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

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According to a certain estimate, the depth N(t) [#permalink]  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) [#permalink]  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) [#permalink]  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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100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

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Re: According to a certain estimate, the depth N(t) [#permalink]  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) [#permalink]  24 Jan 2012, 00:35
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Expert's post
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) [#permalink]  24 Jan 2012, 01:45
Expert's post
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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Re: According to a certain estimate, the depth N(t) [#permalink]  28 Jan 2012, 02:48
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Re: According to a certain estimate, the depth N(t) [#permalink]  29 Sep 2013, 05:22
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Re: According to a certain estimate, the depth N(t)   [#permalink] 29 Sep 2013, 05:22
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