BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

If \(n\) is a prime number and \(n \ne 3,\) which of the following could be the remainder when \(100! + n\) is divided

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

If \(n\) is a prime number and \(n \ne 3,\) which of the following could be the remainder when \(100! + n\) is divided

by Vincen » Tue Jun 30, 2020 7:23 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

If \(n\) is a prime number and \(n \ne 3,\) which of the following could be the remainder when \(100! + n\) is divided by \(3?\)

I. 0
II. 1
III. 2

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II and III

[spoiler]OA=D[/spoiler]

Source: Princeton Review
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

Re: If \(n\) is a prime number and \(n \ne 3,\) which of the following could be the remainder when \(100! + n\) is divid

by Jay@ManhattanReview » Wed Jul 01, 2020 1:08 am
Vincen wrote: ↑
Tue Jun 30, 2020 7:23 am
 If \(n\) is a prime number and \(n \ne 3,\) which of the following could be the remainder when \(100! + n\) is divided by \(3?\)

I. 0
II. 1
III. 2

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II and III

[spoiler]OA=D[/spoiler]

Source: Princeton Review
We know that 100! = 1*2*3*...*100. So 100! is divisible by 3; the remainder upon dividing \(100! + n\) by 3 would come from dividing \(n\) by 3.

Knowing that \(n\) is a prime number and \(n \ne 3,\) the remainder cannot be 0. If n = 5, the remainder is 2 and if n = 7, the remainder is 1.

Correct answer: D

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Manhattan GRE | LSAT Practice Questions | SAT Practice Test | GMAT Info | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
Post new topic Post Reply
• Page 1 of 1