Data Sufficiency

[GMAT math practice question]

What is the area of a right triangle?

1) The length of one side is 3
2) The length of one side is 4

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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.

Since questions about triangles involve three variables, E is most likely to be the answer.

Conditions 1) & 2)
If the sides given are legs, then the area of the right triangle is (1/2)*3*4 = 6.
If one leg has length 3 and the hypotenuse has length 4, then, by Pythagoras' theorem, the length of the other leg is √(4^2 - 3^2) = √7, and the area of the triangle is (1/2)*3*√7 =(3√7)/2.
Thus, both conditions together are not sufficient, since they do not yield a unique solution.

Therefore, E is the answer.
Answer: E

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.