Data Sufficiency

[Math Revolution GMAT math practice question]

After t seconds, the height of a ball from the ground is given by the equation h =-9.8t^2+ft+g (f and g are constants). If the ball is at its maximum height, then t=?

1) f = 10
2) g = 10

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

After t seconds, the height of a ball from the ground is given by the equation h =-9.8t^2+ft+g (f and g are constants). If the ball is at its maximum height, then t=?

1) f = 10
2) g = 10

f(x) = ax² + bx + c is the equation of a parabola.
If a<0, then the parabola opens DOWNWARD, with a maximum value when:
$$x\ =\ \frac{-b}{2a}$$

Given quadratic:
h = -9.8t² + ft + g.
Here, the maximum height will be yielded when:
$$t\ =\ \frac{-f}{\left(2\right)\left(-9.8\right)}$$

Thus, to determine what value of t will yield the maximum height, we need to know the value of f.

Statement 1: f=10
SUFFICIENT.

Statement 2: g=10
No information about f.
INSUFFICIENT.

The correct answer is A.

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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.

Y = aX^2 + bX + c has a maximum or a minimum when X = -b/2a.
Thus h =-9.8t^2+ft+g has a maximum when t = f/(2*9.8).
Condition 1) is sufficient on its own.

Condition 2) is not sufficient since it gives us no information about the value of f.

Therefore, A is the answer.
Answer: A