NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 10:43 It is currently 27 Apr 2024, 10:43
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Working together at their constant rates, pumps X and Y can fill an

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
javzprobz
Intern
Intern
Joined: 04 Sep 2012
Posts: 1
Own Kudos [?]: 23 [20]
Given Kudos: 33
Send PM
Working together at their constant rates, pumps X and Y can fill an [#permalink] New post   Updated on: 30 Jun 2022, 08:14
3
Kudos
17
Bookmarks
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

75% (01:17) correct 25% (01:16) wrong based on 442 sessions
Hide Show timer Statistics
Working together at their constant rates, pumps X and Y can fill an empty pool to capacity in 1/3 hours. How many minutes does it take pump Y, working alone, to fill the pool?

(1) The capacity of the pool is 900 gallons.
(2) The rate of Pump X is 30 gallons per minute.

Show Spoiler
Hi everyone,

I do have a specific problem with THE SOLUTION THAT BUNNEL HAS PROVIDED (reveal the first spoiler to see Bunnel's solution and my analysis of it) for this question. Let's first take a look at the question, then I'll explain my problem.

I do understand that we need both statements together in order to solve the question since statement 2 just tells us that pump X can fill 30 gallons per minute and we don't how many gallons the job actually is, thus we need statement 2 as well in order to answer the question. Now for the sake of solving a DS question, it's enough to pick answer choice C and move on since we have enough information to answer the question. However, for the sake of discussing the solution that Bunnel has provided, let's take a look at his solution: "Rate*Time=Job time = 1/3 hrs = 20 minutes so (x+y)*20=work now statement 1 gives us: work=900 and statement 2: x=30. So combining statement 1 and 2, we can solve for y since we have (30+y)*20=900, which gives us y=15. Now, my problem is that I solved the problem the way that some of us used to do (also explained in GMATCLUB Math Book, work problem section). I initially set the equation 1/x+1/y=1/20, after reading the question stem (x and y refer to time that pump x and pump y respectively take to do 1 unit of the job). Then I read statement 1 and noticed that it is insufficient, since it just tells us about how much the work is. And read statement 2, which also is insufficient since now we don't how many gallons the work is. But combining statement 1 and 2, I got to this point that pump x can do 1 unit of the job in 30 minutes (900 gallons/30 minutes=30 gallons/1 minute or in other words 1 unit of job/30 minutes). So now I have 1/30 + 1/y = 1/20, and solving this would give me y=60 minutes. Now, why is my answer to how many minutes pump y takes to do the job alone different than Bunnel's to this question? Is there something wrong with my solution or how I solved the question? I would appreciate your help!


Experience a GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
ShowHide Answer
Official Answer
C

Originally posted by javzprobz on 09 Oct 2014, 01:46.
Last edited by Bunuel on 30 Jun 2022, 08:14, edited 2 times in total.
RENAMED THE TOPIC.
Most Helpful Reply
User avatar
G
mikemcgarry
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4452
Own Kudos [?]: 28578 [5]
Given Kudos: 130
Re: Working together at their constant rates, pumps X and Y can fill an [#permalink] New post   09 Oct 2014, 11:28
5
Kudos
Expert Reply
javzprobz wrote:
Hi everyone,

I do have a specific problem with THE SOLUTION THAT BUNNEL HAS PROVIDED (reveal the first spoiler to see Bunnel's solution and my analysis of it) for this question. Let's first take a look at the question, then I'll explain my problem.

Working together at their constant rates, pumps X and Y can fill an empty pool to capacity in 1/3 hours. How many minutes does it take pump Y, working alone, to fill the pool?

(1) The capacity of the pool is 900 gallons.
(2) The rate of Pump X is 30 gallons per minute.

Open the spoiler to read my problem with the solution that Bunnel has provided for this question:
I do understand that we need both statements together in order to solve the question since statement 2 just tells us that pump X can fill 30 gallons per minute and we don't how many gallons the job actually is, thus we need statement 2 as well in order to answer the question. Now for the sake of solving a DS question, it's enough to pick answer choice C and move on since we have enough information to answer the question. However, for the sake of discussing the solution that Bunnel has provided, let's take a look at his solution: "Rate*Time=Job time = 1/3 hrs = 20 minutes so (x+y)*20=work now statement 1 gives us: work=900 and statement 2: x=30. So combining statement 1 and 2, we can solve for y since we have (30+y)*20=900, which gives us y=15. Now, my problem is that I solved the problem the way that some of us used to do (also explained in GMATCLUB Math Book, work problem section). I initially set the equation 1/x+1/y=1/20, after reading the question stem (x and y refer to time that pump x and pump y respectively take to do 1 unit of the job). Then I read statement 1 and noticed that it is insufficient, since it just tells us about how much the work is. And read statement 2, which also is insufficient since now we don't how many gallons the work is. But combining statement 1 and 2, I got to this point that pump x can do 1 unit of the job in 30 minutes (900 gallons/30 minutes=30 gallons/1 minute or in other words 1 unit of job/30 minutes). So now I have 1/30 + 1/y = 1/20, and solving this would give me y=60 minutes. Now, why is my answer to how many minutes pump y takes to do the job alone different than Bunnel's to this question? Is there something wrong with my solution or how I solved the question? I would appreciate your help!

Dear javzprobz,
I'm happy to respond. :-)

You seem to appreciate the ideas of work-rate well, but if you want reinforcement, here's a blog article about it:
https://magoosh.com/gmat/2012/gmat-work-rate-problems/

Your problem was that you used the generic variable "y" and were not careful about exactly what it meant. In Bunuel's solution, y is rate of pump Y, and he correctly finds that the rate is y = 15 gallons/minute. You used the formula to solve for y = 60, but that formula was designed to give you the time of pump Y. You correctly found that the time is 60 minutes. This is all correct. If Pump Y has a rate of 15 gallons/ minute, it would fill a 900 gallon pool in a time of 60 minutes.

I think your takeaways should be:
1) pick more meaningful variables, and be rigorous in defining exactly what you variables mean
2) don't ignore units; you need to be meticulous clear on the units of each and every number in your calculation
3) don't use a formula unless you are 100% clear on exactly what it does and what it is giving you.

As a general rule, relying on formulas is an exceptionally poor way to approach GMAT Quant.

Does all this make sense?
Mike :-)
General Discussion
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14831
Own Kudos [?]: 64948 [3]
Given Kudos: 427
Location: Pune, India
Send PM
Re: Working together at their constant rates, pumps X and Y can fill an [#permalink] New post   26 Dec 2023, 08:30
3
Kudos
Expert Reply
javzprobz wrote:
Working together at their constant rates, pumps X and Y can fill an empty pool to capacity in 1/3 hours. How many minutes does it take pump Y, working alone, to fill the pool?

(1) The capacity of the pool is 900 gallons.
(2) The rate of Pump X is 30 gallons per minute.


Let's see the information we have with respect to the quantities we know: Rate, Time, Work

Time taken together = 1/3 hr = 20 mins (I will prefer to work with 20 mins here because the question is asking the time in minutes and the statement 2 provides rate is mins)

We need the time taken by Y alone.

(1) The capacity of the pool is 900 gallons.

This is the capacity of the pool i.e. the work that has to be done. I can say that work done = 1 pool or I can say that work done = 900 gallons. They both represent the same thing in different units.
Now I know the work that has to be done in different units i.e. 900 gallons. From the question stem, I knew that the work to be done is 1 pool.
This means that their rate together was either 1/(1/3) = 3 pools/hr
or it can be written as 900/20 = 45 gallons/min
They both represent the same rate (of both pumps working together)
I don't know the rate of pump X so I cannot find the rate of pump Y. Not sufficient alone.

(2) The rate of Pump X is 30 gallons per minute.

Rate of pump X = 30 gallons/min but I still don't know the rate of pump Y because these units are different from the units of pool/hr that the question gives us. Since I don't know the equivalency of pool and gallons, I cannot convert one rate to another.
I don't know the combined rate in terms of gallons/min so I cannot find the rate of pump Y. Not sufficient alone.


Using both statements together,
We know that combined rate is 45 gallons/min i.e. both pumps together are putting in 45 gallons of water in one min. But pump X is putting in 30 gallons every min. So pump Y must be putting in the other 15 gallons per min.
Rate of pump Y = 15 gallons/min.

