It is currently 19 Oct 2017, 17:03

### 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: 79

Kudos [?]: 17 [2], given: 1

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

### Show Tags

20 Mar 2013, 16:14
2
KUDOS
00:00

Difficulty:

15% (low)

Question Stats:

88% (00:45) correct 12% (01:09) wrong based on 233 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
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 Jul 2017, 09:20, edited 2 times in total.
Renamed the topic and edited the question.

Kudos [?]: 17 [2], given: 1

Manager
Joined: 24 Jan 2013
Posts: 77

Kudos [?]: 151 [2], given: 6

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

### Show Tags

20 Mar 2013, 16:40
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.

Kudos [?]: 151 [2], given: 6

Intern
Joined: 04 Sep 2012
Posts: 15

Kudos [?]: 22 [0], given: 14

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, 21:53
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)

Kudos [?]: 22 [0], given: 14

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 627

Kudos [?]: 1355 [0], given: 136

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

### Show Tags

20 Mar 2013, 21:54
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.
_________________

Kudos [?]: 1355 [0], given: 136

Intern
Status: Currently Preparing the GMAT
Joined: 15 Feb 2013
Posts: 30

Kudos [?]: 25 [0], given: 11

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, 01:36
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.

Kudos [?]: 25 [0], given: 11

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 128909 [0], given: 12183

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

### Show Tags

21 Mar 2013, 04:16
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.

Hope it's clear.
_________________

Kudos [?]: 128909 [0], given: 12183

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16652

Kudos [?]: 273 [0], given: 0

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

### Show Tags

13 Nov 2014, 10:49
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.
_________________

Kudos [?]: 273 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16652

Kudos [?]: 273 [0], given: 0

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

### Show Tags

05 Jul 2017, 15:53
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.
_________________

Kudos [?]: 273 [0], given: 0

Director
Joined: 22 May 2016
Posts: 814

Kudos [?]: 264 [1], given: 552

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

### Show Tags

06 Jul 2017, 09:11
1
KUDOS
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.

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?

Last edited by genxer123 on 06 Jul 2017, 09:24, edited 1 time in total.

Kudos [?]: 264 [1], given: 552

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 128909 [0], given: 12183

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

### Show Tags

06 Jul 2017, 09:21
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.

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.
_________________

Kudos [?]: 128909 [0], given: 12183

Math Forum Moderator
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3003

Kudos [?]: 1087 [0], given: 325

Location: India
GPA: 3.5
Re: If a positive integer n, divided by 5 has a remainder 2 [#permalink]

### Show Tags

06 Jul 2017, 11:10
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 )

Kudos [?]: 1087 [0], given: 325

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1545

Kudos [?]: 836 [0], given: 5

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

### Show Tags

14 Jul 2017, 10:40
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.

_________________

Jeffery Miller

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

Kudos [?]: 836 [0], given: 5

Re: If a positive integer n, divided by 5 has a remainder 2   [#permalink] 14 Jul 2017, 10:40
Display posts from previous: Sort by