GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Mar 2019, 08:55 ### 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # Pump A can empty a pool in A minutes, and pump B can empty

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern  Joined: 17 Jun 2013
Posts: 24
Pump A can empty a pool in A minutes, and pump B can empty  [#permalink]

### Show Tags

3
15 00:00

Difficulty:   75% (hard)

Question Stats: 61% (02:31) correct 39% (02:33) wrong based on 385 sessions

### HideShow timer Statistics

Pump A can empty a pool in A minutes, and pump B can empty the same pool in B minutes. Pump A begins emptying the pool for 1 minute before pump B joins. Beginning from the time pump A starts, how many minutes will it take to empty the pool?

A. $$\frac{A+B-1}{2}$$

B. $$\frac{A(B+1)}{A+B}$$

C. $$\frac{AB}{(A+B)}$$

D. $$\frac{AB}{(A+B)} -1$$

E. $$\frac{A(B-1)}{(A+B)}$$

Originally posted by gmatgambler on 24 Jan 2014, 07:13.
Last edited by Bunuel on 24 Jan 2014, 07:19, edited 2 times in total.
Edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 53768
Re: Pump A can empty a pool in A minutes, and pump B can empty  [#permalink]

### Show Tags

6
6
gmatgambler wrote:
Pump A can empty a pool in A minutes, and pump B can empty the same pool in B minutes. Pump A begins emptying the pool for 1 minute before pump B joins. Beginning from the time pump A starts, how many minutes will it take to empty the pool?

A. $$\frac{A+B-1}{2}$$

B. $$\frac{A(B+1)}{A+B}$$

C. $$\frac{AB}{(A+B)}$$

D. $$\frac{AB}{(A+B)} -1$$

E. $$\frac{A(B-1)}{(A+B)}$$

The rate of pump A is $$\frac{1}{A}$$ pool/minute;
The rate of pump B is $$\frac{1}{B}$$ pool/minute.

Their combined rate is $$\frac{1}{A} + \frac{1}{B} = \frac{A+B}{AB}$$ pool/minute.

In one minute that A works alone it does (rate)*(time) = $$\frac{1}{A} * 1= \frac{1}{A}$$ part of the job, thus $$1-\frac{1}{A}=\frac{A-1}{A}$$ part of the job is remaining to be done by A and B together.

To do $$\frac{A-1}{A}$$ of the job both pumps working together will need (time) = (job)/(combined rate) = $$\frac{A-1}{A}*\frac{AB}{A+B}=\frac{(A-1)B}{A+B}$$.

So, the total time is $$1+\frac{(A-1)B}{A+B}=\frac{A(B+1)}{A+B}$$.

_________________
##### General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 53768
Re: Pump A can empty a pool in A minutes, and pump B can empty  [#permalink]

### Show Tags

1
1
Bunuel wrote:
gmatgambler wrote:
Pump A can empty a pool in A minutes, and pump B can empty the same pool in B minutes. Pump A begins emptying the pool for 1 minute before pump B joins. Beginning from the time pump A starts, how many minutes will it take to empty the pool?

A. $$\frac{A+B-1}{2}$$

B. $$\frac{A(B+1)}{A+B}$$

C. $$\frac{AB}{(A+B)}$$

D. $$\frac{AB}{(A+B)} -1$$

E. $$\frac{A(B-1)}{(A+B)}$$

The rate of pump A is $$\frac{1}{A}$$ pool/minute;
The rate of pump B is $$\frac{1}{B}$$ pool/minute.

Their combined rate is $$\frac{1}{A} + \frac{1}{B} = \frac{A+B}{AB}$$ pool/minute.

In one minute that A works alone it does (rate)*(time) = $$\frac{1}{A} * 1= \frac{1}{A}$$ part of the job, thus $$1-\frac{1}{A}=\frac{A-1}{A}$$ part of the job is remaining to be done by A and B together.

To do $$\frac{A-1}{A}$$ of the job both pumps working together will need (time) = (job)/(combined rate) = $$\frac{A-1}{A}*\frac{AB}{A+B}=\frac{(A-1)B}{A+B}$$.

So, the total time is $$1+\frac{(A-1)B}{A+B}=\frac{A(B+1)}{A+B}$$.

