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After t seconds, the height of a ball from the ground is given by the

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New post 27 Jul 2018, 00:51
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[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) \(g = 10\)

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After t seconds, the height of a ball from the ground is given by the  [#permalink]

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New post 27 Jul 2018, 02:38
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MathRevolution 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) \(g = 10\)



I solved this using some basic calculus

We need to find the value of t for which the equation \(h =-9.8t^2+ft+g\) is maximum

=> The value of t for which the derivative of the equation is zero

Also note the derivative of a pure constant is 0

=> The derivative doesn't involve "g" and involves only "t" and "f"

From statement 1, we have the value of f which is sufficient

We don't need the value of "g" and statement 2 doesn't tell the value of f

Hence option A
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Re: After t seconds, the height of a ball from the ground is given by the  [#permalink]

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New post 27 Jul 2018, 04:51
1
MathRevolution 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) \(g = 10\)


\(f(x) = ax^2 + bx + c\) 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:
\(h = -9.8t^2 + ft + g\)
Here, the maximum height will be yielded when:
\(t = \frac{-f}{(2 * -9.8)}\)

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.


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Re: After t seconds, the height of a ball from the ground is given by the  [#permalink]

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New post 29 Jul 2018, 18:32
=>

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 \(X = \frac{-b}{2a}.\)
Thus \(h =-9.8t^2+ft+g\) has a maximum when \(t = \frac{f}{(2*9.8)}\).
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
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Re: After t seconds, the height of a ball from the ground is given by the &nbs [#permalink] 29 Jul 2018, 18:32
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