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.
What is the remainder when x is divided by 3?
(1) The sum of the digits of x is 5
(2) When x is divided by 9, the remainder is 2
In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation for 2) 1 equation, which is likely to make D the answer.
In case of 1), the remainder derived by dividing some number by 3 is as same as the remainder derived by dividing sum of all digits by 3. In 5=3*1+2, the remainder is 2, which is unique and sufficient.
For 2), in x=9p+2=3(3q)+2, the remainder derived by dividing with 3 is 2, which is unique and sufficient.
Therefore, the answer is D.
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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