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

Redeem

Two inlets P and Q are working on alternate hour for filling

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

Two inlets P and Q are working on alternate hour for filling

by GMATinsight » Thu Sep 27, 2018 9:49 pm
Two inlets P and Q are working on alternate hour for filling an empty tank and only one inlet works at any point of time. How much time will it take to fill the tank completely?

1) Inlet P can fill the tank in 10 hours while working alone while Inlet Q takes 12 hours to fill the tank alone
2) Inlet P works for first hour to fill the tank

Source: www.GMATinsight.com
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Top
Source: — Data Sufficiency |
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

by deloitte247 » Mon Oct 01, 2018 1:01 pm
Question = How much time will it take to fill the tank completely?
STATEMENT 1= Inlet P can fill the tank in 10 hours while working alone while inlet Q takes 12 hours to fill the tank alone.
If inlet P can fill the tank in 10 hours, how many portion of the tank will it fill in 1 hour ?
10 hours = 1
$$1\ hour\ =\ \frac{\left(1\ \cdot1\right)}{10}=\ \frac{1}{10}$$
$$Inlet\ P\ will\ fill\ \frac{1}{10}\ of\ the\ \tan k\ in\ 1\ hour\ $$
Therefore, after working for 5 hours inlet P would have filled half of the tank.

If inlet P can fill the tank completely in 12 hours, how many portion of the tank will it fill in 1 hour?
12 hours = 1
$$1\ hour\ =\ \frac{\left(1\ \cdot\ 1\ \right)}{12}\ =\ \frac{1}{12}$$
$$Inlet\ P\ will\ fill\ =\ \frac{1}{12}\ of\ the\ \tan k\ in\ 1\ hour$$
After working for 6 hours, inlet P would have filled half of the tank.

If P starts the first hour it will take the two inlets 10 hours to fill the tank, but, if Q starts the first hour, it will take 10 hours to fill the tank.
$$\frac{1}{10}+\frac{1}{12}+\frac{1}{10}+\frac{1}{12}+\frac{1}{10}+\frac{1}{12}+\frac{1}{10}+\frac{1}{12}+\frac{1}{10}+\frac{1}{12}$$
$$=\ \frac{10}{110}=0.09$$
Each fraction stands for 1 hour so they will complete it in 10 hours. Hence, statement 1 is SUFFICIENT.

STATEMENT 2 = Inlet P works for the first hour to fill the tank.
There is no information on the work rate of inlet P and Q, hence statement 2 is NOT SUFFICIENT.

Option A is CORRECT.
Top
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

Two inlets P and Q are working on alternate hour for filling

by fskilnik@GMATH » Mon Oct 01, 2018 1:54 pm
GMATinsight wrote:Two inlets P and Q are working on alternate hour for filling an empty tank and only one inlet works at any point of time. How much time will it take to fill the tank completely?

1) Inlet P can fill the tank in 10 hours while working alone while Inlet Q takes 12 hours to fill the tank alone
2) Inlet P works for the first hour to fill the tank
Source: www.GMATinsight.com
\[job\,\, = {\text{fill}}\,\,{\text{the}}\,\,{\text{tank}}\]
\[?\,\,\,:\,\,\,{\text{time}}\,\,\,{\text{for}}\,\,{\text{job}}\,\,\,\left( {{\text{1 - h}}\,\,{\text{alternating}}} \right)\]

(1) Insufficient:

Let´s imagine one job is defined by 60 identical tasks (60 = LCM(10,12)). From this statement, we know that:

P does 6 tasks/h
Q does 5 tasks/h

In two hours 11tasks are done, therefore in 5*2 = 10 hours we have 5*11 = 55 tasks done without taking into account who started.

After that, there are still 5 tasks to be completed.

> If P starts (meaning P started at first hour), we need less than 1 additional hour to finish the job.
> If Q starts (meaning Q started at first hour), we need exactly 1h to finish the job.

Obs.: check this slightly different problem when you finish reading this one...
https://www.beatthegmat.com/two-inlets- ... tml#820747

(2) Insufficient:

If each inlet fills the tank in 2h, then ? equals 2h.
If each inlet fills the tank in 3h, then ? equals 3h.

(1+2) Sufficient: as explained in (1), after 10h there is still 5 tasks left, and it´s time for P to work (taking into account statement (2)):
\[? = 10{\text{h}} + 5\,{\text{tasks}} \cdot \left( {\frac{{1\,\,{\text{h}}}}{{6\,\,{\text{tasks}}}}\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\, = \,\,\,10\frac{5}{6}h\]
Obs.: arrows indicate licit converter.

The correct answer is therefore (C).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top
Post new topic Post Reply
• Page 1 of 1