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

The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.

Since 38 has a remainder 1 when it is divided by 4, the question asks if 3n has a remainder 3 if it is divided by 4.

3^1 = 3 has the remainder 3, when it is divided by 4.

3^2 = 9 has the remainder 1, when it is divided by 4.

3^3 = 27 has the remainder 3, when it is divided by 4.

3^4 = 81 has the remainder 1, when it is divided by 4.

...

Thus, the question asks if n is an odd number.

Condition 1)

Since n is a multiple of 3, it is unknown if n is odd or even.

This is not sufficient.

Condition 2)

“3^2 +3^n+2 is divisible by 4” means 3^n+2 has a remainder of 3 when divided by 4.

It means n + 2 and n are odd integers.

Thus, this condition is sufficient.

Therefore, the answer is B.

Answer: B

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