GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 20:21

### 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

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

# 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

Manager
Joined: 22 Dec 2011
Posts: 211
If n is a prime number and n ≠ 3, which of the following  [#permalink]

### Show Tags

Updated on: 03 Nov 2012, 01:55
3
12
00:00

Difficulty:

35% (medium)

Question Stats:

65% (01:29) correct 35% (01:34) wrong based on 383 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.

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.
Math Expert
Joined: 02 Sep 2009
Posts: 58445
Re: If n is a prime number and n ≠ 3, which of the following  [#permalink]

### Show Tags

03 Nov 2012, 01:59
2
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.

Hope it's clear.
_________________
Manager
Joined: 22 Dec 2011
Posts: 211
Re: If n is a prime number and n ≠ 3, which of the following  [#permalink]

### Show Tags

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.

Hope it's clear.

ohh my god. Ok thanks.
Manager
Joined: 25 Jun 2012
Posts: 56
Re: If n is a prime number and n ≠ 3, which of the following  [#permalink]

### Show Tags

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!...

if n = 6 - 6 is not prime
GMAT Tutor
Status: Private GMAT Tutor
Joined: 22 Oct 2012
Posts: 142
Location: India
Concentration: Economics, Finance
Schools: IIMA (A)
GMAT 1: 780 Q51 V47
Re: If n is a prime number and n ≠ 3, which of the following  [#permalink]

### Show Tags

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.

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
_________________
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]

### Show Tags

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
Senior Manager
Joined: 16 Dec 2011
Posts: 286
Re: If n is a prime number and n ≠ 3, which of the following  [#permalink]

### Show Tags

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.

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1749
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

13 Aug 2014, 02:45
2
2
$$\frac{100! + n}{3} = \frac{100!}{3} + \frac{n}{3}$$

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

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

_________________
Kindly press "+1 Kudos" to appreciate
Intern
Joined: 25 Mar 2018
Posts: 1
Location: India
GMAT 1: 640 Q44 V33
GPA: 3.3
Re: If n is a prime number and n ≠ 3, which of the following  [#permalink]

### Show Tags

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.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: If n is a prime number and n ≠ 3, which of the following  [#permalink]

### Show Tags

23 Aug 2018, 16:38
1
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).

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

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

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Status: No Progress without Struggle
Joined: 04 Aug 2017
Posts: 42
Location: Armenia
GPA: 3.4
Re: If n is a prime number and n ≠ 3, which of the following  [#permalink]

### Show Tags

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 http://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.

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

_________________
Seryozha Sargsyan 21

Contact: sargsyanseryozha@gmail.com

What you think, you become,
What you feel, you attract,
What you imagine, you create.
Re: If n is a prime number and n ≠ 3, which of the following   [#permalink] 29 Aug 2018, 05:43
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

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