Similar questions to practice:
a-husband-and-wife-started-painting-their-house-but-husband-77973.html
a-can-complete-a-project-in-20-days-and-b-can-complete-the-139311.html
two-water-pumps-working-simultaneously-at-their-respective-155865.html
at-their-respective-rates-pump-a-b-and-c-can-fulfill-an-77440.html
a-work-crew-of-4-men-takes-5-days-to-complete-one-half-of-a-91378.html
matt-and-peter-can-do-together-a-piece-of-work-in-20-days-61130.html
al-can-complete-a-particular-job-in-8-hours-boris-can-31757.html

Hope this helps.
_________________
SVP  Joined: 06 Sep 2013
Posts: 1676
Concentration: Finance
Re: Pump A can empty a pool in A minutes, and pump B can empty  [#permalink]

### Show Tags

2
I did this question using smart numbers

A = 6
B = 3

Therefore in 1 minute A did 1/6 of the job.
5/6 of the job remains

Together A and B work at a rate of 1/2.

Thus 1/2 (x) = 5/6

x = 5/3 minutes

Now we need to add the minute worked by A so total of 5/3 + 1 = 8/3 minutes

Replacing we can see that in (B)

(6)(4) / 9 = 8/3

Therefore it is the correct answer choice

Gimme some freaking Kudos!
Cheers
J
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 8998
Location: Pune, India
Re: Pump A can empty a pool in A minutes, and pump B can empty  [#permalink]

### Show Tags

jlgdr wrote:
I did this question using smart numbers

A = 6
B = 3

Therefore in 1 minute A did 1/6 of the job.
5/6 of the job remains

Together A and B work at a rate of 1/2.

Thus 1/2 (x) = 5/6

x = 5/3 minutes

Now we need to add the minute worked by A so total of 5/3 + 1 = 8/3 minutes

Replacing we can see that in (B)

(6)(4) / 9 = 8/3

Therefore it is the correct answer choice

Gimme some freaking Kudos!
Cheers
J

Taking numbers is a great strategy but try to take easier numbers. Say, 1, 0 etc as long as you meet all conditions mentioned.
I would take A = B = 1 (since there are no symmetric options in A and B such as A/(A+B) and B(A + B), I can take both A and B equal)
Now I need to do no calculations. A starts and works for a minute. In that time, the pool is empty. B joins but has nothing to do. Total time taken to empty the pool is 1 min.
Only option (B) gives 1.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

SVP  G
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1530
GMAT 1: 780 Q51 V48 GRE 1: Q800 V740 Re: Pump A can empty a pool in A minutes, and pump B can empty  [#permalink]

### Show Tags

1
2
Method 1:
The time taken by both pumps working together to do the work = AB/(A+B) minutes
Now, since Pump A has already worked for 1 minute, 1*(1/A) of the work has already been done.
Time taken to do the remaining work = [AB/(A+B)]*(1-1/A) = B(A-1)/(A+B) minutes
Total time taken from the start = [B(A-1)/(A+B)] + 1 = A*(B+1)/(A+B)
Option (B).

Method 2:
Let t be the time taken from the start. Then pump A works for t minutes to finish the work and pump B for (t-1) minutes
=> t(1/A) + (t-1)(1/B) = 1
=> t = A*(B+1)/(A+B)
Option (B).

Method 3:
We know that the time taken to do the work by both pumps working together right from the beginning is AB/(A+B) minutes.
Lets flip the question around to say that the two pumps worked together to do the work, except pump B was off in the first minute. So we must add the time it would take the two pumps to do the work that pump B would have done in this one minute to the total time. In this one minute, pump B would have done 1*(1/B) of the work = 1/B of the work.
Total time taken is therefore = AB/(A+B) + AB*(1/B)/(A+B)
= A*(B+1)/(A+B)
Option (B).
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Top MBA Admissions Consulting | Top MiM Admissions Consulting

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Manager  Joined: 24 Apr 2012
Posts: 50
Concentration: Strategy
WE: Project Management (Consulting)
Solve Work Problem using Numerical approach  [#permalink]

### Show Tags

Q. Pump A can empty a pool in A minutes, and pump B can empty the same pool in B minutes. Pump A begins emptying the pool for 1 minute before pump B joins. Beginning from the time pump A starts, how many minutes will it take to empty the pool?

