What is the value of the positive integer n? What is the va : GMAT Data Sufficiency (DS)
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What is the value of the positive integer n? What is the va

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New post 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.
[Reveal] Spoiler: OA
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New post 18 Feb 2012, 01:24
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.

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

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

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New post 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
Re: What is the value of the positive integer n? What is the va   [#permalink] 01 Nov 2016, 09:56
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