Is the positive integer N a prime number?

Statement 1: N could be 2, a prime no or it could be 4 a non prime no. Hence Insufficient

Statement 2: as N is integer and 73<N<79, there are no prime numbers in this range. The numbers in the mentioned range are 74,75,76,77 & 78 all are composite nos.
Hence N cannot be Prime. Sufficient

Option B

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.

There are 1 variable and 0 equation. Thus D could be the answer most likely.

Condition 1)
\(N = 2\) => Answer: Yes
\(N = 4\) => Answer: No
Thus this condition alone is not sufficient.

Condition 2)
\(N = 74, 75, 76, 77, 78\): No, since all of them are not prime numbers.
Thus this condition alnoe is sufficient, since "No" is also an answer, which is Common Mistake Type 1 of VA method.

Therefore, B is the answer unlike our expectation.


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.
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