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.


1. If the sum of three different numbers is 54, what is the largest number?
(1) The largest number is twice the smallest number
(2) The sum of the two smaller numbers is 30

-> When you modify the original condition and the question, based on a<b<c, you only need to know a+b from a+b+c=54, c=54-(a+b). Since 2) a+b=30, c=54-30=24, which is unique and sufficient. Therefore the answer is B.

2. What is the remainder when the positive integer n is divided by 6?
(1) n is a multiple of 5
(2) n is a mulitple of 12

-> In the original condition, there is 1 variable(n), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. 1) n=5, r=5/ n=30, r=0, which is not unique and therefore not sufficient.
In 2), n=12,24,36..... and all r=0 is unique and sufficient. Therefore the answer is B.

3. If p is a positive integer, what is the value of p?
(1) p/4 is a prime number
(2) p is divisble by three

In the original condition, there is 1 variable(n), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. For 1), p=8, 12 is not unique and not sufficient. For 2), p=3, 12 is not unique and not sufficient. In 1) & 2), only p=12 is possible, which is unique and sufficient. Therefore the answer is B.