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 Machine X can produce 80 widgets in 4 hours, how long would it take machine X and Y working together, to produce 500 widgets?

(1) Machine Y works at 3/4 the speed of machine X

(2) If Machine Y's speed doubled, it would produce 120 widgets in 4 hours

In the original condition, it gives power of X and 500 widgets. So you need to figure out power of Y, which makes 1 variable. In order to match with the number of equations, you need 1 equation. However, for 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.

For 1), power of Y=power of (3/4)X=(3/4)(80widgets/4hrs)=15widgets/1hr, which is unique and sufficient.

For 2), power of 2Y=120widgets/4hrs. Then, power of Y is 13widgets/1hr, 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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