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OG 2016 PS #97

This topic has 2 expert replies and 0 member replies
lfa713 Newbie | Next Rank: 10 Posts Default Avatar
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01 Jan 2016
Posted:
4 messages

OG 2016 PS #97

Post Fri Feb 05, 2016 1:26 pm
According to a certain estimate, the depth N(t), in cm, of water in a tank at t hours past 2 a.m. is given by N(t)=-20(t-5)^2+500 for all t from 0 to 10 hours, inclusive. According to this estimate, at what time does the tank's depth reach its maximum?

A) 5:30
B) 7:00
C) 7:30
D) 8:00
E) 9:00

My dilemma:

1) I understand that the equation is meant to equal the maximum depth at a certain value of t. How does one test values of t from 0 to 10 in less than 2 minutes?? Is there a quicker way to solve this?

2) If the answer to 1) is "when t-5=0" then how does one conclude that 500 is the target depth? For example, why could it not be 420 when t=7?

3)Is there something inherent in these types of questions that signals a given term in the formula (in this case, the +500) is the target value, even when the question doesn't specifically say so?

-L

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GMAT/MBA Expert

Post Fri Feb 05, 2016 10:19 pm
Hi lfa713,

These specific types of "limit" questions are relatively rare on Test Day, although you'll likely be tested on the concept at least once. Whenever you're asked to minimize or maximize a value, you should look to do something with the other "pieces" of the equation (usually involving maximizing or minimizing those pieces).

In the given equation, notice how you have two "parts": the -20(something) and a +500. Here, to MAXIMIZE the value of N(t), we have to minimize the "impact" that the -20(something) has on the +500. By making that first part equal 0, we'll be left with 0 + 500. Mathematically, we have to make whatever is inside the parentheses equal 0....

(T-5) = 0

T = 5

Since T represents the number of hours past 2:00am, we know that at 7:00am, the water will reach 500cm (the maximum value).

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

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GMAT/MBA Expert

Post Fri Feb 05, 2016 1:31 pm
Quote:
According to a certain estimate, the depth N(t), in centimeters, of the water in a certain tank at t hours past 2:00 in the morning is given by N(t)= -20(t-5)²+500 for 0≤t≤10. According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum?

a) 5:30 b) 7:00 c) 7:30 d) 8:00 e)9:00
Depth = 500 - 20(t-5)².

To MAXIMIZE the depth, we must MINIMIZE the value in red.
Since the square of a value cannot be negative, (t-5)² ≥ 0.
Thus, the value in red will be minimized when (t-5)² = 0.
Since (t-5)² = 0 when t=5, the depth will be at its maximum 5 hours after 2am:
2am + 5 hours = 7am.

The correct answer is B.

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