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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6526
GMAT 1: 760 Q51 V42
GPA: 3.82
After t seconds, the height of a ball from the ground is given by the  [#permalink]

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26 Jul 2018, 23:51
00:00

Difficulty:

55% (hard)

Question Stats:

40% (00:56) correct 60% (01:25) wrong based on 57 sessions

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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) $$g = 10$$

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" MBA Section Director Affiliations: GMATClub Joined: 22 May 2017 Posts: 1005 Concentration: Nonprofit GPA: 4 WE: Engineering (Computer Software) After t seconds, the height of a ball from the ground is given by the [#permalink] ### Show Tags 27 Jul 2018, 01:38 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 _________________ Senior Manager Joined: 04 Aug 2010 Posts: 307 Schools: Dartmouth College Re: After t seconds, the height of a ball from the ground is given by the [#permalink] ### Show Tags 27 Jul 2018, 03:51 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. _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6526 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: After t seconds, the height of a ball from the ground is given by the [#permalink] ### Show Tags 29 Jul 2018, 17:32 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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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, 17:32
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