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# Let n~ be defined for all positive integers n as the remainder when (n

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Let n~ be defined for all positive integers n as the remainder when (n [#permalink]

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05 Nov 2015, 05:57
2
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9
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Difficulty:

25% (medium)

Question Stats:

65% (00:55) correct 35% (01:04) wrong based on 243 sessions

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Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.

What is the value of 32~ ?

A. 0
B. 1
C. 2
D. 8
E. 31
[Reveal] Spoiler: OA

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Re: Let n~ be defined for all positive integers n as the remainder when (n [#permalink]

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05 Nov 2015, 07:14
2
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n~ = (n-1)!

so 32~ = (32-1)! = 31!

when 31!/32 we have 16*2 inside 31!

hence 32 gets cancelled and we get remainder as 0

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Re: Let n~ be defined for all positive integers n as the remainder when (n [#permalink]

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16 Mar 2016, 01:57
2
KUDOS
32 = 8*4 which are both present in 31!
so Remainder =0
hence A
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Re: Let n~ be defined for all positive integers n as the remainder when (n [#permalink]

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15 Apr 2017, 13:24
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Re: Let n~ be defined for all positive integers n as the remainder when (n [#permalink]

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15 Apr 2017, 13:39
1
KUDOS
Ok so I was initially not able to do this problem because I didn't understand how to divide 31!/32...

Now that you guys have made the problem more clear I have a question-

5!/15 must be an integer? Because 5x4x3x2x1 contains the factors of 15 (5 x 3)

When I do 17!/30 in a calculator the result is not an integer?

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Re: Let n~ be defined for all positive integers n as the remainder when (n [#permalink]

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16 Apr 2017, 01:27
1
KUDOS
Expert's post
Nunuboy1994 wrote:
Ok so I was initially not able to do this problem because I didn't understand how to divide 31!/32...

Now that you guys have made the problem more clear I have a question-

5!/15 must be an integer? Because 5x4x3x2x1 contains the factors of 15 (5 x 3)

When I do 17!/30 in a calculator the result is not an integer?

First of all, 17!/30 = 11856247603200 = integer, but what 17!/30 has to do with this problem?
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Re: Let n~ be defined for all positive integers n as the remainder when (n [#permalink]

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16 Apr 2017, 19:09
1
KUDOS
Bunuel wrote:
Nunuboy1994 wrote:
Ok so I was initially not able to do this problem because I didn't understand how to divide 31!/32...

Now that you guys have made the problem more clear I have a question-

5!/15 must be an integer? Because 5x4x3x2x1 contains the factors of 15 (5 x 3)

When I do 17!/30 in a calculator the result is not an integer?

First of all, 17!/30 = 11856247603200 = integer, but what 17!/30 has to do with this problem?

I trying to demonstrate the concept in this problem, which is new to me, in a different example- I think the calculator's notation just makes it appear as 1.something^e even though that doesn't necessarily mean it's not an integer. It's clear now.

Kudos [?]: 36 [1], given: 164

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Re: Let n~ be defined for all positive integers n as the remainder when (n [#permalink]

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16 Apr 2017, 23:51
Nunuboy1994 wrote:
Bunuel wrote:
Nunuboy1994 wrote:
Ok so I was initially not able to do this problem because I didn't understand how to divide 31!/32...

Now that you guys have made the problem more clear I have a question-

5!/15 must be an integer? Because 5x4x3x2x1 contains the factors of 15 (5 x 3)

When I do 17!/30 in a calculator the result is not an integer?

First of all, 17!/30 = 11856247603200 = integer, but what 17!/30 has to do with this problem?

I trying to demonstrate the concept in this problem, which is new to me, in a different example- I think the calculator's notation just makes it appear as 1.something^e even though that doesn't necessarily mean it's not an integer. It's clear now.

For big numbers do not user calculator (unless it's not advanced on) or Excell, use Wolframalpha: https://www.wolframalpha.com/

Hope it helps.
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Re: Let n~ be defined for all positive integers n as the remainder when (n [#permalink]

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27 Jun 2017, 16:09
Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.

What is the value of 32~ ?

A. 0
B. 1
C. 2
D. 8
E. 31

Simple- all this question is asking is if you have 31!/32 then what is the remainder? You don't necessarily have to expand 31!- 32 fits in because you have 16 and 2 so there is no remainder

Thus
"A"

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Re: Let n~ be defined for all positive integers n as the remainder when (n [#permalink]

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09 Jul 2017, 04:12
Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.

What is the value of 32~ ?

A. 0
B. 1
C. 2
D. 8
E. 31

$$= \frac{(32-1)!}{32}$$

$$= \frac{31!}{32}$$

Numbers $$8 * 4 = 32$$, will cancel out the denomintor and hence the reminder will be ZERO.

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Re: Let n~ be defined for all positive integers n as the remainder when (n   [#permalink] 09 Jul 2017, 04:12
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