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Prime Factorial Problem

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by EMAN » Mon Sep 14, 2009 10:02 am
Which of the following numbers is NOT prime?

(A) 6! - 1
(B) 6! + 21
(C) 6! + 41
(D) 7! - 1
(E) 7! + 11
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imo

by xcusemeplz2009 » Mon Sep 14, 2009 10:25 am
IMO b

6!=720
+ 21=741 div by 3( applying rule for div by 3)
It does not matter how many times you get knocked down , but how many times you get up
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by geemat » Mon Sep 14, 2009 10:29 am
IMO B

6! + 21 = 3(6*5*4*2*1 + 7)
=> 3 is a factor, so it's not prime...
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B

by EMAN » Mon Sep 14, 2009 4:43 pm
Great job. B is correct. Geemat, could you elaborate on your answer please? Are saying it's not prime because 21 shares a factor of 3 and is in 6!? Thanks.
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by geemat » Mon Sep 14, 2009 7:24 pm
@EMAN: Yes, we don't need to expand the factorial and check if it's prime.

PRIME number are those numbers, which has an integer factor other than 1 and themselves.

So here we are seeing that 3 is a factor 0f (6! + 21), so this number is not prime.
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by estode » Tue Sep 15, 2009 10:40 am
Is there a short way to check if 7!-1 is prime?
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by Ian Stewart » Tue Sep 15, 2009 10:50 am
estode wrote:Is there a short way to check if 7!-1 is prime?
There's no fast way (without a computer) to demonstrate that a large number (like 7! - 1) *is* prime, though it is often easy to prove that a large number is *not* prime (if it's even, for example). To prove a large number is prime, you really have to try dividing it by every prime up to its square root. The square root of 7! - 1 is just less than 71, so to prove 7! - 1 is prime, you'd need to try dividing it by every prime up to 67, which is a long and boring process. You won't ever need to do that on the GMAT.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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