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.
A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?
(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.
(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.
Transforming the original condition and checking them gives us que y-r=?. Since there are 3 variables (r,y,b) we need 3 equations to match the number of variable and equations, and since we have 1 each in 1) and 2), there is high probability that E is the answer to the question.
Using both 1) & 2), b+y=13, r+b=7 gives us b=13-y and if we substitute it, r+13-y=7, y-r=6. Therefore the conditions are sufficient and the answer is C.
P.S: Solving the question using both 1) & 2) from the beginning saves us time.
Normally for cases where we need 2 more equation, such as original conditions with 2 variable, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. 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 according to DS definition, we solve the question assuming C would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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