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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: Collection of work/rate problems? [#permalink]

Show Tags

22 Oct 2011, 07:47

Need help understanding this 7.If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost? (1) Tom makes 20% less per hour than Jim does. (2) x + y = $43.75

The answer is B, but I want to understand how I can figure this out without solving the whole problem.

From the question we have 4x = 5y

From (1) we have y = 0.8x (or y - 0.8x = 0) From (2) we have x + y = 43.75 (or y = 43.75 - x)

At this point I see I have a new equation from both (1) and (2) and my initial response is that both are individually sufficient (D).

How can I figure out at this point that (1) is not sufficient and (2) is sufficient without spending much time in solving all the equations.

Re: Collection of work/rate problems? [#permalink]

Show Tags

16 Dec 2011, 09:13

No need to use any algebra here.

A = tap that is filling the pool B = leak in the pool

A is running for 10 hrs, which means it can fill 2.5 times the pool in that time. However, it is able to fill just 1 pool, which means that B leaks 1.5 times the pool in that time. Now, B can empty 1 pool in 5 hrs, so it will take 7.5 hrs to empty 1.5 times the pool.

Therefore, leak started 2.5 hrs after A started = which is 3.30pm.

h2polo wrote:

8. A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened? *at 2:00 pm * at 2:30 pm * at 3:00 pm * at 3:30 pm * at 4:00 pm

Here is how I solved the problem:

let A = the number of hours the filling valve is open by itself let B = the number of hours the filling and draining valve are open together

Filling rate: 1 pool / 4 hrs Draining rate: 1 pool / 5 hrs

therefore,

(1 pool / 4 hrs)*(A+B hrs) - (1 pool / 5 hrs)*(B hrs) = 1 pool

and we know that the pool was filled in 10 hours:

A + B = 10

so now we have two equations and two unknowns; solve for A:

(A+B)/4 - B/5 = 1 5*(A+B) - 4*5 = 20 5*A + B = 20

substitute B for 10-A:

5*A + 10 - A = 20 A = 2.5

So the pool was filled 2 and half hours after 1 PM or 3:30 PM

Re: Collection of work/rate problems? [#permalink]

Show Tags

29 May 2012, 10:54

I'm having some trouble with #28.

I'm having some difficulty understanding this problem (28) I got an answer B, or that statement 2 is sufficient alone to determine how many hours it would have taken machine X to fill out everything.

Machine X: xrate/ hour, 4 hours, so output = 4x Machine Y: y rate/hour, 3 hours, so output = 3y.

Machine X: xrate/ hour, 4 hours, so output = 4x Machine Y: 2/3x rate/hour, 3 hours, so output = 2x.

we know that the entire lot = 4x + 3y, so the new total output is 6x.

If machine X is to operate on its own, at rate X... x (rate) * time = 6x.

Time = 6 hours to operate the entire thing. Is this logic flawed?

Quote:

****28.Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken machine X operating alone to fill the entire production lot?

(1) Machine X produced 30 bottles per minute. (2) Machine X produced twice as many bottles in 4hours as machine Y produced in 3 hours.

let X = time it takes Machine X to fill lot let Y = time it takes Machine Y to fill lot

4*(1/X) + 3*(1/Y) = 1

From Statement 1 we know the total number of bottles made in four hours by Machine X

NOT SUFFICIENT

From Statement 2 we know that Machine Y produced half the total mentioned above in three hours

Using this info, we can determine how long it would take Machine X to fill the lot:

Total # of bottles * (1 hr / (30*60) bottles) = Number of Hours it would take Machine X to fill the lot

ANSWER: C. Both statements together are sufficient***

Re: Collection of work/rate problems? [#permalink]

Show Tags

29 May 2012, 11:17

jsnkwok wrote:

I'm having some trouble with #28.

I'm having some difficulty understanding this problem (28) I got an answer B, or that statement 2 is sufficient alone to determine how many hours it would have taken machine X to fill out everything.

Machine X: xrate/ hour, 4 hours, so output = 4x Machine Y: y rate/hour, 3 hours, so output = 3y.

Machine X: xrate/ hour, 4 hours, so output = 4x Machine Y: 2/3x rate/hour, 3 hours, so output = 2x.

we know that the entire lot = 4x + 3y, so the new total output is 6x.

If machine X is to operate on its own, at rate X... x (rate) * time = 6x.

