If n is an integer, is n + 4 a prime number?

Question

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

Is there a better method to solve this question than picking numbers?

Source: gmathacks.com

ksp · Answer

Prime numbers > 6 are of the form 6n+1 or 6n-1 with multiples of 5 avoided in between. Just one of the rules that i know regd the prime numbers. 
I guess this question is targeted at this rule.

Difference between consecutive 6n+1 and 6n-1 is 4.

Hope it helps

kostyan5 · Answer

This question is simple enough that plugging numbers will be quickest. Especially if it can be disproved.

Sam1 · Answer

Is B the answer?
As 2 is the only even prime number and if n+2= not a prime number then n cant be two with any other prime number n+4 will be prime

Bunuel · Answer

The answer is E. You can check the OA under the spoiler in the original post.

Consider n=2 for a NO answer and n=7 for an YES answer.

Hope it helps.

Sam1 · Answer

Thanks Bunuel. This is very helpful

jlgdr · Answer

Hi Ksp

Although I'm quite familiar with this rule, I don't know how it can be applied to this problem. Could you please elaborate a little bit more on this?

Thanks
Cheers
J

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If n is an integer, is n + 4 a prime number?

(1) n is a prime number.
(2) n + 2 is not a prime number. 
 
There is one variable (n) and 2 equations are given by the conditions, so there is high chance that (D) will become the answer.
For condition 1, the answer to the question becomes 'no' for n=2, but 'yes' for n=7, so this is insufficient
For condition 2, the answer to the question becomes 'no' for n=2, but 'yes' for n=7, so this is insufficient as well.
Looking at the conditions together, the answer to the question becomes 'no' for n=2, but 'yes' for n=7, so this is insufficient, and the answer becomes (E).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

If n is an integer, is n + 4 a prime number?

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GMAT Data Sufficiency (DS) Questions

If n is an integer, is n + 4 a prime number?

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