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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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16 Apr 2017, 19:09

1

This post received 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.

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/

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

shasadou wrote:

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

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

shasadou wrote:

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.

Hence, Answer is A _________________

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