If n is a prime number and n ≠ 3, which of the following : Problem Solving (PS)

Jp27

Manager

Joined: 22 Dec 2011

Posts: 175

If n is a prime number and n ≠ 3, which of the following [#permalink]

Updated on: 03 Nov 2012, 01:55

3

Kudos

20

Bookmarks

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

64% (01:32) correct

36% (01:34) wrong

based on 438 sessions

Hide Show timer Statistics

If n is a prime number and n ≠ 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

Bunuel - I checked out reminders concepts in the math book compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html
but the below idea wasn't mentioned

You can add and subtract remainders directly, as long as you correct excess or negative remainders. "

if x leaves a remainder of 4 after division by 7, and y leaves a remainder of 2 after division by 7, then x +y leaves a remainder of 4 + 2 = 6 after division by 7.

Similarly 100! leaves a remainder 0 on division by 3 so we are only interested in the remainder when N divided by 3,which will be actual remainders of 100! + n is divided by 3

if n =1 remainder 1 so overall remainder is 1
if n = 2 remainder 2 so overall remainder is 2
if n = 6 remainder = 0 so overall remainder is 0

All 3 are possible right then why Princeton says D?

Cheers.

Show Answer

Official Answer

Official Answer and Stats are available only to registered users. Register/Login.

Originally posted by Jp27 on 03 Nov 2012, 01:49.
Last edited by Bunuel on 03 Nov 2012, 01:55, edited 2 times in total.

Renamed the topic and edited the question.

L

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92747

Re: If n is a prime number and n ≠ 3, which of the following [#permalink]

03 Nov 2012, 01:59

2

Kudos

Expert Reply

Jp27 wrote:

If n is a prime number and n ≠ 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

Bunuel - I checked out reminders concepts in the math book compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html
but the below idea wasn't mentioned

You can add and subtract remainders directly, as long as you correct excess or negative remainders. "

if x leaves a remainder of 4 after division by 7, and y leaves a remainder of 2 after division by 7, then x +y leaves a remainder of 4 + 2 = 6 after division by 7.

Similarly 100! leaves a remainder 0 on division by 3 so we are only interested in the remainder when N divided by 3,which will be actual remainders of 100! + n is divided by 3

if n =1 remainder 1 so overall remainder is 1
if n = 2 remainder 2 so overall remainder is 2
if n = 6 remainder = 0 so overall remainder is 0

All 3 are possible right then why Princeton says D?

Cheers.

Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1.

n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0.

It can be 1 for n=7 and 2 for n=5.

Answer: D.

Hope it's clear.
_________________

New to the GMAT CLUB Forum?

Ultimate GMAT Quantitative Megathread

All You Need for Quant

GMAT Club's Complete Questions' Bank

My Signature Questions' Collection:

Bunuel's Signature Questions' Collection

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Signature Read More

Jp27

Manager

Joined: 22 Dec 2011

Posts: 175

Re: If n is a prime number and n ≠ 3, which of the following [#permalink]

03 Nov 2012, 02:14

Bunuel wrote:

Jp27 wrote:

If n is a prime number and n ≠ 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

Bunuel - I checked out reminders concepts in the math book compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html
but the below idea wasn't mentioned

You can add and subtract remainders directly, as long as you correct excess or negative remainders. "

if x leaves a remainder of 4 after division by 7, and y leaves a remainder of 2 after division by 7, then x +y leaves a remainder of 4 + 2 = 6 after division by 7.

Similarly 100! leaves a remainder 0 on division by 3 so we are only interested in the remainder when N divided by 3,which will be actual remainders of 100! + n is divided by 3

if n =1 remainder 1 so overall remainder is 1
if n = 2 remainder 2 so overall remainder is 2
if n = 6 remainder = 0 so overall remainder is 0

All 3 are possible right then why Princeton says D?

Cheers.

Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1.

n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0.

It can be 1 for n=2 and 2 for n=5.

Answer: D.

Hope it's clear.

ohh my god. Ok thanks.

actleader

Manager

Joined: 25 Jun 2012

Posts: 54

Re: If n is a prime number and n ≠ 3, which of the following [#permalink]

03 Nov 2012, 08:30

Jp27 wrote:

If n is a prime number and n ≠ 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

Bunuel - I checked out reminders concepts in the math book compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html
but the below idea wasn't mentioned

You can add and subtract remainders directly, as long as you correct excess or negative remainders. "

if x leaves a remainder of 4 after division by 7, and y leaves a remainder of 2 after division by 7, then x +y leaves a remainder of 4 + 2 = 6 after division by 7.

Similarly 100! leaves a remainder 0 on division by 3 so we are only interested in the remainder when N divided by 3,which will be actual remainders of 100! + n is divided by 3

if n =1 remainder 1 so overall remainder is 1
if n = 2 remainder 2 so overall remainder is 2
if n = 6 remainder = 0 so overall remainder is 0

All 3 are possible right then why Princeton says D?

Cheers.

My answer is D.

if a number n is prime,
and together with that does not equal 3
we can divide it on 3 whithout a remainder.

0 can't be the answer.

we can also check it with, for example 5! and list of primes such as 2!,5!,7!...

in your example
if n = 6 - 6 is not prime

D

ChiranjeevSingh

Tutor

Joined: 22 Oct 2012

Status:Private GMAT Tutor

Posts: 364

Location: India

Concentration: Economics, Finance

Schools: IIMA (A)

GMAT Focus 1:
735 Q90 V85 DI85 Verified score

GMAT Focus 2:
735 Q90 V85 DI85 Verified score

GMAT 1: 780 Q51 V47 Verified score

GRE 1: Q170 V168

Re: If n is a prime number and n ≠ 3, which of the following [#permalink]

03 Nov 2012, 18:30

Expert Reply

Bunuel wrote:

Jp27 wrote:

If n is a prime number and n ≠ 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

Bunuel - I checked out reminders concepts in the math book compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html
but the below idea wasn't mentioned

You can add and subtract remainders directly, as long as you correct excess or negative remainders. "

if x leaves a remainder of 4 after division by 7, and y leaves a remainder of 2 after division by 7, then x +y leaves a remainder of 4 + 2 = 6 after division by 7.

Similarly 100! leaves a remainder 0 on division by 3 so we are only interested in the remainder when N divided by 3,which will be actual remainders of 100! + n is divided by 3

if n =1 remainder 1 so overall remainder is 1
if n = 2 remainder 2 so overall remainder is 2
if n = 6 remainder = 0 so overall remainder is 0

All 3 are possible right then why Princeton says D?

Cheers.

Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1.

n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0.

It can be 1 for n=2 and 2 for n=5.

Answer: D.

Hope it's clear.

Hi,

A minor correction in your post:
for n=2, the remainder will be 2, not 1.
for n=7, remainder will be 1.

With respect,
CJ

nityamskhurana

Intern

Joined: 19 Apr 2012

Posts: 7

Concentration: Technology, General Management

GMAT Date: 06-26-2014

GPA: 4

WE:Programming (Computer Software)

Re: If n is a prime number and n ≠ 3, which of the following [#permalink]

26 Nov 2012, 11:22

Another way to look at it is:

100!+n where n ≠ 3, since 100! will be a factor or 3, so we just have to care about n.
Hence, if n=2 then remainder of 2/3 is 2.
for any value of n>3, and n being prime it can be written as (6k+1) or (6k-1).
Hence, factor (6k+1)/3 will give remainder as 1, and (6k-1) would leave remainder as 2.

Please correct me if I am wrong.

Regards,
Nityam

doe007

Manager

Joined: 16 Dec 2011

Posts: 236

Re: If n is a prime number and n ≠ 3, which of the following [#permalink]

06 Apr 2013, 06:37

100! is divisible by 3. So we need to find out the remainder when the prime number n is divided by 3.

For n = 2 or 5, remainder is 2.
For n = 7, remainder is 1.

n cannot be 3 as specified and cannot be any other multiple of 3 as n is prime. So the remainder cannot be 0.

Answer is D.

PareshGmat

SVP

Joined: 27 Dec 2012

Status:The Best Or Nothing

Posts: 1563

Location: India

Concentration: General Management, Technology

WE:Information Technology (Computer Software)

Re: If n is a prime number and n ≠ 3, which of the following [#permalink]

13 Aug 2014, 02:45

2

Kudos

2

Bookmarks

$\frac{100! + n}{3} = \frac{100!}{3} + \frac{n}{3}$

$\frac{100!}{3}$ is a perfect division

$\frac{n}{3}$ may give remainder either 1 or 2 as n is prime

Answer = D

B

jemiljacob09

Intern

Joined: 25 Mar 2018

Posts: 1

Location: India

Schools: Krannert '21 (A$)

GMAT 1: 640 Q44 V33

GPA: 3.3

Re: If n is a prime number and n ≠ 3, which of the following [#permalink]

20 Aug 2018, 06:27

100! is sure to have last digit as 0. (100 x 99 x 98 x......)
Therefore the question narrows down to n/3, where n is prime.
Since n is not equal to 3, n/3 will leave a remainder for all cases.

Hence the answer is Option D

Please let me know if this approach is correct.

L

ScottTargetTestPrep

Target Test Prep Representative

Joined: 14 Oct 2015

Status:Founder & CEO

Affiliations: Target Test Prep

Posts: 18738

Location: United States (CA)

Re: If n is a prime number and n ≠ 3, which of the following [#permalink]

23 Aug 2018, 16:38

1

Kudos

Expert Reply

Jp27 wrote:

If n is a prime number and n ≠ 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

Since 100! is divisible by 3, then the remainder when 100! + n is divided by 3 is same as when n is divided by 3. If n is 5, then the remainder is 2. If n is 7, then the remainder is 1. However, the remainder can’t be 0 since n is neither 3 nor it is a multiple of 3 (since n is a prime ≠ 3).

Answer: D
_________________

Scott Woodbury-Stewart | Founder and CEO | Scott@TargetTestPrep.com

Try 5-Day Full Access Trial For FREE
Perfect 5-Star Rating on GMAT Club
Conner Scored GMAT Focus 755 (100%)

See why Target Test Prep is the top rated GMAT course on GMAT Club. Read Our Reviews

Signature Read More

B

Seryozha

Intern

Joined: 04 Aug 2017

Status:No Progress without Struggle

Posts: 40

Location: Armenia

GPA: 3.4

Re: If n is a prime number and n ≠ 3, which of the following [#permalink]

29 Aug 2018, 05:43

ChiranjeevSingh wrote:

Bunuel wrote:

Jp27 wrote:

If n is a prime number and n ≠ 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

Bunuel - I checked out reminders concepts in the math book https://gmatclub.com/forum/compilation-o ... 86714.html
but the below idea wasn't mentioned

You can add and subtract remainders directly, as long as you correct excess or negative remainders. "

if x leaves a remainder of 4 after division by 7, and y leaves a remainder of 2 after division by 7, then x +y leaves a remainder of 4 + 2 = 6 after division by 7.

Similarly 100! leaves a remainder 0 on division by 3 so we are only interested in the remainder when N divided by 3,which will be actual remainders of 100! + n is divided by 3
I wonder why the remainder is 2, when we have 2/3?

if n =1 remainder 1 so overall remainder is 1
if n = 2 remainder 2 so overall remainder is 2
if n = 6 remainder = 0 so overall remainder is 0

All 3 are possible right then why Princeton says D?

Cheers.

Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1.

n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0.

It can be 1 for n=2 and 2 for n=5.

Answer: D.

Hope it's clear.

Hi,

A minor correction in your post:
for n=2, the remainder will be 2, not 1.
for n=7, remainder will be 1.

With respect,
CJ

B

narenbs

Intern

Joined: 14 Mar 2018

Posts: 13

GMAT 1: 690 Q47 V38

Re: If n is a prime number and n ≠ 3, which of the following [#permalink]

24 Feb 2022, 17:13

Since n is a prime number greater than 3, n can be expressed as 6p + 1 or 6p - 1. Therefore 100! + n can be expressed as either 100! + 6p + 1 or 100! + 6p - 1. When divided by 3 these expressions leave remainders of either 1 or -1 (i.e. 2). Therefore remainders can be 1 or 2. Therefore answer is D.

bumpbot

Non-Human User

Joined: 09 Sep 2013

Posts: 32533

Re: If n is a prime number and n 3, which of the following [#permalink]

13 Dec 2023, 12:15

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Signature Read More

gmatclubot

Re: If n is a prime number and n 3, which of the following [#permalink]

13 Dec 2023, 12:15

GMAT Problem Solving (PS) Questions

If n is a prime number and n ≠ 3, which of the following

GMAT Question Banks