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.
Ann bought five different kinds of fruit: apples, oranges, pears, mangoes, and bananas. If the number of apples that Ann bought was twice the number of oranges and if the number of pears that Ann bought was the same as the number of apples and oranges combined, what fraction of the total number of pieces of fruit that Ann bought were pears?
(1) Ann bought a total of 18 pieces of fruit.
(2) Ann bought 5 bananas.
We have 5 variables (a,o,p,m,b) and 2 equations (a=2o, p=a+o) in the original condition, but only 2 equations are given by the conditions, so there is high chance (E) will be the answer.
Looking at the conditions together, a+o+p+m+b=18, b=5, but a=2o, p=a+o=3o still does not give the number of p, so is insufficient, making the answer (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.
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