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.

Two persons A and B run at constant speeds of a miles per hour and b miles per hour respectively. They start running toward each other at the same time from a distance of d miles. What is the speed of A and B?

(1) If A and B ran at speeds of a/2 and 2b respectively, they would take the same amount of time to meet.

(2) If they both ran at 1 mile per hour slower, they would take double the time to meet.

When you modify the original condition and the question, they become at+bt=d.(t is a time until they meet) That is, there are 4 variables(a,b,t,d) and 1 equation((a+b)t=d), which should match with the number of equations. So you need 3 more equations. For 1) 1 equation, For 2) 1 equation, which is likely to make E the answer.

When 1 & 2), they make (a/2+b)t=d, (a+b-2)2t=d and a+b=2a+2b-4, a/2+b=a+2b -> a=2b -> b=4/3, a=8/3, which is unique and sufficient.

Thus, C is the answer.

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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