BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Pipe P can drain the liquid from a tank in 3/4 the time

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

Pipe P can drain the liquid from a tank in 3/4 the time

by Vincen » Tue Feb 13, 2018 3:49 am
Pipe P can drain the liquid from a tank in 3/4 the time that it takes pipe Q to drain it and in 2/3 the time that it takes pipe R to do it. If all 3 pipes operating simultaneously but independently are used to drain liquid from the tank, then pipe Q drains what portion of the liquid from the tank?

A. 9/29
B. 8/23
C. 3/8
D. 17/29
E. 3/4

The OA is the option A.

I am really confused here. Experts, may you clarify this question for me? I don't know how to solve it. Thanks in advanced.
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8083
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Wed Feb 14, 2018 10:16 am
Vincen wrote:Pipe P can drain the liquid from a tank in 3/4 the time that it takes pipe Q to drain it and in 2/3 the time that it takes pipe R to do it. If all 3 pipes operating simultaneously but independently are used to drain liquid from the tank, then pipe Q drains what portion of the liquid from the tank?

A. 9/29
B. 8/23
C. 3/8
D. 17/29
E. 3/4
We can let p = the time it takes pipe P to drain the liquid from the tank. Thus, the rate of pipe P = 1/p.

Since pipe P can drain the liquid from the tank in 3/4 the time that it takes pipe Q to drain it, the rate of pipe Q is:

(3/4)(1/p) = 3/(4p)

Since pipe P can drain the liquid from the tank in 2/3 the time that it takes pipe R to do it, the rate of pipe R is:

(2/3)(1/p) = 2/(3p)

Thus, the portion of liquid pipe Q drains is:

[3/(4p)] / [1/p + 3/(4p) + 2/(3p)]

Multiplying the numerator and denominator by 12p, we have:

9/(12 + 9 + 8)

9/29

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Legendary Member
Posts: 712
Joined: Fri Sep 25, 2015 4:39 am
Thanked: 14 times
Followed by:5 members

by Mo2men » Wed Feb 14, 2018 3:54 pm
Vincen wrote:Pipe P can drain the liquid from a tank in 3/4 the time that it takes pipe Q to drain it and in 2/3 the time that it takes pipe R to do it. If all 3 pipes operating simultaneously but independently are used to drain liquid from the tank, then pipe Q drains what portion of the liquid from the tank?

A. 9/29
B. 8/23
C. 3/8
D. 17/29
E. 3/4

The OA is the option A.

I am really confused here. Experts, may you clarify this question for me? I don't know how to solve it. Thanks in advanced.
Time of P = (2/3) R & time of P = (3/4) Q
Let time taken by Pipe R = 9...then time taken by P = 6 .....then time taken by Q = 8

Total time taken to drain the tank = (6)(8)(9)/ [(6)(8)+(6)(9)+(8)(9)] = 72/29

proportion drain by Pipe Q = time taken by Q / total time = (8) / (72/29) = 29/9..........However is inverse the OA

If I use rates instead, I got the right answer as follows:

Rate of pipe Q = 1/8 ...Combines rate = 29/72

proportion drain by Pipe Q = rate of pipe Q / Combined rate = (1/8)/(29)(72) = 9/29

Where did I go wrong??? Is not time indicative the same as rate?
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Feb 15, 2018 4:15 am
Vincen wrote:Pipe P can drain the liquid from a tank in 3/4 the time that it takes pipe Q to drain it and in 2/3 the time that it takes pipe R to do it. If all 3 pipes operating simultaneously but independently are used to drain liquid from the tank, then pipe Q drains what portion of the liquid from the tank?

A. 9/29
B. 8/23
C. 3/8
D. 17/29
E. 3/4
(P's time)/(Q's time) = 3/4 = 6/8.
(P's time)/(R's time) = 2/3 = 6/9.

Let:
P's time = 6 hours.
Q's time = 8 hours.
R's time = 9 hours.
Let the tank = the LCM of the 3 times = 72 liters.

Since P takes 6 hours to drain the 72-liter tank, P's rate = w/t = 72/6 = 12 liters per hour.
Since Q takes 8 hours to drain the 72-liter tank, Q's rate = w/t = 72/8 = 9 liters per hour.
Since R takes 9 hours to drain the 72-liter tank, R's rate = w/t = 72/9 = 8 liters per hour.
Combined rate for all 3 pumps = 12+9+8 = 29 liters per hour.
Of the 29 liters drained every hour when all 3 pumps work together, Q drains 9 liters.
Thus:
Fraction drained by Q = 9/29.

The correct answer is A.
proportion drain by Pipe Q = time taken by Q / total time = (8) / (72/29) = 29/9..........However is inverse the OA
Time and rate have a RECIPROCAL RELATIONSHIP.
If Mary's rate is 2 times John's rate, then Mary time is 1/2 John's time.
If Mary's rate is 3 times John's rate, then Mary time is 1/3 John's time.
If Mary's rate is 4 times John's rate, then Mary time is 1/4 John's time.

Since the TIME RATIO for Q and all 3 pumps = 29/9, the RATE RATIO for Q and all 3 pumps is the RECIPROCAL:
9/29.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1