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

 It is currently 18 Nov 2018, 13:00

### 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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
• ### The winning strategy for 700+ on the GMAT

November 20, 2018

November 20, 2018

06:00 PM EST

07:00 PM EST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# If a positive integer n, divided by 5 has a remainder 2

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

### Hide Tags

Manager
Joined: 04 Jan 2013
Posts: 71
If a positive integer n, divided by 5 has a remainder 2  [#permalink]

### Show Tags

Updated on: 06 Jul 2017, 08:20
2
00:00

Difficulty:

5% (low)

Question Stats:

83% (01:13) correct 17% (01:33) wrong based on 275 sessions

### HideShow timer Statistics

If a positive integer n, divided by 5 has a remainder 2, which of the following must be true

I. n is odd
II. n+1 cannot be a prime number
III. (n+2) divided by 7 has remainder 2

A. None
B. I only
C. I and II only
D. II and III only
E. I, II and III

Originally posted by chiccufrazer1 on 20 Mar 2013, 15:14.
Last edited by Bunuel on 06 Jul 2017, 08:20, edited 2 times in total.
Renamed the topic and edited the question.
Manager
Joined: 24 Jan 2013
Posts: 72
Re: If a positive integer n, divided by 5 has a remainder 2  [#permalink]

### Show Tags

20 Mar 2013, 15:40
2
If a positive integer n,divided by 5 has a remainder 2,which of the following must be true
I. n is odd
II. n+1 cannot be a prime number
III. (n+2)divided by 7 has remainder 2

Some valid values for n: 7, 12, 17, 22, 27, 32... or, in other words: $$n=(i * 5) + 2$$ for i=1,2,3...

I. FALSE: we see that n can we odd or even.
II. FALSE: (n+1) could be a prime number. Example: n=12 --> (n+1)=13 is prime. Other example: for n=22, (n+1)=23 is prime.
III. FALSE: for n=12, (n+2)=14, divided by 7 has remainder zero.

None answer is true.

Answer: A
Intern
Joined: 04 Sep 2012
Posts: 15
Location: India
WE: Marketing (Consumer Products)
Re: If a positive integer n, divided by 5 has a remainder 2  [#permalink]

### Show Tags

20 Mar 2013, 20:53
I. 22 and 27 both have a reminder of 2. So False (Options remaining - A,D,E)
II. 22 + 1 = 23 is a prime number. So False (Options remaining - A)

Ans (A)
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 612
Re: If a positive integer n, divided by 5 has a remainder 2  [#permalink]

### Show Tags

20 Mar 2013, 20:54
chiccufrazer1 wrote:
If a positive integer n,divided by 5 has a remainder 2,which of the following must be true I. n is odd
II. n+1 cannot be a prime number
III. (n+2)divided by 7 has remainder 2

A.none
B.I only
C.I and II only
D.II and III only
E.I,II and III

n can be written as :

n = 5k+2. Thus, taking k=0, we have n=2.

I.n=2,even.False
II.2+1=3, is a prime. False.
III.n+2 = 4,4 divided by 7 leaves a remainder of 4. False.

A.
_________________
Intern
Status: Currently Preparing the GMAT
Joined: 15 Feb 2013
Posts: 29
Location: United States
GMAT 1: 550 Q47 V23
GPA: 3.7
WE: Analyst (Consulting)
Re: If a positive integer n, divided by 5 has a remainder 2  [#permalink]

### Show Tags

21 Mar 2013, 00:36
chiccufrazer1, you forgot to provide the OA in your post. Just make sure you do provide it for your future problems.

Alright, let's solve this :

We know that n, a positive integer, yields a remainder of 2 when divided by 5. So according to the algebraic form of the division operation, we'll have :

$$n = 5*q + 2$$ with q being a positive integer as well.

This expression allows us to give out some valid possibilities for n by playing with the value of q, such as :

q = 0 => n = 2
q = 1 => n = 7
q= 2 => n =12

Now, from these first values we can already cross off statement I.(n is odd) , since n can be 7 (which is odd) or n can be 12 (which is even).

