Data Sufficiency

[GMAT math practice question]

The lengths of two sides of a certain triangle are 3 and 9. What is the length of the 3rd side of the triangle?

1) The perimeter of the triangle is 20
2) The length of the 3rd side of the triangle is a multiple of 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.

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

Assume x is the length of the 3rd side of the triangle.
Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Note:
Since (using the triangle inequality) x > 9 + 3 = 12 and x < 9 - 3 = 6, we have 6 < x < 12.

Condition 1)
x + 3 + 9 = 20
Thus x = 8.
Condition 1) is sufficient.

Condition 2)
The only integer between 6 and 12 that is a multiple of 4 is 8.
Thus, x = 8.
Condition 2) is sufficient, too.

In addition, since conditions 1) and 2) are similar, D is most likely to be the answer.

Therefore, D is the answer.

Answer: D

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.