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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] New post 18 Feb 2012, 00:55
00:00
A
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D
E

Difficulty:

  25% (low)

Question Stats:

81% (02:06) correct 18% (01:13) wrong based on 49 sessions
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] 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] 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] 11 Aug 2013, 08:23
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