Last visit was: 06 Sep 2026, 20:09 It is currently 06 Sep 2026, 20:09
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 06 Sep 2026
Posts: 113,167
Own Kudos:
839,601
 [23]
Given Kudos: 111,337
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,167
Kudos: 839,601
 [23]
The restorative power of sleep is graphically approximated by the func 30 Nov 2016, 03:04
1
Kudos
Add Kudos
22
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

62% (01:59) correct 38% (01:49) wrong based on 688 sessions

History

Date
Time
Result
Not Attempted Yet
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
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 05 Sep 2026
Posts: 16,645
Own Kudos:
81,206
 [6]
Given Kudos: 491
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,645
Kudos: 81,206
 [6]
The restorative power of sleep is graphically approximated by the func 30 Nov 2016, 04:50
5
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
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
Show more

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)
General Discussion
avatar
jagp20
avatar
Current Student
Joined: 01 Oct 2016
Last visit: 10 Jan 2024
Posts: 3
Own Kudos:
12
GMAT 1: 640 Q42 V35
GMAT 2: 700 Q48 V38
WE:Research (Mutual Funds and Brokerage)
Products:
My Reviews
GMAT 2: 700 Q48 V38
Posts: 3
Kudos: 12
The restorative power of sleep is graphically approximated by the func 30 Nov 2016, 07:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
Nunuboy1994
User avatar
Joined: 12 Nov 2016
Last visit: 24 Apr 2019
Posts: 554
Own Kudos:
129
 [1]
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
Posts: 554
Kudos: 129
 [1]
The restorative power of sleep is graphically approximated by the func 16 Jun 2017, 23:50
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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
Show more

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"
avatar
adyoy93
avatar
Joined: 25 Jul 2015
Last visit: 11 Jan 2026
Posts: 2
Own Kudos:
1
Given Kudos: 32
Posts: 2
Kudos: 1
The restorative power of sleep is graphically approximated by the func 13 Jul 2019, 03:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasKarishma
Bunuel
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

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)
Show more


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.
User avatar
AOBang
User avatar
Joined: 18 Jun 2019
Last visit: 11 Aug 2021
Posts: 11
Own Kudos:
85
 [3]
Given Kudos: 206
Location: Bangladesh
Concentration: Operations, International Business
Schools: ISB'22 IIMA PGPX'22 Mannheim
Schools: ISB'22 IIMA PGPX'22 Mannheim
Posts: 11
Kudos: 85
 [3]
The restorative power of sleep is graphically approximated by the func 15 Jul 2019, 09:59
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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' !!
Attachments

2019-07-15 21_55_28--x^2 + 16x + 36 - Google Search.jpg
2019-07-15 21_55_28--x^2 + 16x + 36 - Google Search.jpg [ 25.74 KiB | Viewed 6152 times ]

User avatar
Fdambro294
User avatar
Joined: 10 Jul 2019
Last visit: 27 Jun 2026
Posts: 1,324
Own Kudos:
787
Given Kudos: 1,656
Posts: 1,324
Kudos: 787
The restorative power of sleep is graphically approximated by the func 24 Sep 2020, 23:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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-
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,223
Own Kudos:
1,157
Posts: 39,223
Kudos: 1,157
The restorative power of sleep is graphically approximated by the func 06 Apr 2026, 22:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderator:
Bunuel
Math Expert
113167 posts