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# According to a certain estimate, the depth N(t), in centimeters, of

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According to a certain estimate, the depth N(t), in centimeters, of [#permalink]

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23 Jan 2012, 21:37
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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
[Reveal] Spoiler: OA

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Re: According to a certain estimate, the depth N(t), in centimeters, of [#permalink]

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23 Jan 2012, 21:44
the expression is N(t)= -20(t-5)^²+500
(of course valid after 2:00 in the morning)

"the depth would be maximum" means the value of the above expression should be maximum
or the value of square term (which has a negative 20 attached to it) should be minimum i.e. zero

the square part is zero at t=5

so the time at which the depth is maximum is 2:00 + 5 hrs= 7:00 (B)
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Re: According to a certain estimate, the depth N(t), in centimeters, of [#permalink]

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23 Jan 2012, 21:52
puneetkr wrote:
the expression is N(t)= -20(t-5)^²+500
(of course valid after 2:00 in the morning)

"the depth would be maximum" means the value of the above expression should be maximum
or the value of square term (which has a negative 20 attached to it) should be minimum i.e. zero

the square part is zero at t=5

so the time at which the depth is maximum is 2:00 + 5 hrs= 7:00 (B)

if -20(t-5)^²=0
then t = 5
But Why is the 500 of the equation is not considered? Show your complete calculation.
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Re: According to a certain estimate, the depth N(t), in centimeters, of [#permalink]

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23 Jan 2012, 22:01
this is the complete calculation

N(t)= -20(t-5)^²+500
now for any value of t we put in; we get some negative value of -20(t-5)^² (say -x)
so our expression is now N(t)=500-x

this expression would have maximum value only when x is minimum
we know the minimum value for a square term is "zero" and (x has a square term)
and that comes when t=5
i.e. when we put t=5 here we get N(t) = 500-0 = 500
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Re: According to a certain estimate, the depth N(t), in centimeters, of [#permalink]

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24 Jan 2012, 00:35
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Baten80 wrote:
puneetkr wrote:
the expression is N(t)= -20(t-5)^²+500
(of course valid after 2:00 in the morning)

"the depth would be maximum" means the value of the above expression should be maximum
or the value of square term (which has a negative 20 attached to it) should be minimum i.e. zero

the square part is zero at t=5

so the time at which the depth is maximum is 2:00 + 5 hrs= 7:00 (B)

if -20(t-5)^²=0
then t = 5
But Why is the 500 of the equation is not considered? Show your complete calculation.

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

Consider this: $$-20(t-5)^2\leq{0}$$ hence $$500-20(t-5)^2$$ reaches its maximum when $$-20(t-5)^2=0$$, thus when $$t=5$$. 2:00AM+5 hours=7:00AM.

Hope it helps.
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Re: According to a certain estimate, the depth N(t), in centimeters, of [#permalink]

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24 Jan 2012, 01:45
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Baten80 wrote:
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

Don't get bogged down by the dirty N(t) expression. Just think of it this way:

N(t) is a combination of two terms: a positive term (500) and a negative term ($$-20(t-5)^2$$).
To maximize N(t), I need to make the positive term as large as possible (It is a constant here so I cannot do much with it) and the absolute value of the negative term as small as possible. The smallest absolute value is 0. Can I make it 0? Yes, if I make t = 5, the negative term becomes 0 and N(t) is maximized. My answer must be 2:00 + 5 hrs i.e. 7:00.

Most of the maximum minimum questions on GMAT will require you to only think logically. The calculations involved will be minimum.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Director Status: No dream is too large, no dreamer is too small Joined: 14 Jul 2010 Posts: 651 Followers: 42 Kudos [?]: 860 [0], given: 39 Re: According to a certain estimate, the depth N(t), in centimeters, of [#permalink] ### Show Tags 28 Jan 2012, 02:48 GMAT Club Legend Joined: 09 Sep 2013 Posts: 13441 Followers: 575 Kudos [?]: 163 [0], given: 0 Re: According to a certain estimate, the depth N(t), in centimeters, of [#permalink] ### Show Tags 29 Sep 2013, 05:22 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 13441 Followers: 575 Kudos [?]: 163 [0], given: 0 Re: According to a certain estimate, the depth N(t), in centimeters, of [#permalink] ### Show Tags 04 Nov 2015, 15:49 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Intern Joined: 07 Dec 2012 Posts: 10 Followers: 0 Kudos [?]: 0 [0], given: 97 Re: According to a certain estimate, the depth N(t), in centimeters, of [#permalink] ### Show Tags 27 Nov 2015, 21:58 Can someone please explain why A is not the answer? Because if I plug in t = 3.5 (which is 5.30 (3.5 after the 2:00) , it gives me the maximum value of -20(t-5)^2 expression, which will be positive. Hence, the height will be at its max of 545. Hence, shouldn't the answer be A? Please explain the reasoning. Thank you Math Expert Joined: 02 Sep 2009 Posts: 36549 Followers: 7078 Kudos [?]: 93146 [0], given: 10553 Re: According to a certain estimate, the depth N(t), in centimeters, of [#permalink] ### Show Tags 28 Nov 2015, 07:33 herein wrote: Can someone please explain why A is not the answer? Because if I plug in t = 3.5 (which is 5.30 (3.5 after the 2:00) , it gives me the maximum value of -20(t-5)^2 expression, which will be positive. Hence, the height will be at its max of 545. Hence, shouldn't the answer be A? Please explain the reasoning. Thank you Please read the solutions above. Also, if t = 3.5, then 500 - 20(3.5 - 5)^2 = 455, not 545. _________________ Math Forum Moderator Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 2301 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Followers: 92 Kudos [?]: 633 [1] , given: 317 Re: According to a certain estimate, the depth N(t), in centimeters, of [#permalink] ### Show Tags 28 Nov 2015, 08:25 1 This post received KUDOS Baten80 wrote: 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?0 N(t)= $$-20(t - 5)^2$$ + 500 ; The red highlighted portion of the equation is the most critical part, further t = 2am + time past 2am Now why $$-20(t - 5)^2$$ is important ; Any value of t less than 5 will result in a negative value of $$-20(t - 5)^2$$ Lets check : Time : 3am , t = 1 { t = 2am + time past 2am } $$-20(t - 5)^2$$ $$-20(1 - 5)^2$$ $$-20(-4)^2$$ $$-20(16)$$ $$-320$$ When put in the final equation : $$-20(t - 5)^2$$ the result will be -320 + 500 => 180 Check a few more any value of t less than 5 will result in -ve value of $$-20(t - 5)^2$$ and will ultimately lead to a depth of water less than 500. Our target is getting t = 5 ; since at t = 5 $$-20(t - 5)^2$$ will be 0 and the final equation $$-20(t - 5)^2$$ + 500 will be maximum ; ie 500 We already know t = 2am + time past 2am So, 7 = 2am + 5 hours. Answer is definitely (B) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8287 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 380 Kudos [?]: 2459 [1] , given: 163 Re: According to a certain estimate, the depth N(t), in centimeters, of [#permalink] ### Show Tags 28 Nov 2015, 15:07 1 This post received KUDOS Expert's post Hi All, 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: [Reveal] Spoiler: B GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: According to a certain estimate, the depth N(t), in centimeters, of   [#permalink] 28 Nov 2015, 15:07
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