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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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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.
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Re: PT #2 DS 12  [#permalink]

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New post 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.

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
1
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
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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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New post 28 Jul 2019, 20:31
32 is a multiple of n -> n could be 1,2,4,8,32,16,8,4
31/n has remainder of 7 -> n > 7 -> 8,16
test -> n = 8
-> 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 30 Dec 2019, 19:33
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.


Let's analyse Statement 1:

32 divided by n gives remainder as 0. That means n can be 1,2,4,8,16,32. Now 33 will give remainder as 1 with all those values of n except 1. But 31/8 gives remainder as 7 and no other value of n will give remainder as 7.

Hence Suff.

Statement 2:

Not enough. n can be any even number.

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 12 Mar 2020, 10:07
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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.


Target question: What is the value of the positive integer n?

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

----ASIDE----------------
When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0
-----------------------------

If 31 divided by n leaves a reminder of 7, then (according to the above property), n > 7

If 32 divided by n leaves a reminder of 0, then n is a divisor of 32.
The divisors of 32 are: 1, 2, 4, 8, 16 and 32
Since we already know that n > 7, n must be 8 or 16 or 32. Let's test these three possible n-values

If n = 8, then 31, 32, and 33 divided by n leaves reminders 7, 0, and 1, respectively. PERFECT.
If n = 16, then 31 divided by n leaves a reminder of 15, when we're hold the remainder is 7. So, n can't be 16.
If n = 32, then 31 divided by n leaves a reminder of 31, when we're hold the remainder is 7. So, n can't be 32.

The process of elimination, n must be 8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n is an even number.
Clearly not sufficient.

Answer: A

Cheers,
Brent

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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 12 Mar 2020, 10:47
From stmnt 1: only n value 8 satisfies the given relation sufficient
Frm stmn2 clearly insufficient
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[quote="eybrj2"]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.[/quote]

[size=80][b][i]Posted from my mobile device[/i][/b][/size]
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Re: What is the value of the positive integer n? What is the va   [#permalink] 12 Mar 2020, 10:47

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

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