If x is a positive integer, is x a prime integer? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 23:01

### 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 x is a positive integer, is x a prime integer?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 25 Jan 2013
Posts: 2
Followers: 0

Kudos [?]: 19 [1] , given: 3

If x is a positive integer, is x a prime integer? [#permalink]

### Show Tags

25 Jan 2013, 02:43
1
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

48% (03:11) correct 52% (01:04) wrong based on 219 sessions

### HideShow timer Statistics

If x is a positive integer, is x a prime integer?

(1) x+1 is a prime number.
(2) x-5 is a prime number.

Can't figure it out.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36548
Followers: 7078

Kudos [?]: 93133 [3] , given: 10552

Re: If x is a positive integer, is x a prime integer? [#permalink]

### Show Tags

25 Jan 2013, 03:47
3
KUDOS
Expert's post
4
This post was
BOOKMARKED
If x is a positive integer, is x a prime integer?

(1) x+1 is a prime number. Notice that x cannot be an odd prime, because in this case (odd prime) + 1 = (even number), and the only even prime is 2, but in this case x=1, which is not prime. So, if x=prime, then it must be 2: 2+1=3=prime. Of course, x can be a non-prime, for example 1. Not sufficient.

(2) x-5 is a prime number. If x=7, then the answer is YES but if x=8, then the answer is NO. Not sufficient.

(1)+(2) From (1) we have that if x IS a prime, then it must be 2. But if x=2, them x-5=-3, which is not a prime. Thus x=prime=2 contradicts the second statement. Therefore x cannot be a prime number. Sufficient.

Hope it's clear.
_________________
Current Student
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 62

Kudos [?]: 593 [1] , given: 355

Re: If x is a positive integer, is x a prime integer? [#permalink]

### Show Tags

29 Jan 2014, 07:01
1
KUDOS
Correct. From both statements together:

X must be higher than 5 because no prime can be negative. All primes higher than 5 are odd. So x+1 will be an even number. There is only one even number that is prime which is 2. Given that x>5 then we know that X cannot be a prime

C
Manager
Status: Working hard to score better on GMAT
Joined: 02 Oct 2012
Posts: 90
Location: Nepal
Concentration: Finance, Entrepreneurship
GPA: 3.83
WE: Accounting (Consulting)
Followers: 0

Kudos [?]: 151 [0], given: 23

Re: If x is a positive integer, is x a prime integer? [#permalink]

### Show Tags

20 May 2013, 02:15
suprememodelrus wrote:
If x is a positive integer, is x a prime integer?

(1) x+1 is a prime number.
(2) x-5 is a prime number.

Hi Bunuel, My approach does not look standard. Is it correct?

From statement 1: X= 1,2,4,6,10,12,16,18........
From statement 2: X= 7,8,10,12,16,22........

common from the both statements are 10,12,16..... Thus X is not a prime integer.

Kindly provide algebric approach if possible.

_________________

Do not forget to hit the Kudos button on your left if you find my post helpful.

SVP
Joined: 05 Jul 2006
Posts: 1743
Followers: 6

Kudos [?]: 316 [0], given: 49

Re: If x is a positive integer, is x a prime integer? [#permalink]

### Show Tags

20 May 2013, 08:41
f x is a positive integer, is x a prime integer?

(1) x+1 is a prime number.
(2) x-5 is a prime number.

I think this is a bad question , however ...

from 1

x , x+1 are 2 successive integers ....... if x is prime and since the only 2 prime that are successive are 2,3 therefore if x is prime it is 2 , however x could be 4 as well .... insuff

from 2

The only 2 primes 5 units apart are 7 and 2 , (since all primes > 3 end in 1,3,7,9) if x were to be prime it is 7 , however x could be 8 and (x-5) could be 3 ... insuff

both together

for x to be prime according to the above 2 statements then it has be less than a prime by 1 and larger than another by 5 .... there exist no such a prime

thus sure x is not a prime ( integers if not prime are composite)
Math Expert
Joined: 02 Sep 2009
Posts: 36548
Followers: 7078

Kudos [?]: 93133 [0], given: 10552

Re: If x is a positive integer, is x a prime integer? [#permalink]

### Show Tags

21 May 2013, 00:05
atalpanditgmat wrote:
suprememodelrus wrote:
If x is a positive integer, is x a prime integer?

(1) x+1 is a prime number.
(2) x-5 is a prime number.

Hi Bunuel, My approach does not look standard. Is it correct?

From statement 1: X= 1,2,4,6,10,12,16,18........
From statement 2: X= 7,8,10,12,16,22........

common from the both statements are 0,12,16..... Thus X is not a prime integer.

Kindly provide algebric approach if possible.

Yes, that's correct. From both statements x must be even (10, 12, 16, ...), but it cannot be 2. So, x is not a prime number.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13441
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If x is a positive integer, is x a prime integer? [#permalink]

### Show Tags

08 Sep 2015, 01:11
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 Club Legend
Joined: 09 Sep 2013
Posts: 13441
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If x is a positive integer, is x a prime integer? [#permalink]

### Show Tags

20 Sep 2016, 23:20
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 x is a positive integer, is x a prime integer?   [#permalink] 20 Sep 2016, 23:20
Similar topics Replies Last post
Similar
Topics:
3 Is a positive integer x a prime number? 7 04 Aug 2016, 18:25
6 Is positive integer x prime? 5 05 Feb 2015, 08:00
33 If x and y are positive integers, is x a prime number? 10 22 May 2014, 16:42
1 Is the positive integer x a prime number? 7 12 Jan 2010, 04:53
20 If x is a positive integer, is x prime? 9 24 Nov 2007, 07:07
Display posts from previous: Sort by