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Collection of work/rate problems?

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

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22 Oct 2011, 06:47
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.

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

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16 Dec 2011, 08:13
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

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

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31 Jan 2012, 23:41
does anyone have all these problems in one document? if yes,please share
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Re: Collection of work/rate problems? [#permalink]

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29 May 2012, 09:54
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.

(1) Insuf
(2) Suff... because:
4x = (3y) * 2
4x = 6y
y = 4/6x, = 2/3x.

New rate table:

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

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29 May 2012, 10:17
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.

(1) Insuf
(2) Suff... because:
4x = (3y) * 2
4x = 6y
y = 4/6x, = 2/3x.

New rate table:

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***

Hi jsnkwok,

You are absolutely correct.

Regards,

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

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09 Nov 2012, 04:20
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.

Discussed here: working-together-at-their-constant-rates-a-and-b-can-fill-97316.html
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Re: Collection of work/rate problems? [#permalink]

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09 Nov 2012, 07:41
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.

Discussed here: working-together-at-their-constant-rates-a-and-b-can-fill-97316.html

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

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15 Nov 2012, 16:43
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.

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

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16 Nov 2012, 04:17
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.

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.

Discussed here: machines-x-and-y-produced-identical-bottles-at-different-104208.html
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Re: Collection of work/rate problems? [#permalink]

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29 Dec 2014, 07:30
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..?

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

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31 Dec 2014, 03:20
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..?

Thank you.

This question is discussed here: micheal-and-adam-can-do-together-a-piece-of-work-in-20-days-61136.html
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Re: Collection of work/rate problems?   [#permalink] 31 Dec 2014, 03:20

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