Is n divisible by 60? (I) n is divisible by 15. (II) n is divisible 20

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
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The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

We can compare divisors of the questions and both conditions.
The divisor of the question is 60.

The divisor of condition 1) is 15, which is not multiple of 60.
Condition 1) is not sufficient.

The divisor of condition 2) is 20, which is not multiple of 60.
Condition 2) is not sufficient.

The lcm of two divisors of both conditions is lcm(15,20) = 60, which is a multiple of the divisor of the question.
Then both conditions together are sufficient.

Therefore, C is the answer.