(a) A+B-1/2

(b) A(B+1)/A+B

(c) AB/A+B

(d) AB/A+B -1/1

(e) A(B-1)/A+B

-----------------------------------------------

METHOD ONE: Algebraic approach

This approach to this question involves some tricky algebra.

Pump A works at a rate of 1/A and pump B, at a rate of 1/B (these rates are given in units of "pools/minute"). For the time they are working together, we add rates. That's a HUGE idea in work problems - when two machines or people work together, we add the rates.

In the first minute, pump A works alone and drains an amount of 1/A (that is, one "A-th" of a pool). This leaves an amount of

The time it will take the two pumps, working at the combined rate, to drain this, is:

That's the time from when the two pumps start working together, which is 1 minute after pump A starts. To get the total time, we need to add 1 to this (this is the trickiest algebra in the whole problem!)

METHOD TWO: Numerical approach

Let's say that Pump A can drain a pool in A = 6 minutes, and pump B can drain a pool in B = 3.

Pump A works for a minute, draining 1/6 of the pool, and leaving 5/6 of the pool left.

Then pump B kicks in --- A & B work at the combined rate of 1/6 + 1/3 = 1/2. How long does it take the two pumps, working at a rate of 1/2, to drain 5/6 of a pool?

Add the first minute for total time.

If we plug in the starter values A = 6 and B = 3, how many of the answers will yield this answer of 8/3 as the total time?

Only answer (B) works, so that the correct answer.
_________________

--------------------------

"The will to win, the desire to succeed, the urge to reach your full potential..."

http://gmatclub.com/forum/powerscore-cr-notes-hope-that-someone-find-it-kudosofiable-174638.html#p1384561

Originally posted by royQV on 17 Apr 2014, 10:57.
Last edited by royQV on 18 Apr 2014, 01:25, edited 1 time in total.
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1817
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Solve Work Problem using Numerical approach  [#permalink]

### Show Tags

1
royQV wrote:
Q. Pump A can empty a pool in A minutes, and pump B can empty the same pool in B minutes. Pump A begins emptying the pool for 1 minute before pump B joins. Beginning from the time pump A starts, how many minutes will it take to empty the pool?

METHOD ONE: Algebraic approach

This approach to this question involves some tricky algebra.

Pump A works at a rate of 1/A and pump B, at a rate of 1/B (these rates are given in units of "pools/minute"). For the time they are working together, we add rates. That's a HUGE idea in work problems - when two machines or people work together, we add the rates.

In the first minute, pump A works alone and drains an amount of 1/A (that is, one "A-th" of a pool). This leaves an amount of

The time it will take the two pumps, working at the combined rate, to drain this, is:

That's the time from when the two pumps start working together, which is 1 minute after pump A starts. To get the total time, we need to add 1 to this (this is the trickiest algebra in the whole problem!)

METHOD TWO: Numerical approach

Let's say that Pump A can drain a pool in A = 6 minutes, and pump B can drain a pool in B = 3.

Pump A works for a minute, draining 1/6 of the pool, and leaving 5/6 of the pool left.

Then pump B kicks in --- A & B work at the combined rate of 1/6 + 1/3 = 1/2. How long does it take the two pumps, working at a rate of 1/2, to drain 5/6 of a pool?

Add the first minute for total time.

If we plug in the starter values A = 6 and B = 3, how many of the answers will yield this answer of 8/3 as the total time?

Only answer (B) works, so that the correct answer.

Can you please post the OA?

Rate of Pump A $$= \frac{1}{a}$$

Rate of Pump B $$= \frac{1}{b}$$

Work done by Pump A in 1 min $$= \frac{1}{a} * 1 = \frac{1}{a}$$

Work remaining (To be done by both pumps) $$= 1 - \frac{1}{a} = \frac{a-1}{a}$$

Combined rate of Pump A & B$$= \frac{1}{a} + \frac{1}{b}$$

Time required to complete the remaining work = t

$$\frac{a+b}{ab} * t = \frac{a-1}{a}$$

$$t = \frac{b(a-1)}{a+b}$$

Total time required

= $$\frac{b(a-1)}{a+b} + 1$$

$$= \frac{a(b-1)}{a+b}$$
_________________

Kindly press "+1 Kudos" to appreciate Math Expert V
Joined: 02 Sep 2009
Posts: 53768
Re: Solve Work Problem using Numerical approach  [#permalink]

### Show Tags

royQV wrote:
Q. Pump A can empty a pool in A minutes, and pump B can empty the same pool in B minutes. Pump A begins emptying the pool for 1 minute before pump B joins. Beginning from the time pump A starts, how many minutes will it take to empty the pool?

