(x – 2)! is divided by x

[sanju09]

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

[ps63739]

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.

[liferocks]

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

Ans option B

[ajith]

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)!

[ps63739]

It asks about prime number.

[ajith]

well what is the remainder when 6 is divided by 120

is it 6 or 1 ???

It asks about prime number.

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

[ps63739]

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

[ajith]

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)

[ps63739]

1,

[ajith]

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=6×4+2."

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

[sumanr84]

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