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

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Senior Manager
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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, 00:55
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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.
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Manager
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Location: Pakistan
GMAT 1: 720 Q49 V40
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Re: PT #2 DS 12 [#permalink]

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18 Feb 2012, 01:24
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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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Director
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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, 08:23
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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Intern
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Re: What is the value of the positive integer n? What is the va [#permalink]

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01 Nov 2016, 09:56
eybrj2 wrote:
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.

The number n has to be greater than 7, since it leaves a remainder 7.

Now 31/n has remainder 7, so 31 is 7 greater than a multiple of n. => 31-7 = 24 is a multiple of n.
on similar lines 32 is a multiple of n.
The greatest number that can divide 24 and 32 is HCF(24,32) = 8
Hence the maximum possible value of n = 8, also since n > 7 so it is the only value.
therefore n = 8

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

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09 Dec 2017, 04:27
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Re: What is the value of the positive integer n? What is the va   [#permalink] 09 Dec 2017, 04:27
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