(a) A+B-1/2

(b) A(B+1)/A+B

(c) AB/A+B

(d) AB/A+B -1/1

(e) A(B-1)/A+B

-----------------------------------------------

METHOD ONE: Algebraic approach

This approach to this question involves some tricky algebra.

Pump A works at a rate of 1/A and pump B, at a rate of 1/B (these rates are given in units of "pools/minute"). For the time they are working together, we add rates. That's a HUGE idea in work problems - when two machines or people work together, we add the rates.

In the first minute, pump A works alone and drains an amount of 1/A (that is, one "A-th" of a pool). This leaves an amount of

The time it will take the two pumps, working at the combined rate, to drain this, is:

That's the time from when the two pumps start working together, which is 1 minute after pump A starts. To get the total time, we need to add 1 to this (this is the trickiest algebra in the whole problem!)

METHOD TWO: Numerical approach

Let's say that Pump A can drain a pool in A = 6 minutes, and pump B can drain a pool in B = 3.

Pump A works for a minute, draining 1/6 of the pool, and leaving 5/6 of the pool left.

Then pump B kicks in --- A & B work at the combined rate of 1/6 + 1/3 = 1/2. How long does it take the two pumps, working at a rate of 1/2, to drain 5/6 of a pool?

Add the first minute for total time.

If we plug in the starter values A = 6 and B = 3, how many of the answers will yield this answer of 8/3 as the total time?

Only answer (B) works, so that the correct answer.

Merging similar topics. Please refer to the discussion above.

Hope it helps.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1, 3, and 8. Thank you.
_________________
Director  P
Joined: 13 Mar 2017
Posts: 704
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Pump A can empty a pool in A minutes, and pump B can empty  [#permalink]

### Show Tags

gmatgambler wrote:
Pump A can empty a pool in A minutes, and pump B can empty the same pool in B minutes. Pump A begins emptying the pool for 1 minute before pump B joins. Beginning from the time pump A starts, how many minutes will it take to empty the pool?

A. $$\frac{A+B-1}{2}$$

B. $$\frac{A(B+1)}{A+B}$$

C. $$\frac{AB}{(A+B)}$$

D. $$\frac{AB}{(A+B)} -1$$

E. $$\frac{A(B-1)}{(A+B)}$$

Since A empties a pool in A minutes. In 1 minute A empties 1/A fraction of the pool.
B empties a pool in B minutes. In 1 minute B empties 1/B fraction of the pool.

So, 1/A + (1/A + 1/B)n = 1 where is n is the time in minutes for which A and B worked together.
(A+b)/AB *n = 1- 1/A
n = AB/(A+B) - B /(A+B)= (AB- B)/(A+B)

SO, total time taken to empty a pool = 1+ (AB- B)/(A+B) = (A+B+ AB-B)/(A+B) = A(B+1)/(A+B)

_________________

CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Manager  S
Joined: 17 Aug 2012
Posts: 123
Location: India
Concentration: General Management, Strategy
Schools: Copenhagen, ESMT"19
GPA: 3.75
WE: Consulting (Energy and Utilities)
Re: Pump A can empty a pool in A minutes, and pump B can empty  [#permalink]

### Show Tags

The fastest time in which tank can be emptied is by working together which is AB /(A+B)

But in this case it would be greater than AB/(A+B) since they have not worked together all time.

out of option B , C , D & E only option "B" is greater than AB /(A+B)
Non-Human User Joined: 09 Sep 2013
Posts: 10166
Re: Pump A can empty a pool in A minutes, and pump B can empty  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: Pump A can empty a pool in A minutes, and pump B can empty   [#permalink] 08 Sep 2018, 05:46
Display posts from previous: Sort by

# Pump A can empty a pool in A minutes, and pump B can empty

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.  