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

Question

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

Bunuel · Accepted Answer

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

(1) n is a prime number --> if  n  is a prime, then  n+1  can be prime if and only  n=2=prime , then  n+1=3=prime  (in all other cases when  n=prime ,  n+1=prime+1=odd+1=even
eq{prime} ). But we don't know whether  n=2 . Not sufficient.

(2) n + 2 is not a prime number. Clearly not sufficient. If  n=2 , then answer is YES  but  if  n=7 , then answer is NO.

(1)+(2) If  n=2  (both statements satisfied), then answer is YES  but  if  n=7  (again both statements satisfied), then answer is NO. Not sufficient.

Answer: E.

alexn49 · Answer

(1) n is a prime number 
Example1: n = 2, so n+1 = 3, they are both prime (the only case by the way)
Example2: n=3, so n+1 = 4, n is prime, not n+1
INSUFFICIENT

(2) n+2 is not a prime number
Example1: n + 2 = 4, so n + 1 = 3, n + 1 is prime
Example2: n + 2 = 9, so n + 1 = 8, n + 1 is not prime
INSUFFICIENT

(1) and (2)
We want n prime so
Example1: n = 2, then n + 1 = 3 is prime and n + 2 = 4 is not prime
Example2: n = 7, then n + 1 = 8 is not not prime and n + 2 = 9 is not prime
INSUFFICIENT

So for me ANS: E.

Ankur9 · Answer

(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

intheend14 · Answer

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

amitshri15 · Answer

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.

kinghyts · Answer

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)

82vkgmat · Answer

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.

Answer = E.

Temurkhon · Answer

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

CrackverbalGMAT · Answer

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.

mvictor · Answer

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

answer is E.

stonecold · Answer

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

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

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