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

Expert replies

Previous Topic Next Topic

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Thu Sep 27, 2018 9:49 pm

Timer

00:00

Answers

Stats

Difficulty—

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

Like this post

Source: Beat The GMAT — Data Sufficiency | Thu Sep 27, 2018 9:49 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed 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.

Like this post

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

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:

LetÂ´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 itÂ´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

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review