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prernamalhotra: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Wed Apr 02, 2014 2:01 amFollowed by: 1 member; Thanked: 2 times

by prernamalhotra » Sat May 03, 2014 1:49 am

An object thrown directly upward at a height of h feet after t seconds, where h=-16(t-3)^2+150. At what height, in feet, is the object 2 seconds after it reaches maximum height?

A)6
B) 86
C) 134
D) 150
E) 166

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Source: Beat The GMAT — Problem Solving | Sat May 03, 2014 1:49 am

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by GMATGuruNY » Sat May 03, 2014 2:09 am

An object thrown directly upward is at a height of h feet after t seconds, where h = -16 (t - 3)^2 +150. At what height, in feet, is the object 2 seconds after it reaches its maximum height?
A. 6
B. 86
C. 134
D 150
E. 214

Equation, rephrased:
h = 150 - 16(t-3)Â².

To MAXIMIZE the value of h, we need to MINIMIZE the value SUBTRACTED from 150: 16(t-3)Â².
Since (t-3)Â² cannot be negative, the smallest possible value of 16(t-3)Â² is 0.
16(t-3)Â² = 0 when t=3.
Thus, the maximum height occurs when t=3.

Two seconds later, t=5.
When t=5, h = 150 - 16(5-3)Â² = 150-64 = 86.

The correct answer is B.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat May 03, 2014 7:33 am

prernamalhotra wrote:An object thrown directly upward at a height of h feet after t seconds, where h = -16(t-3)Â² + 150. At what height, in feet, is the object 2 seconds after it reaches maximum height?

A)6
B) 86
C) 134
D) 150
E) 166

This is a great example of how GMAT questions often exploit our experience with similar questions. In the real world, a question of this nature would concern the MAXIMUM height that the object reaches. In fact, most students have probably solved tons of questions in which they were required to find the maximum height of some object. The GMAT uses this experience against us and asks for the height 2 seconds after the maximum height is reached. Tricky!

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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