Time = 6 hours to operate the entire thing. Is this logic flawed?

Quote:

****28.Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken machine X operating alone to fill the entire production lot?

(1) Machine X produced 30 bottles per minute. (2) Machine X produced twice as many bottles in 4hours as machine Y produced in 3 hours.

let X = time it takes Machine X to fill lot let Y = time it takes Machine Y to fill lot

4*(1/X) + 3*(1/Y) = 1

From Statement 1 we know the total number of bottles made in four hours by Machine X

NOT SUFFICIENT

From Statement 2 we know that Machine Y produced half the total mentioned above in three hours

Using this info, we can determine how long it would take Machine X to fill the lot:

Total # of bottles * (1 hr / (30*60) bottles) = Number of Hours it would take Machine X to fill the lot

ANSWER: C. Both statements together are sufficient***

Re: Collection of work/rate problems? [#permalink]

Show Tags

09 Nov 2012, 05:20

Expert's post

brooksbrahs wrote:

h2polo wrote:

15. working together at their constant rates , A and B can fill an empty tank to capacity in1/2 hr.what is the constant rate of pump B? 1) A's constant rate is 25LTS / min 2) the tanks capacity is 1200 lts.

From the original statement we know that: 1/A + 1/B = 1/(1/2)

From Statement 1 we can plug in and find B: SUFFICIENT

Statement 2 is completely unnecessary:

ANSWER: A. Statement 1 alone is sufficient

I don't think this is correct. We know that the rate of A and B = 1/30 of a tank per minute (given in the stem). If A had said that pump A fills X OF THE TANK per minute, then it'd be sufficient alone since A + B = rate of A + rate of B and can solve for rate of B given that we know A. However, this gives it to us in units other than what the stem gave us, so we need to know the tank's capacity. Statement 2 gives us the capacity, so if we use them in conjunction, we can solve the problem. Should be C, not A, IMO.

Yes, the answer to this question is C not A.

Working together at their constant rates, A and B can fill an empty tank to capacity in 1/2 hours. What is the constant rate of pump B?

\(rate*time=job\).

We are told that \((A+B)*30=C\), where \(A\) is the rate of pump A in lts/min, \(B\) is the rate of pump B in lts/min and C is the capacity of the tank in liters.

Question: \(B=?\)

(1) A's constant rate is 25 LTS / min --> \(A=25\) --> \((25+B)*30=C\) --> clearly insufficient (two unknowns), if \(C=1200\), then \(B=15\) but of \(C=1500\), then \(B=25\).

(2) The tanks capacity is 1200 lts. --> \(C=1200\). \((A+B)*30=1200\) --> \(A+B=40\). Also insufficient.

(1)+(2) \(A=25\) and \(A+B=40\) --> \(B=15\). Sufficient.

Re: Collection of work/rate problems? [#permalink]

Show Tags

09 Nov 2012, 08:41

Bunuel wrote:

brooksbrahs wrote:

h2polo wrote:

15. working together at their constant rates , A and B can fill an empty tank to capacity in1/2 hr.what is the constant rate of pump B? 1) A's constant rate is 25LTS / min 2) the tanks capacity is 1200 lts.

From the original statement we know that: 1/A + 1/B = 1/(1/2)

From Statement 1 we can plug in and find B: SUFFICIENT

Statement 2 is completely unnecessary:

ANSWER: A. Statement 1 alone is sufficient

I don't think this is correct. We know that the rate of A and B = 1/30 of a tank per minute (given in the stem). If A had said that pump A fills X OF THE TANK per minute, then it'd be sufficient alone since A + B = rate of A + rate of B and can solve for rate of B given that we know A. However, this gives it to us in units other than what the stem gave us, so we need to know the tank's capacity. Statement 2 gives us the capacity, so if we use them in conjunction, we can solve the problem. Should be C, not A, IMO.

Yes, the answer to this question is C not A.

Working together at their constant rates, A and B can fill an empty tank to capacity in 1/2 hours. What is the constant rate of pump B?

\(rate*time=job\).

We are told that \((A+B)*30=C\), where \(A\) is the rate of pump A in lts/min, \(B\) is the rate of pump B in lts/min and C is the capacity of the tank in liters.

Question: \(B=?\)

(1) A's constant rate is 25 LTS / min --> \(A=25\) --> \((25+B)*30=C\) --> clearly insufficient (two unknowns), if \(C=1200\), then \(B=15\) but of \(C=1500\), then \(B=25\).

