n is an even number. Can be any even number. Hence Insufficient.

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Re: What is the value of the positive integer n? What is the va [#permalink]

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11 Aug 2013, 09:23
Easiest I must say:

Remainders

31 - 7
32 - 0
33 - 1

REM(31/8) = 7
REM(32/8) = 0
REM(33/8) = 1

Hence (A) it is
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Re: What is the value of the positive integer n? What is the va [#permalink]

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14 Jul 2016, 02:54
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Re: What is the value of the positive integer n? What is the va   [#permalink] 14 Jul 2016, 02:54
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