(x â€“ 2)! is divided by x

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu May 06, 2010 5:06 am

What is the remainder when (x - 2)! is divided by x? (x is a prime number)
(A) 0
(B) 1
(C) x - 6
(D) x - 3
(E) x - 1

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Source: Beat The GMAT — Problem Solving | Thu May 06, 2010 5:06 am

ps63739: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Tue Apr 20, 2010 9:09 am

by ps63739 » Thu May 06, 2010 5:15 am

Assume x = 5.
Now (x-2)! = 3! = 6.

(x-2)!/x = 1.

Now for the options C, D and E, none satisfies for this prime number. So has to be B.

To ensure, let's take x=3. Will be 1/3
Say x = 7, 5!/7 R= 1.

By the way, answer should be clear after first two steps.

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liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Thu May 06, 2010 5:19 am

by picking numbers as x=5,7 I am getting the ans as 1

Ans option B

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Thu May 06, 2010 5:43 am

sanju09 wrote:What is the remainder when (x - 2)! is divided by x? (x is a prime number)
(A) 0
(B) 1
(C) x - 6
(D) x - 3
(E) x - 1

(x-2)!/x! = 1/(x*(x-1))

(x-2)! divided by x! will leaves the same remainder when 1 is divided by x*(x-1)
so the answer must be 1

on second thoughts, what is the remainder when 10 is divided by 20 ( is it 10 or 1??)

I vote for 10! in that way the answer should be (x-2)!

Always borrow money from a pessimist, he doesn't expect to be paid back.

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ps63739: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Tue Apr 20, 2010 9:09 am

by ps63739 » Thu May 06, 2010 5:45 am

It asks about prime number.

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Thu May 06, 2010 5:49 am

well what is the remainder when 6 is divided by 120

is it 6 or 1 ???

ps63739 wrote:It asks about prime number.

That doesn't solve the problem, does it???

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ps63739: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Tue Apr 20, 2010 9:09 am

by ps63739 » Thu May 06, 2010 5:53 am

Ah.. I thought you were asking specifically about the question.

Well if your question is remainder when 6 is devided by 120, answer is 6 and

if your question is 6!/120! then answer is 1

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Thu May 06, 2010 5:56 am

ps63739 wrote:Ah.. I thought you were asking specifically about the question.

Well if your question is remainder when 6 is devided by 120, answer is 6 and

if your question is 6!/120! then answer is 1

I am asking about the problem

I am asking about 3!/5! is it 1 or 6??

(3! =6 and 5! is 120)

Always borrow money from a pessimist, he doesn't expect to be paid back.

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ps63739: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Tue Apr 20, 2010 9:09 am

by ps63739 » Thu May 06, 2010 5:58 am

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Thu May 06, 2010 7:49 am

ps63739 wrote:1,

I differ!

referring to examples in the page - https://en.wikipedia.org/wiki/Remainder

"When dividing 26 by 4, 6 is the quotient and 2 is the remainder, because 26=6Ã—4+2."

26/4 = 13/2 ; so by your logic remainder should have been 1 but, instead it is 2.

Always borrow money from a pessimist, he doesn't expect to be paid back.

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sumanr84: Legendary Member; Posts: 758; Joined: Sat Aug 29, 2009 9:32 pmFollowed by: 2 members; Location: Bangalore,India; Thanked: 67 times

by sumanr84 » Thu May 06, 2010 9:57 am

Ajith,
Question is not the one you are working out,
(x-2)!/x! = 1/(x*(x-1))

its simply,
(x-2)!/x [ NOT x! ]

Ans : 1

I am on a break !!

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