Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
18 Jun 2019, 06:38
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
58% (03:04) correct
42%
(03:09)
wrong
based on 73
sessions
History
Date
Time
Result
Not Attempted Yet
It takes 28 hours for John to paint four walls and the ceiling of a room of volume 800 cubic feet. The ceiling height of the room is 8 feet. If John paints at a constant rate of 0.25 square feet per minute, how long will it take him to paint the four walls?
A. 21 hours and 20 minutes
B. 21 hours and 40 minutes
C. 22 hours
D. 23 hours and 10 minutes
E. 24 hours
A. 21 hours and 20 minutes
B. 21 hours and 40 minutes
C. 22 hours
D. 23 hours and 10 minutes
E. 24 hours
20 Jun 2019, 04:15
Kudos
Bookmarks
This is an interesting question which combines the concepts of Rates (Time & Work) and Mensuration. At first sight, it might appear as though it’s a tad difficult, but, as you work your way through it, you will actually realize that it’s not all that difficult.
We do not have any information about the shape of the room. So is it something we have to worry about? Maybe not.
Whatever the shape of the room may be, the volume of a 3 dimensional object may always be obtained by multiplying the floor area (or ceiling area, since both are same) with the height of the room.
Note: A sphere is an exception to this rule.
Here, since the volume of the room is 800 cubic feet and the height of the room is 8 feet, we can conclude that the area of the floor (or the ceiling) = \(\frac{800}{8}\) = 100 square feet.
To paint 100 square feet, John will take \(\frac{100}{¼}\)= 400 minutes.
But, the question says that he took a total of 28 hours i.e. 1680 minutes to paint the ceiling and 4 walls. This means that he took 1280 minutes to paint the walls.
1280 minutes, when converted to hours, represents 21 hours and 20 minutes (\(\frac{1280}{60}\)). Therefore, the correct answer option is A.
In this question, you do not have to worry about the other two dimensions of the room, as long as you have the height and the volume.
But, at least when you start off, you may go in that direction for a brief period of time. As long as you are able to correct course and understand that you have ALL the data needed to find the answer, you’ll end up solving this question in about 2 minutes.
Hope this helps!
We do not have any information about the shape of the room. So is it something we have to worry about? Maybe not.
Whatever the shape of the room may be, the volume of a 3 dimensional object may always be obtained by multiplying the floor area (or ceiling area, since both are same) with the height of the room.
Note: A sphere is an exception to this rule.
Here, since the volume of the room is 800 cubic feet and the height of the room is 8 feet, we can conclude that the area of the floor (or the ceiling) = \(\frac{800}{8}\) = 100 square feet.
To paint 100 square feet, John will take \(\frac{100}{¼}\)= 400 minutes.
But, the question says that he took a total of 28 hours i.e. 1680 minutes to paint the ceiling and 4 walls. This means that he took 1280 minutes to paint the walls.
1280 minutes, when converted to hours, represents 21 hours and 20 minutes (\(\frac{1280}{60}\)). Therefore, the correct answer option is A.
In this question, you do not have to worry about the other two dimensions of the room, as long as you have the height and the volume.
But, at least when you start off, you may go in that direction for a brief period of time. As long as you are able to correct course and understand that you have ALL the data needed to find the answer, you’ll end up solving this question in about 2 minutes.
Hope this helps!
27 Sep 2020, 23:18
Kudos
Bookmarks
another one, you don't stop lol....
1st) When he paints the 4 Walls and Ceiling in 28 hours, he paints the following Surface Area of the Room:
L*H + W*H + L*H + W*H + (Ceiling of Dimensions L*W)
2nd) Since we are given the Volume = 800 and the Ceiling Height = 8, we can determine the Surface Area of the Ceiling = L*W
L*W*H = 800
L*W*8 = 800
L*W = 100 = Surface Area of Ceiling
3rd) Calculate his Constant Painting Rate based on what he finished in 28 hours
His Constant Work Rate = (1/4) ft/min
Work Rate = (Work Completed) / (Time Taken)
He Painted the 4 Walls and Ceiling in 28 hours (or 1,680 minutes):
Work Completed = L*H + W*H + L*H + W*H + Ceiling Area of 100
Work Completed = 8L + 8W + 8L + 8W + 100
Work Completed = 16 * (L +W) + 100
Time needed to Complete this Work = 1, 680 minutes
Now we can Set this Rate of Work EQUAL to the Given Rate of Work = (1/4) ft/min
1/4 = [ 16 * (L + W) + 100 ] / 1,680
---cross-multiplying---
1, 680 = 64 * (L + W) + 400
1,280 = 64 * (L + W)
L + W = 1, 280 / 64 ----- equation 1
The Question asks us how long it will take to Paint the JUST the 4 Walls and NOT the Ceiling:
Time = (Work) / (Rate)
The Surface Area WORK of the 4 Walls that needs to be completed = 8L + 8W + 8L + 8W = 16 * (L + W)
His Constant Rate of work is given by = (1/4) ft/min
Time in minutes = [ 16 * (L + W) ] / (1/4)
Substitute in --- equation 1 ---- (L + W) = 1, 280 / 64
Time in minutes = [ 16 * (1, 280 / 64) ] / (1/4)
---simplifying----
Time = (1, 280 * 4) / 4 = 1,280 minutes
Converting to Hours ---- 1,280 minutes / 60 minutes = 21 + (20/60)
or
21 hours and 20 minutes
Answer -A-
1st) When he paints the 4 Walls and Ceiling in 28 hours, he paints the following Surface Area of the Room:
L*H + W*H + L*H + W*H + (Ceiling of Dimensions L*W)
2nd) Since we are given the Volume = 800 and the Ceiling Height = 8, we can determine the Surface Area of the Ceiling = L*W
L*W*H = 800
L*W*8 = 800
L*W = 100 = Surface Area of Ceiling
3rd) Calculate his Constant Painting Rate based on what he finished in 28 hours
His Constant Work Rate = (1/4) ft/min
Work Rate = (Work Completed) / (Time Taken)
He Painted the 4 Walls and Ceiling in 28 hours (or 1,680 minutes):
Work Completed = L*H + W*H + L*H + W*H + Ceiling Area of 100
Work Completed = 8L + 8W + 8L + 8W + 100
Work Completed = 16 * (L +W) + 100
Time needed to Complete this Work = 1, 680 minutes
Now we can Set this Rate of Work EQUAL to the Given Rate of Work = (1/4) ft/min
1/4 = [ 16 * (L + W) + 100 ] / 1,680
---cross-multiplying---
1, 680 = 64 * (L + W) + 400
1,280 = 64 * (L + W)
L + W = 1, 280 / 64 ----- equation 1
The Question asks us how long it will take to Paint the JUST the 4 Walls and NOT the Ceiling:
Time = (Work) / (Rate)
The Surface Area WORK of the 4 Walls that needs to be completed = 8L + 8W + 8L + 8W = 16 * (L + W)
His Constant Rate of work is given by = (1/4) ft/min
Time in minutes = [ 16 * (L + W) ] / (1/4)
Substitute in --- equation 1 ---- (L + W) = 1, 280 / 64
Time in minutes = [ 16 * (1, 280 / 64) ] / (1/4)
---simplifying----
Time = (1, 280 * 4) / 4 = 1,280 minutes
Converting to Hours ---- 1,280 minutes / 60 minutes = 21 + (20/60)
or
21 hours and 20 minutes
Answer -A-
