Source: Official Guide for GMAT Review 2016 Problem Solving; #97

1

According to a certain estimate, the depth N( t)

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?

1 Explanation

1

Diego Scharifker

I find this answer given by the OG to be wrong, but I must be missing out on something.
I tried with t=9 and got that N(t)=180 which obviously is a positive, not a negative as the explanation states.

Any ideas?

When t = 5, the value of 20(t 5)2 + 500 is 500. For all values of t between 0 and 10, inclusive, except t = 5, the value of 20(t 5)2 is negative and 20(t 5)2 + 500 < 500. Therefore, the tank reaches its maximum depth 5 hours after 2:00 in the morning, which is 7:00 in the morning.

Nov 12, 2017 • Comment

Adam

Hi Diego,

The explanation states that for all values of t other than 5, the part "-20(t - 5)^2" is negative, not that the depth of the water "N(t)" is negative.

You (correctly) found N(9) = 180. The explanation is saying that when we plug 9 in, we get a negative value for the -20(9 - 5)^2 portion.

Nov 21, 2017 • Reply

Add Your Explanation

You must have a Magoosh account in order to leave an explanation.

Learn More About Magoosh

Official GMAT Material

Official Guide for GMAT Review 2016

Official Guide for the GMAT 2015 14th Ed.

Official Guide for the GMAT 13th Ed.

Nova's GRE Prep

Official Guide for the GMAT 12th Ed.

Revised GRE PDF 2nd Ed.


Section 5.3 Problem Solving

Improve Your Score

Magoosh GMAT is an affordable online course for studying the GMAT.

Learn More About Magoosh

Share Post

Email

Facebook