(2) The tanks capacity is 1200 lts. --> \(C=1200\). \((A+B)*30=1200\) --> \(A+B=40\). Also insufficient.

(1)+(2) \(A=25\) and \(A+B=40\) --> \(B=15\). Sufficient.

Thanks for the detailed answer, it was useful, but did my logic in my previous post make sense? I've found that for a lot of these data sufficiency questions, the best way to solve them is to figure out what the stem has given and what information needs to be found to solve it. From there, one can just analyze what the two statements give independently and then figure out if each or both together are sufficient together without necessarily solving it. Obviuosly, there will need to be calculation done to figure out what it's giving you, but I have noticed that I can save A LOT of time by not formally solving them and just conjecturing logically as to whether or not it's useful, particularly if I'm in a time crunch. Therefore, I just wanted to check if what I stated in my previous post made sense logically, because that's how I solved it and I want to make sure my method seems somewhat sound. _________________

Please give kudos if you found my post useful, I give kudos back

Re: Collection of work/rate problems? [#permalink]

Show Tags

15 Nov 2012, 17:43

I think B would be the correct answer.

Let machine y produce = Y bottles in 3 hrs ( rate = y/3 bottles/hr) Let machine x produce = 2Y bottles in 4 hrs ( rate = 2y/4 = y/2 bottles/hr)

Total no of bottles produced by both x and y = 3Y.

So, time machine x takes to produce 3Y bottles is = 3Y/(Y/2) = 6hrs.

snipertrader wrote:

28.Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken machine X operating alone to fill the entire production lot?

(1) Machine X produced 30 bottles per minute. (2) Machine X produced twice as many bottles in 4hours as machine Y produced in 3 hours.

Ans C With Statement 1 - we cant find out the total work With Statement II - we can only express the speed of one machine in terms of the other

Both statements are needed for the complete picture

Re: Collection of work/rate problems? [#permalink]

Show Tags

16 Nov 2012, 05:17

Expert's post

ks4gsb wrote:

I think B would be the correct answer.

Let machine y produce = Y bottles in 3 hrs ( rate = y/3 bottles/hr) Let machine x produce = 2Y bottles in 4 hrs ( rate = 2y/4 = y/2 bottles/hr)

Total no of bottles produced by both x and y = 3Y.

So, time machine x takes to produce 3Y bottles is = 3Y/(Y/2) = 6hrs.

snipertrader wrote:

28.Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken machine X operating alone to fill the entire production lot?

(1) Machine X produced 30 bottles per minute. (2) Machine X produced twice as many bottles in 4hours as machine Y produced in 3 hours.

Ans C With Statement 1 - we cant find out the total work With Statement II - we can only express the speed of one machine in terms of the other

Both statements are needed for the complete picture

Yes, the answer to this question is B.

Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken Machine X operating alone to fill the entire production lot?

Let the rate of X be \(x\) bottle/hour and the rate of Y \(y\) bottle/hour. Given: \(4x+3y=job\). Question: \(t_x=\frac{job}{rate}=\frac{job}{x}=?\)

(1) Machine X produced 30 bottles per minute --> \(x=30*60=1800\) bottle/hour, insufficient as we don't know how many bottles is in 1 lot (job). (2) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours --> \(4x=2*3y\), so \(3y=2x\) --> \(4x+3y=4x+2x=6x=job\) --> \(t_x=\frac{job}{rate}=\frac{job}{x}=\frac{6x}{x}=6\) hours. Sufficient.

Re: Collection of work/rate problems? [#permalink]

Show Tags

10 Nov 2014, 18:19

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: Collection of work/rate problems? [#permalink]

Show Tags

29 Dec 2014, 08:30

Hello,

Can I have the solution for 23 please? I am not sure if I understand the question to be honest though. Are we looking for the number of days that it would take Michael to finish the whole project seperately of after the 12 days that they have been working together? Or neither of the two..?

Re: Collection of work/rate problems? [#permalink]

Show Tags

31 Dec 2014, 04:20

Expert's post

pacifist85 wrote:

Hello,

Can I have the solution for 23 please? I am not sure if I understand the question to be honest though. Are we looking for the number of days that it would take Michael to finish the whole project seperately of after the 12 days that they have been working together? Or neither of the two..?

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...