Is r*s a multiple of 25? (r and s are positive integers)

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.

Is rs a multiple of 25? (r and s are positive integers)

(1) r - s is a multiple of 5
(2) rs is a multiple of 5

In the original condition, there are 2 variables(r,s), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), rs=5's multiple becomes r=5's multiple. Then r-s=5's multiple becomes s=5's multiple. rs=5's multiple becomes multiple of rs=5*multiple of 5=multiple of 25, which is yes. Also, when it is multiple of s=5, r=5's multiple is derived from r-s=5's multiple. Then multiple of rs=5*multiple of 5=multiple of 25, which is yes and the answer is C. You cannot calculate them separately.



->For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.