GRE Prep 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.
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
A pump can be used to either fill or empty a 3600 m^3 tank.
[#permalink]
15 May 2021, 23:02
15 May 2021, 23:02
10
Bookmarks
00:00
Question Stats:
45% (02:41) correct
54% (02:53) wrong based on 33 sessions
Hide Show timer Statistics
A pump can be used to either fill or empty a 3600 \(m^3\) tank. The emptying capacity is 10 \(m^3/min\) higher than the filling capacity and it requires 12 more minutes to fill the tank than to empty it.
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Emptying capacity in \(m^3/min\) |
50 |
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Re: A pump can be used to either fill or empty a 3600 m^3 tank.
[#permalink]
16 May 2021, 08:44
16 May 2021, 08:44
1
I think that the answer is A
*capacity : 3600 m^3
rate to fill: x (m^3/min)
time to fill: 3600/x (min)
rate to empty: x + 10 (m^3/min)
time to empty: 3600/(x+10) = time to fill - 12 = (3600/x)-12 = (3600-12x)/x (min)
set "time to empty" expressions equal to each other:
3600/(x + 10) = (3600 - 12x) / x
-> 3600x = 3600x + 36000 - 12x^2 - 120x
-> 12x^2 + 120x - 36000 = 0
-> x^2 + 10x - 3000 = 0
-> x = [-10 +- sqrt(100-(4 * -3000)]/2 = [-10 +- sqrt(100+12000)]/2 = [-10 +- sqrt(12100)]/2 = (-10 +- 110)/2
->-> x = -5 +- 55
->->-> x = 50; x = - 60
x = 50
...so:
*capacity : 3600 m^3
rate to fill: 50 (m^3/min)
time to fill: 72 min
rate to empty: 60 (m^3/min)
time to empty: 60 min
A: emptying capacity in m^3/min = 60
B: 50
Answer: A is greater
*capacity : 3600 m^3
rate to fill: x (m^3/min)
time to fill: 3600/x (min)
rate to empty: x + 10 (m^3/min)
time to empty: 3600/(x+10) = time to fill - 12 = (3600/x)-12 = (3600-12x)/x (min)
set "time to empty" expressions equal to each other:
3600/(x + 10) = (3600 - 12x) / x
-> 3600x = 3600x + 36000 - 12x^2 - 120x
-> 12x^2 + 120x - 36000 = 0
-> x^2 + 10x - 3000 = 0
-> x = [-10 +- sqrt(100-(4 * -3000)]/2 = [-10 +- sqrt(100+12000)]/2 = [-10 +- sqrt(12100)]/2 = (-10 +- 110)/2
->-> x = -5 +- 55
->->-> x = 50; x = - 60
x = 50
...so:
*capacity : 3600 m^3
rate to fill: 50 (m^3/min)
time to fill: 72 min
rate to empty: 60 (m^3/min)
time to empty: 60 min
A: emptying capacity in m^3/min = 60
B: 50
Answer: A is greater
Senior Manager
Joined: 23 Jan 2021
Posts: 294
Given Kudos: 81
Concentration: , International Business
Re: A pump can be used to either fill or empty a 3600 m^3 tank.
[#permalink]
19 Jun 2021, 17:01
19 Jun 2021, 17:01
1
2
Bookmarks
KarunMendiratta wrote:
A pump can be used to either fill or empty a 3600 \(m^3\) tank. The emptying capacity is 10 \(m^3/min\) higher than the filling capacity and it requires 12 more minutes to fill the tank than to empty it.
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Emptying capacity in \(m^3/min\) |
50 |
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Here given,
Total capacity of the tank = \(3600 [m]m^3\) [/m]
and we are told that emptying capacity is 10 \(m^3/min\) higher than the filling capacity .
also,
it requires 12 more minutes to fill the tank than to empty it.
So,
Time difference = filling time - time required to empty
Let, filling rate be x.
>> \(10 = \frac{3600}{x} - \frac{3600}{(x + 10)}
\)
Doing some math,
>> \(x^2 + 10x - 3000 = 0\)
upon solving,
\(x = -60, 50\)
since, capacity cant be negative, simply we can discarded negative value.
Hence, filling capacity = 50
emptying capacity = 60
Hence, Quantity A is greater.
