WoundedTiger wrote:

A sports team played 100 games last season. Did this team win at least half of the games it played last season?

(1) The team won 60% of its first 65 games last season.

(2) The team won 60% of its last 65 games last season.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Assume a, b, c and d are numbers of games the team won from the first 35 games, the next 15 games, the next 15 games and the last 35 games, respectively.

The question asks if a + b + c + d ≥ 50.

Since we have 4 variables and 0 equations, E is most likely to be the answer. So, we should consider 1) & 2) first, since we can save time by first checking whether conditions 1) and 2) are sufficient, when taken together.

Conditions 1) & 2)

a + b + c = 38 ( = 65 * 0.6)

b + c + d = 38 ( = 65 * 0.6)

a = 37, b + c = 1, d = 37 ⇒ a + b + c + d = 75 : Yes

a = 8, b + c = 30, d = 8 ⇒ a + b + c + d = 46 : No

Both conditions together are not sufficient.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

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