Statement II. (n+1 cannot be a prime number) can also be crossed off. Consider n = 12, which is not a prime number and yields a remainder of 2 when divided by 5. If we add 1 to it, we get 13, which IS a prime number, so that contradicts statement II.

Finally, statement III. (n+2 yields a remainder of 2 when divided by 7) can also be crossed off. Again consider n = 12. Add 2 to it and we get a 14 which is a multiple of 7.

In short, all statements have been contradicted and the correct answer choice to the question is A : none of the statements above are true.

Hope that helped.
Math Expert
Joined: 02 Sep 2009
Posts: 50627
Re: If a positive integer n, divided by 5 has a remainder 2  [#permalink]

### Show Tags

21 Mar 2013, 03:16
If a positive integer n, divided by 5 has a remainder 2, which of the following must be true

I. n is odd
II. n+1 cannot be a prime number
III. (n+2) divided by 7 has remainder 2

A. None
B. I only
C. I and II only
D. II and III only
E. I, II and III[/quote]

A positive integer n, divided by 5 has a remainder 2 --> $$n=5q+2$$, so n could be 2, 7, 12, 17, 22, 27, ...

I. n is odd. Not necessarily true, since n could be 2, so even.

II. n+1 cannot be a prime number. Not necessarily true, since n could be 2, so n+1=3=prime.

III. (n+2) divided by 7 has remainder 2. Not necessarily true, since n could be 2, so n+2=4 and 4 divided by 7 has remainder 4.

Answer: A.

Hope it's clear.
_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 2110
If a positive integer n, divided by 5 has a remainder 2  [#permalink]

### Show Tags

Updated on: 06 Jul 2017, 08:24
1
Bunuel wrote:
If a positive integer n, divided by 5 has a remainder 2, which of the following must be true

I. n is odd
II. n+1 cannot be a prime number
III. (n+2) divided by 7 has remainder 2

A. None
B. I only
C. I and II only
D. II and III only
E. I, II and III

Quote:
A positive integer n, divided by 5 has a remainder 2 --> $$n=5q+2$$, so n could be 2, 7, 12, 17, 22, 27, ...

I. n is odd. Not necessarily true, since n could be 2, so even.

II. n+1 cannot be a prime number. Not necessarily true, since n could be 2, so n+1=3=prime.

III. (n+2) divided by 7 has remainder 2. Not necessarily true, since n could be 7, so n+2=9.

Answer: A.

Hope it's clear.

Bunuel ,
I am confused by your analysis of III: (n+2) divided by 7 has remainder 2

If n = 7 and (n + 2) = 9, then $$\frac{9}{7}$$ = 1 + R2.

n could be 2, 7, 12, 17 ...

If n = 12, then (n+2) = 14, which, when divided by 7, leaves remainder 0.

If n = 17, (n+2) = 19, which, when divided by 7, leaves remainder 5.

Those two examples (or others) seem to me to be what should be used to show that III does not satisfy the condition "must be true."

The one you chose proves that III could be true; I'm having a hard time understanding how n = 7 proves that III does not have to be true. Am I missing something?

Originally posted by generis on 06 Jul 2017, 08:11.
Last edited by generis on 06 Jul 2017, 08:24, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 50627
Re: If a positive integer n, divided by 5 has a remainder 2  [#permalink]

### Show Tags

06 Jul 2017, 08:21
genxer123 wrote:
Bunuel wrote:
If a positive integer n, divided by 5 has a remainder 2, which of the following must be true

I. n is odd
II. n+1 cannot be a prime number
III. (n+2) divided by 7 has remainder 2

A. None
B. I only
C. I and II only
D. II and III only
E. I, II and III

Quote:
A positive integer n, divided by 5 has a remainder 2 --> $$n=5q+2$$, so n could be 2, 7, 12, 17, 22, 27, ...

I. n is odd. Not necessarily true, since n could be 2, so even.

II. n+1 cannot be a prime number. Not necessarily true, since n could be 2, so n+1=3=prime.

III. (n+2) divided by 7 has remainder 2. Not necessarily true, since n could be 7, so n+2=9.

Answer: A.

Hope it's clear.

Bunuel ,
I am confused by your analysis of III: (n+2) divided by 7 has remainder 2

If n = 9, then $$\frac{9}{7}$$ = 1 + R2.

n could be 2, 7, 12, 17 ...

If n = 12, then (n+2) = 14, which, when divided by 7, leaves remainder 0.

If n = 17, (n+2) = 19, which, when divided by 7, leaves remainder 5.

Those two examples (or others) seem to me to be what should be used to show that III does not satisfy the condition "must be true."

The one you chose proves that III could be true; I'm having a hard time understanding how n = 7 proves that III does not have to be true. Am I missing something?

You are right. Edited the question.
_________________
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4224
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: If a positive integer n, divided by 5 has a remainder 2  [#permalink]

### Show Tags

06 Jul 2017, 10:10
chiccufrazer1 wrote:
If a positive integer n, divided by 5 has a remainder 2, which of the following must be true

I. n is odd
II. n+1 cannot be a prime number
III. (n+2) divided by 7 has remainder 2

A. None
B. I only
C. I and II only
D. II and III only
E. I, II and III

Possible values of n are { 7 , 12 , 17 , 22 , 27 ................... }

Now, check the options -

I. n can be Odd/Even
II. n can be Prime / Non Prime
III. n can/can not have remainder 2

Thus, the answer will be (A)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If a positive integer n, divided by 5 has a remainder 2  [#permalink]

### Show Tags

14 Jul 2017, 09:40
chiccufrazer1 wrote:
If a positive integer n, divided by 5 has a remainder 2, which of the following must be true

I. n is odd
II. n+1 cannot be a prime number
III. (n+2) divided by 7 has remainder 2

A. None
B. I only
C. I and II only
D. II and III only
E. I, II and III

We can express n as:

n = 5q + 2

Let’s now analyze each Roman numeral:

I. n is odd

If q = 2, then 5q + 2 = 12, so n does not have to be odd.

II. n+1 cannot be a prime number

If q = 2, then 5q + 2 = 12, so n + 1 = 13, which is prime. So II does not have to be true.

III. (n+2) divided by 7 has remainder 2

n + 2 = 5q + 4

If q = 2, then 5q + 4 = 14, which has a remainder of zero when divided by 7. So III does not have to be true.

Answer: A
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

CEO
Joined: 11 Sep 2015
Posts: 3122
Location: Canada
Re: If a positive integer n, divided by 5 has a remainder 2  [#permalink]

### Show Tags

13 Nov 2017, 14:12
1
Top Contributor
chiccufrazer1 wrote:
If a positive integer n, divided by 5 has a remainder 2, which of the following must be true

I. n is odd
II. n+1 cannot be a prime number
III. (n+2) divided by 7 has remainder 2

A. None
B. I only
C. I and II only
D. II and III only
E. I, II and III

-----------------ASIDE----------------------------------
When it comes to remainders, we have a nice rule that says:

If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
------ONTO THE QUESTION!!!------------------------

Positive integer n, divided by 5 has a remainder 2
Some possible values of n: 2, 7, 12, 17, 22, 27, 32, 37, . . . etc

Now let's examine the statements:
I. n is odd.
This need not be true.
Among the possible values of n, we see that n need not be odd
So statement 1 is FALSE

II. n+1 cannot be a prime number.
Not true.
Among the possible values of n, we see that n COULD equal 2
2+1 = 3, and 3 IS a prime number
So, n+1 CAN BE a prime number
So statement 2 is FALSE

NOTE: Since statements I and II are false, we need not examine statement III, since there are no answer choices that suggest that only statement III is true.
So, the correct must be A

RELATED VIDEO FROM OUR COURSE

_________________

Test confidently with gmatprepnow.com

Re: If a positive integer n, divided by 5 has a remainder 2 &nbs [#permalink] 13 Nov 2017, 14:12
Display posts from previous: Sort by

# If a positive integer n, divided by 5 has a remainder 2

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

 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®.