If a positive integer n, divided by 5 has a remainder 2 : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 03 Dec 2016, 02:41

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 04 Jan 2013
Posts: 80
Followers: 0

Kudos [?]: 8 [1] , given: 1

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

### Show Tags

20 Mar 2013, 15:14
1
KUDOS
00:00

Difficulty:

(N/A)

Question Stats:

94% (01:41) correct 6% (00:28) wrong based on 126 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

Last edited by Bunuel on 21 Mar 2013, 02:27, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 24 Jan 2013
Posts: 79
Followers: 5

Kudos [?]: 126 [2] , given: 6

Re: if a positive integer n,divided by 5 has a remainder 2 [#permalink]

### Show Tags

20 Mar 2013, 15:40
2
KUDOS
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.

Intern
Joined: 04 Sep 2012
Posts: 15
Location: India
WE: Marketing (Consumer Products)
Followers: 0

Kudos [?]: 18 [0], given: 14

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: 631
Followers: 77

Kudos [?]: 1086 [0], given: 136

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: 31
Location: United States
GMAT 1: 550 Q47 V23
GPA: 3.7
WE: Analyst (Consulting)
Followers: 1

Kudos [?]: 16 [0], given: 11

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: 35840
Followers: 6828

Kudos [?]: 89683 [0], given: 10381

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 7, so n+2=9.

Hope it's clear.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12843
Followers: 559

Kudos [?]: 157 [0], given: 0

Re: If a positive integer n, divided by 5 has a remainder 2 [#permalink]

### Show Tags

13 Nov 2014, 09:49
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.
_________________
Re: If a positive integer n, divided by 5 has a remainder 2   [#permalink] 13 Nov 2014, 09:49
Similar topics Replies Last post
Similar
Topics:
If a positive integer n, divided by 5 has a remainder 2, which of the 1 16 May 2016, 01:40
1 N is a positive integer. When N + 1 is divided by 5, the remainder is 6 31 Jan 2016, 07:04
25 When positive integer n is divided by 13, the remainder is 2. When n 14 02 Apr 2015, 05:09
45 When positive integer n is divided by 3, the remainder is 2. When n is 19 02 Apr 2015, 05:06
13 When positive integer n is divided by 5, the remainder is 1. When n is 8 09 Apr 2011, 15:08
Display posts from previous: Sort by