Last visit was: 24 Jul 2024, 05:50 It is currently 24 Jul 2024, 05:50
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# If n is an integer, is n + 1 a prime number?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94605
Own Kudos [?]: 643508 [9]
Given Kudos: 86734
Math Expert
Joined: 02 Sep 2009
Posts: 94605
Own Kudos [?]: 643508 [5]
Given Kudos: 86734
General Discussion
Intern
Joined: 18 Jul 2010
Posts: 33
Own Kudos [?]: 95 [1]
Given Kudos: 6
Intern
Joined: 25 May 2014
Posts: 43
Own Kudos [?]: 46 [0]
Given Kudos: 125
Re: If n is an integer, is n + 1 a prime number? [#permalink]
(1):- n can be any prime number , n=3 ; n+1=4 not prime
n=2; n+1 =3 prime
Not sufficient.

(2):- n+2 not prime.
n=2 ; n+2=4 NP ; n+1=3 Prime
n=4 ; n+2=6 NP ; n+1=5 Prime
n=-1 ; n+2=1 NP ; n+1=0 not Prime
Not sufficient.

(1)+(2):-
n= prime and n+2 = not prime
n=2 ; n+2=4 NP ; n+1=3 Prime
n=7 ; n+2 = 9 NP ; n+1= 8 Not prime
Not sufficient. E
Manager
Joined: 12 Sep 2014
Posts: 127
Own Kudos [?]: 139 [1]
Given Kudos: 103
GMAT 1: 740 Q49 V41
GPA: 3.94
Re: If n is an integer, is n + 1 a prime number? [#permalink]
1
Bookmarks
Statement 1 says that n is a prime, but that could mean n=2 and n+1=3, both are primes. Or, n=3 and n+1=4, n+1 is not a prime. Insufficient.
Statement 2 says that n+2 is not a prime. So, n=2 or n=13. Meaning, n+1=3 (prime) or n+1=14 (not prime). Insufficient.

Combining, we can use the same numbers from Statement 2 example above: n=2 and n=13. Insufficient.

E
Intern
Joined: 10 Mar 2014
Posts: 36
Own Kudos [?]: 17 [1]
Given Kudos: 82
Concentration: General Management, Technology
GMAT 1: 650 Q47 V32
GPA: 4
Re: If n is an integer, is n + 1 a prime number? [#permalink]
1
Kudos
Statement 1: n =2 , n+1 =3 (Prime) --- Yes
n = 3, n+1=4 (Composite)--- No
Insufficient.

Statement 2: n= 2, n+2 = 4 , n+1=3(Prime) ---Yes
n= 7, n+2 = 9, n+1=8(composite) ---No
Insufficient

Statement 1 & 2: Consider case of n=2 and n=7 ---Insufficient.

Hence answer is E.
Manager
Joined: 22 Sep 2012
Posts: 109
Own Kudos [?]: 147 [0]
Given Kudos: 49
Concentration: Strategy, Technology
WE:Information Technology (Computer Software)
Re: If n is an integer, is n + 1 a prime number? [#permalink]
Qs: If n is an integer, is n + 1 a prime number?

(1) n is a prime number.
If n =2, n+1 = 3 = prime number (True)
if n = 3, n+1 = 4 = not a prime number (False)

Therefore clearly insufficient

(2) n + 2 is not a prime number.

if n = 2, n+2 = 4 (not a prime number), n+1 = 3 = prime number = (True)
if n = 7, n+2 = 9 (not a prime number), n+1 = 8 = not a prime number (False)

Even after combining 1 and 2 we can't still get a definitive answer. Hence the answer is E)
Manager
Joined: 02 Sep 2014
Posts: 70
Own Kudos [?]: 535 [0]
Given Kudos: 32
Location: United States
GMAT 1: 770 Q50 V44
GPA: 3.97
Re: If n is an integer, is n + 1 a prime number? [#permalink]
Bunuel wrote:

Tough and Tricky questions: Number Properties.

If n is an integer, is n + 1 a prime number?

(1) n is a prime number.
(2) n + 2 is not a prime number.

Kudos for a correct solution.

Source: Chili Hot GMAT

Individually both can be shown to be insufficient by taking test cases.
1) n=2, n=7--> different outcomes. NOT SUFFICIENT
2) n=2, n=3 --> different outcomes, NOT SUFFICIENT.

If combined, then again n=2, n=7 give different outcomes. NOT SUFFICIENT.

Senior Manager
Joined: 23 Jan 2013
Posts: 424
Own Kudos [?]: 268 [0]
Given Kudos: 43
Schools: Cambridge'16
If n is an integer, is n + 1 a prime number? [#permalink]
Scenario chart is best but time consuming

St1. n (prime)--------n+1
--------2----------------Y
--------3----------------N
--------5----------------N

INSUFF

St.2. n+2 (not prime)---------n+1
----------4------------------------Y
----------6------------------------Y
----------8------------------------Y
----------9------------------------N

INSUFF

St.1+St.2
-----n (prime)-------n+2 (not prime)-------n+1
--------2-----------------4----------------------Y
--------7-----------------9----------------------N

INSUFF

E
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4915
Own Kudos [?]: 7817 [0]
Given Kudos: 221
Location: India
Re: If n is an integer, is n + 1 a prime number? [#permalink]
Hi,
This is a tricky question. Few may pick C as the answer. But its not.
Statement 1 not sufficient:
If n =2, 2 is a prime no. and answer to the question is YES.
If n= 3, 3 is a prime no. and answer to the question is NO.
Statement 2 not sufficient:
If n =2, n+2 is not a prime no. but answer to the question is YES.
If n= 13, n+2 is not a prime no. But answer to the question is NO.
Together not sufficient (We can use the same examples):
If n =2, 2 is a prime no., n+2 is not a prime no and answer to the question is YES.
If n= 13, 13 is a prime no., n+2 is not a prime no. But answer to the question is NO.
Together not sufficient.
So answer is E.
Board of Directors
Joined: 17 Jul 2014
Posts: 2145
Own Kudos [?]: 1192 [0]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Re: If n is an integer, is n + 1 a prime number? [#permalink]
Bunuel wrote:

Tough and Tricky questions: Number Properties.

If n is an integer, is n + 1 a prime number?

(1) n is a prime number.
(2) n + 2 is not a prime number.

Kudos for a correct solution.

Source: Chili Hot GMAT

i tried to plug in values and see if it works:
1. n=2. n+1=3 yes prime number; n=3, n+1=4 - not prime number - A and D out
2. n=2, 2+2 = 4, not prime, 2+1 = 3, prime number. n=7. n+2=9 - not prime. n+1=8, not prime so B is out.

1+2
n=2 => n+1 = 3 - yes
n=7 => n+1 = 8 - no

C is out

Alum
Joined: 12 Aug 2015
Posts: 2270
Own Kudos [?]: 3199 [0]
Given Kudos: 893
GRE 1: Q169 V154
Re: If n is an integer, is n + 1 a prime number? [#permalink]
Great Question
Here is what i did =>
We need to check if n+1 is prime or not
Statement 1
n=2 => yes
n=3=> no
Hence Not sufficient

Statement 2
n=2=> yes
n=3=> no
Hence insufficient

Combing the two statements
n=2 => yes
n=7=> no
Hence E
Non-Human User
Joined: 09 Sep 2013
Posts: 34061
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: If n is an integer, is n + 1 a prime number? [#permalink]
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 n is an integer, is n + 1 a prime number? [#permalink]
Moderator:
Math Expert
94605 posts