Then if I had to find the time taken by pump Y alone, I simply do
Time = work/rate = 900 gallons/15 gallons per min = 60 mins
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92956
Own Kudos [?]: 619440 [1]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
Working together at their constant rates, pumps X and Y can fill an [#permalink] New post   11 Oct 2016, 06:28
1
Kudos
Expert Reply
javzprobz wrote:
Hi everyone,

I do have a specific problem with THE SOLUTION THAT BUNNEL HAS PROVIDED (reveal the first spoiler to see Bunnel's solution and my analysis of it) for this question. Let's first take a look at the question, then I'll explain my problem.

Working together at their constant rates, pumps X and Y can fill an empty pool to capacity in 1/3 hours. How many minutes does it take pump Y, working alone, to fill the pool?

(1) The capacity of the pool is 900 gallons.
(2) The rate of Pump X is 30 gallons per minute.

Open the spoiler to read my problem with the solution that Bunnel has provided for this question:
Show Spoiler
I do understand that we need both statements together in order to solve the question since statement 2 just tells us that pump X can fill 30 gallons per minute and we don't how many gallons the job actually is, thus we need statement 2 as well in order to answer the question. Now for the sake of solving a DS question, it's enough to pick answer choice C and move on since we have enough information to answer the question. However, for the sake of discussing the solution that Bunnel has provided, let's take a look at his solution: "Rate*Time=Job time = 1/3 hrs = 20 minutes so (x+y)*20=work now statement 1 gives us: work=900 and statement 2: x=30. So combining statement 1 and 2, we can solve for y since we have (30+y)*20=900, which gives us y=15. Now, my problem is that I solved the problem the way that some of us used to do (also explained in GMATCLUB Math Book, work problem section). I initially set the equation 1/x+1/y=1/20, after reading the question stem (x and y refer to time that pump x and pump y respectively take to do 1 unit of the job). Then I read statement 1 and noticed that it is insufficient, since it just tells us about how much the work is. And read statement 2, which also is insufficient since now we don't how many gallons the work is. But combining statement 1 and 2, I got to this point that pump x can do 1 unit of the job in 30 minutes (900 gallons/30 minutes=30 gallons/1 minute or in other words 1 unit of job/30 minutes). So now I have 1/30 + 1/y = 1/20, and solving this would give me y=60 minutes. Now, why is my answer to how many minutes pump y takes to do the job alone different than Bunnel's to this question? Is there something wrong with my solution or how I solved the question? I would appreciate your help!


Official Solution:

Working together at their constant rates, pumps X and Y can fill an empty pool to capacity in \(\frac{1}{3}\) hours. How many minutes does it take pump Y, working alone, to fill the pool?

To solve the problem, we can use the formula \(rate*time=job\). In the problem, we are given the expression \((x+y)*20=c\), where \(x\) and \(y\) are the flow rates of pumps X and Y, respectively, and \(c\) is the pool's capacity in gallons. The problem asks us to find the value of \(y\).

(1) The capacity of the pool is 900 gallons.

The above gives \(c=900\), which implies that \((x+y)*20 = 900\). As a result, we can deduce that \(x+y=45\). However, this information is not sufficient to get \(y\).

(2) The rate of Pump X is 30 gallons per minute.

Given that \(x=30\), we can then express the equation as \((30+y)*20 = c\). With two unknowns and just one equation, we lack sufficient information. For instance, if \(c = 1000\), then \(y = 20\). However, if \(c = 900\), \(y = 15\).

(1)+(2) From the previous statements, we know that \(x=30\) and \(x+y=45\). By solving these equations, we can determine that \(y=15\) gallons per minute. Therefore, pump Y working alone will take \(\frac{900}{15}=60\) minutes to fill the pool. Sufficient.


Answer: C
User avatar
S
MissBong
Manager
Manager
Joined: 02 Apr 2021
Posts: 57
Own Kudos [?]: 42 [0]
Given Kudos: 167
Location: India
Schools: Tepper '25 (A$) Ross '25 (M)
GMAT 1: 720 Q49 V38 (Online)
Send PM
Re: Working together at their constant rates, pumps X and Y can fill an [#permalink] New post   30 Jun 2022, 06:36
Bunuel wrote:
javzprobz wrote:
Hi everyone,

I do have a specific problem with THE SOLUTION THAT BUNNEL HAS PROVIDED (reveal the first spoiler to see Bunnel's solution and my analysis of it) for this question. Let's first take a look at the question, then I'll explain my problem.

Working together at their constant rates, pumps X and Y can fill an empty pool to capacity in 1/3 hours. How many minutes does it take pump Y, working alone, to fill the pool?

