Max@Math Revolution wrote:[GMAT math practice question]

In the x-y plane, y = f(x) = ax^2+bx+c passes through (1,0) and (2,0). Is f(3)>0?

1) a > 0
2) f(0) > 0

f(x) = ax²+bx+c will be a U-shaped parabola if a>0.
f(x) = ax²+bx+c will be a ∩-shaped parabola if a<0.

Since f(x) = ax²+bx+c has x-intercepts at (1, 0) and (2, 0), f(3)>0 if the parabola is U-shaped.
Question stem, rephrased:
Is the parabola U-shaped?

Statement 1:
Since a>0, the parabola is U-shaped.
SUFFICIENT.

Statement 2:
x=0 is to the LEFT of the x-intercept at (1, 0).
Since x=0 yields a POSITIVE y-value, the parabola must be U-shaped.
SUFFICIENT.

The correct answer is D.

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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. We then recheck the question.

Since f(x) passes through (1,0) and (2,0), 1 and 2 are roots of f(x) and we have f(x) = a(x-1)(x-2). If f(x) is concave up, then f(3) > 0. Thus, knowing that f(x) is concave up will allow us to answer the question. In addition, since we have 3 variables (a, b, c) and 2 conditions, D is most likely to be the answer.

Condition 1)
If a > 0, then f(x) is concave up.
Thus, condition 1) is sufficient.

Condition 2)
Since 1 and 2 are roots of f(x) = 0, f(0) > 0 implies that f(x) is concave up.
Thus, condition 2) is sufficient, too.

Therefore, D is the answer.

Answer: D

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).