If a + b = 20, then what is the value of c − d?

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.

If a + b = 20, then what is the value of c − d?

(1) ac − bd + bc − ad = 60
(2) d = 4


In the original condition, there are 4 variables(a,b,c,d) and 1 equation(a+b=20), which should match with the number of equations. So you need 3 more equation. For 1) 1 equation, for 2) 1 equation and you need 1 more equation, which is likely to make E the answer. In 1) & 2), it is ac-bd+bc-ad=60, (a+b)(c-d)=60, 20(c-4)=60, which is not unique and therefore not sufficient. So, the answer is E.


-> For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% 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 E 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, C or D.