(1) The capacity of the pool is 900 gallons.
(2) The rate of Pump X is 30 gallons per minute.

Open the spoiler to read my problem with the solution that Bunnel has provided for this question:
Show Spoiler
I do understand that we need both statements together in order to solve the question since statement 2 just tells us that pump X can fill 30 gallons per minute and we don't how many gallons the job actually is, thus we need statement 2 as well in order to answer the question. Now for the sake of solving a DS question, it's enough to pick answer choice C and move on since we have enough information to answer the question. However, for the sake of discussing the solution that Bunnel has provided, let's take a look at his solution: "Rate*Time=Job time = 1/3 hrs = 20 minutes so (x+y)*20=work now statement 1 gives us: work=900 and statement 2: x=30. So combining statement 1 and 2, we can solve for y since we have (30+y)*20=900, which gives us y=15. Now, my problem is that I solved the problem the way that some of us used to do (also explained in GMATCLUB Math Book, work problem section). I initially set the equation 1/x+1/y=1/20, after reading the question stem (x and y refer to time that pump x and pump y respectively take to do 1 unit of the job). Then I read statement 1 and noticed that it is insufficient, since it just tells us about how much the work is. And read statement 2, which also is insufficient since now we don't how many gallons the work is. But combining statement 1 and 2, I got to this point that pump x can do 1 unit of the job in 30 minutes (900 gallons/30 minutes=30 gallons/1 minute or in other words 1 unit of job/30 minutes). So now I have 1/30 + 1/y = 1/20, and solving this would give me y=60 minutes. Now, why is my answer to how many minutes pump y takes to do the job alone different than Bunnel's to this question? Is there something wrong with my solution or how I solved the question? I would appreciate your help!


POSTING OFFICIAL SOLUTION:

Working together at their constant rates, pumps X and Y can fill an empty pool to capacity in \(\frac{1}{3}\) hours. How many minutes does it take pump Y, working alone, to fill the pool?

\(rate*time=job\).

We are told that \((x+y)*20=c\), where \(x\) is the rate of pump X in gallons per minute, \(y\) is the rate of pump Y in gallons per minute and \(c\) is the capacity of the pool in gallons.

The question asks to find the value of \(y\).

(1) The capacity of the pool is 900 gallons. \(c=900\), hence we have that \((x+y)*20=900\), so \(x+y=45\). Not sufficient.

(2) The rate of Pump X is 30 gallons per minute. \(x=30\), hence we have that \((30+y)*20=c\). We have two unknowns and only one equation. Not sufficient. Consider this if \(c=1,000\), then \(y=20\) but if \(c=900\), then \(y=15\).

(1)+(2) \(x=30\) and \(x+y=45\). Solving gives \(y=15\). Sufficient.


Answer: C

Hi Bunuel,

Though it makes no difference onto the answer, you said that the question asks us to find the "rate (y)", but that's not the case. Question says, "How many minutes does it take pump Y, working alone, to fill the pool?" Thus, it not the "rate" but the time Y takes alone to fill the pool.
One can find time through rate undoubtedly, but that's not what question has asked us.

If it were a PS question, 60 minutes not 15 would have been the right answer. Isn't it?
User avatar
G
TargetMBA007
Manager
Manager
Joined: 22 Nov 2019
Posts: 232
Own Kudos [?]: 100 [0]
Given Kudos: 197
Schools: Stanford MSx '25 HBS '26
GPA: 4
Send PM
Forum Quiz Mode
Re: Working together at their constant rates, pumps X and Y can fill an [#permalink] New post   26 Dec 2023, 06:27
KarishmaB - would love to see how you would tackle this one.

I can relate to the concept.

I also find the connection between the rate and work interesting here
Based on the stem the time is 1/3rd of an hour, so our rate should be 3 pools/hour.

Then in St 1, we get the size of the pool as 900 gallons, but when I divide this by the rate 900/3, I get 300. This is obv not correct, because I guess the work here, and the volume of the pool are two different concepts, but would be great if you can detangle this and how such questions should be dealth with, especially when working with a rate-time-work matrix?

Thanks
GMAT Club Bot
gmatclubot
Re: Working together at their constant rates, pumps X and Y can fill an [#permalink]
26 Dec 2023, 06:27
Moderator:
Bunuel
Math Expert
92954 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions