The restorative power of sleep is graphically approximated by the func

Question

The restorative power of sleep is graphically approximated by the function −x^2 + 16x + 36, where the x-axis measures sleeping hours and the y-axis measures the restoration value. After how many hours does sleep no longer perform restorative duties according to the function?

A. −2
B. 4
C. 8
D. 13
E. 18

A. −2
B. 4
C. 8
D. 13
E. 18

KarishmaB · Accepted Answer

The restorative power is given by  -x^2 + 16x + 36 .

We want the value of x (number of hours) for which it will become 0.

-x^2 + 16x + 36 = 0
x = 18, -2

After 18 hours, the graph will be negative so there will be no positive restoration value. 
Answer (E)

jagp20 · Answer

The restorative power is given by the equation -x^{2}+16x+36, which is equal to x^2-16x-36. We are told that the restoration value is in the y-axis, and we want to find out after how much sleep we would not get any restoration for our sleep.
So if y becomes 0, we have x^2-16x-36=0.
or
(x-18)(x+2)=0
Which means that x=18 or x=-2
Since we are counting hours of sleep, the answer cannot be negative, thus x=18 and the answer is E.

Nunuboy1994 · Answer

This question is simple yet has a very subtle trap answer- in order to find the values of x we must factor the equation- if you simply plug in values and solve for 0 you would also find that -2 and 18 equal 0. However, theoretically, you cannot have a negative amount of sleep therefore the answer is simply 18. This is just a matter of reading the question

Thus
 "E"

adyoy93 · Answer

The quadratic function here opens downwards. After the maxima point the effect of sleep is negative. I think point of maxima is the correct answer. As the question asks when does the restorative duties end and not when does the effect of sleep becomes zero.

AOBang · Answer

Every equation can be represented as a graph on X-Y coordinate plot.
For this problem we do not actually need to plot a graph, but having understanding of where a graph lies on coordinate system help in better understanding.
So before reading the explanation I would suggest to google some simple graph of  x^2 ,  -x^2 ,  x^2 +1 , and  x^2 +x+1 etc
(You can also copy paste same equation on Google ; see attached graph)

Now from figure i.e. understanding of equation, this is an equation of downwards open parabola. As its parabola it  can  cut x-axis at two point
When it cuts x-axis its y coordinate will be 0.
So putting value in Y=0
0 = - x^2  + 16x + 36
x = -2 or 18

After both this point 'restorative power' i.e. Y coordinate gets negative. So -2 or 18 is Ans
But Sleep hours practically could not be -2. So correct ans is 18
 Option E

To encourage please hit 'Kudos' !!

Fdambro294 · Answer

Wow, this question got me. Too Late.

Concept: Since the A Coefficient in front of (x)^2 is a (-)Negative Value, the Parabola will Open DOWNWARDS and the Vertex, which occurs at the TOP of the Parabola, will be the Maximum Y Value of the restoration you can get.

The Axis of Symmetry/Vertical X-Line that creates a Mirror Image can be found by finding the X-Coordinate:

X = - (b / 2a) = - (16 / 2(-1) = +8

At X = +8 hours of Sleep you can get the MAXIMUM Y Value of restorative value (actually makes sense from a logical perspective).

However, when the Parabola crosses the X-Axis and starts to head down into Quadrant IV, the Restorative Power will no longer kick in.

The amount of hours, after which, the Y-Value starts to become (-)Negative is given by the (+)Positive X-Intercept of the Parabola.

This can be found by setting the Y-Value = 0 and finding the X-Intercepts.

-(x^2) + 16x + 36 = 0

x^2 - 16x - 36 = 0

(x - 18) (x + 2) = 0

At the (+)Positive X-Intercept of X = 18 hours, the Y Value will STOP Existing (y will = 0) and the Restorative powers of sleep will no longer work.

-Answer E-

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

The restorative power of sleep is graphically approximated by the func

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

The restorative power of sleep is graphically approximated by the func

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards