It is currently 22 Sep 2017, 06:47

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 22 Dec 2011
Posts: 295

Kudos [?]: 282 [2], given: 32

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

Show Tags

New post 03 Nov 2012, 01:49
2
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

65% (00:58) correct 35% (01:05) wrong based on 295 sessions

HideShow 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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Nov 2012, 01:55, edited 2 times in total.
Renamed the topic and edited the question.

Kudos [?]: 282 [2], given: 32

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41684

Kudos [?]: 124424 [1], given: 12078

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

Show Tags

New post 03 Nov 2012, 01:59
1
This post received
KUDOS
Expert's post
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 Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

Kudos [?]: 124424 [1], given: 12078

Senior Manager
Senior Manager
avatar
Joined: 22 Dec 2011
Posts: 295

Kudos [?]: 282 [0], given: 32

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

Show Tags

New post 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.

Kudos [?]: 282 [0], given: 32

Manager
Manager
avatar
Joined: 25 Jun 2012
Posts: 65

Kudos [?]: 63 [0], given: 21

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

Show Tags

New post 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

Kudos [?]: 63 [0], given: 21

Manager
Manager
User avatar
B
Status: Private GMAT Tutor
Joined: 22 Oct 2012
Posts: 86

Kudos [?]: 251 [0], given: 43

Location: India
Concentration: Economics, Finance
Schools: IIMA (A)
GMAT 1: 780 Q51 V47
Premium Member CAT Tests
Re: If n is a prime number and n ≠ 3, which of the following [#permalink]

Show Tags

New post 03 Nov 2012, 18:30
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
_________________

Website: http://www.GMATwithCJ.com

My articles:
My experience with GMAT (Score 780) and My analysis of my ESR
Three pillars of a successful GMAT strategy
Critical Reasoning and The Life of a GMAT Student
The 'Although' Misconception
Dear GMAT Aspirant, You need not swim against the tide

Kudos [?]: 251 [0], given: 43

Intern
Intern
avatar
Joined: 19 Apr 2012
Posts: 15

Kudos [?]: 4 [0], given: 30

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]

Show Tags

New post 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

Kudos [?]: 4 [0], given: 30

Senior Manager
Senior Manager
avatar
Joined: 16 Dec 2011
Posts: 426

Kudos [?]: 230 [0], given: 70

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

Show Tags

New post 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.

Kudos [?]: 230 [0], given: 70

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 17592

Kudos [?]: 270 [0], given: 0

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

Show Tags

New post 08 Aug 2014, 09:13
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 270 [0], given: 0

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1854

Kudos [?]: 2521 [0], given: 193

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]

Show Tags

New post 13 Aug 2014, 02:45
1
This post was
BOOKMARKED
\(\frac{100! + n}{3} = \frac{100!}{3} + \frac{n}{3}\)

\(\frac{100!}{3}\) is a perfect division

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

Answer = D
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2521 [0], given: 193

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 17592

Kudos [?]: 270 [0], given: 0

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

Show Tags

New post 20 Nov 2015, 05:57
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 270 [0], given: 0

Re: If n is a prime number and n ≠ 3, which of the following   [#permalink] 20 Nov 2015, 05:57
    Similar topics Author Replies Last post
Similar
Topics:
21 EXPERTS_POSTS_IN_THIS_TOPIC Which of the following numbers is not prime ? abhi47 20 03 Apr 2017, 23:55
4 EXPERTS_POSTS_IN_THIS_TOPIC If n is the product of 3 same prime numbers and 1 different prime numb MathRevolution 4 02 Aug 2017, 00:58
4 EXPERTS_POSTS_IN_THIS_TOPIC If n is a positive integer, which one of the following numbers BrainLab 3 22 Feb 2016, 23:43
3 EXPERTS_POSTS_IN_THIS_TOPIC If n is the product of the first 10 prime numbers, which of the follow shasadou 3 15 Sep 2017, 09:41
6 EXPERTS_POSTS_IN_THIS_TOPIC If n is a prime number, which of the following could be true? janosfazekas91 8 22 Sep 2017, 01:05
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.