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Math Expert V
Joined: 02 Sep 2009
Posts: 58402
If n is an integer, is n + 2 a prime number? (1) n is a prime number.  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 77% (01:37) correct 23% (01:37) wrong based on 244 sessions

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If n is an integer, is n + 2 a prime number?

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

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Manager  G
Status: In last prep stage
Joined: 11 Jun 2017
Posts: 156
GMAT 1: 630 Q44 V33 GMAT 2: 680 Q47 V37 GPA: 3.2
Re: If n is an integer, is n + 2 a prime number? (1) n is a prime number.  [#permalink]

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1
Bunuel wrote:
If n is an integer, is n + 2 a prime number?

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

Used variable substitution,
suppose n=3,7
Stmt 1- When n=3 - n is prime ,n+2 is prime .Ans Yes
When n=7 ,n+ 2 is not prime .Ans No
since Yes and No insufficient

Stmt 2:When n=3 ,n+1 is not prime ,n+2 is prime Ans Yes
When n=7,n+1 is not prime ,n+2 is not prime Ans No

So since Yes and No insufficient

Ans E
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Re: If n is an integer, is n + 2 a prime number? (1) n is a prime number.  [#permalink]

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From statement 1:

n is a prime number. If n = 2. Then n+2 = 4. Not a prime. If n = 3. Then n+2 = 5. Prime. Hence insufficient.

From statement 2:

If n = 3. n+1 = 4. Not a prime. And n+2 = 5. Prime number.
If n = 8. n+1 = 9. Not a prime. And n+3 = 10. Not a prime.
Insufficient.

Combining both:
If n = 7. Then n+1 is not prime and n+2 = 9. Not a prime.
If n = 11. Then n+1 is not prime but n+2 = 13. Prime.
Hence insufficient.

E is the answer

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Re: If n is an integer, is n + 2 a prime number? (1) n is a prime number.  [#permalink]

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Bunuel wrote:
If n is an integer, is n + 2 a prime number?

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

Statement 1)

n = 2,3,5,7, 11 etc..

If 2+2 = 4 not a prime
If 3+2 = 5 prime

Insufficient.

Statement 2)

n+1 not a prime

Let n = 3
4 is not a prime (satisfying the statement)
3+2 = 5 a prime.

Try n = 7

7+2 = 9 not a prime. Insufficient.

Now combine (1) and (2)

n = 3 or 7 will give two different answers

Insufficient.

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If n is an integer, is n + 2 a prime number? (1) n is a prime number.  [#permalink]

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N = Integer, N + 2 = Prime?

St 1: N is prime
Case 1: Let N be 2 & 2+2=4 (Not prime)
Case 2: Let N be 3 & 3+2 =5 (Prime)
Insufficient

St 2: N + 1 = Not Prime
Case 1: Let N be 5, 5+1=6(NP) & 5+2 =7(P)
Case 2: Let N be 7, 7+1=8(NP) & 7+2=9(NP)

Insufficient

St 1 & St 2:
N is prime & N + 1 is not prime.
The cases in St 2(Highlighted in green) will prove the Statements 1 and 2 together prove insufficient.

Hence E is the answer
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Re: If n is an integer, is n +2 a prime number? (1) n is a prime  [#permalink]

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_________________ Re: If n is an integer, is n +2 a prime number? (1) n is a prime   [#permalink] 25 Jul 2019, 23:21
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