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Difficulty:   25% (medium)

Question Stats: 76% (01:33) correct 24% (01:55) wrong based on 269 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.
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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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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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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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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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GMAT 1: 600 Q46 V27 Re: What is the value of the positive integer n? What is the va  [#permalink]

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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.

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.

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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.

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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From stmnt 1: only n value 8 satisfies the given relation sufficient
Frm stmn2 clearly insufficient
IMOA
[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] 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  