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Bunuel
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When working together, printers A and B can finish printing the entire Updated on: 29 Nov 2023, 00:58
Originally posted by Bunuel on 01 Sep 2010, 11:12.
Last edited by Bunuel on 29 Nov 2023, 00:58, edited 3 times in total.
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When working together, printers A and B can finish printing the entire document in 24 minutes. If printer A by itself can finish printing the document in 60 minutes, how many pages does the document have if printer B prints 5 pages more per minute than printer A?

A. 600
B. 800
C. 1000
D. 1200
E. 1500

M23-16

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Bunuel
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When working together, printers A and B can finish printing the entire 01 Sep 2010, 12:56
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When working together, printers A and B can finish printing the entire document in 24 minutes. If printer A by itself can finish printing the document in 60 minutes, how many pages does the document have if printer B prints 5 pages more per minute than printer A?

A. 600
B. 800
C. 1000
D. 1200
E. 1500


Let \(a\) denote the number of pages Printer A prints in one minute.

Let \(b\) denote the number of pages Printer B prints in one minute.

Given that printers A and B together can print the entire document in 24 minutes, the total number of pages in the document is \(24a + 24b\).

However, when Printer A works alone, it completes the document in 60 minutes, implying the document consists of \(60a\) pages.

Thus, \(24a + 24b = 60a\). Given that \(b = a + 5\), we would get \(24a + 24(a + 5) = 60a\), which results in \(a=10\).

Therefore, the document has \(60a=600\) pages.


Answer: A

Hope it helps.
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When working together, printers A and B can finish printing the entire 03 Sep 2010, 11:26
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B in a minute=x/40
A in a minute=x/60
then,
x/40-x/60=5

Solving x=600
General Discussion
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When working together, printers A and B can finish printing the entire 08 Sep 2012, 05:51
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First thing i did was i found out time that is required to B to complete the task alone: 1/24-1/60=3/120=1/40. Then i looked at the information which states that the rate of B is 5+ page than that of A so, lets say x is the number of pages printed by A per minute, so the task consists of 60*x or 40*(x+5) pages. I can make an equation: 60x=40(x+5), 20x=200, x=10, total number of pages is 60*10=600 or 40*15=600

Answer is A.

It is clear but it took me about 3 min to do it, does it because i am doing it slow or i am using longer route?
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When working together, printers A and B can finish printing the entire 15 Nov 2012, 05:37
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\(\frac{1}{A}=\frac{1}{60}\)
\(\frac{1}{B}+\frac{1}{A}=\frac{1}{24}\)

Get: \(\frac{1}{B}\)

\(\frac{1}{B}=\frac{1}{24}-\frac{1}{60}=\frac{1}{40}\)

Let p be the number of pages produced by A.
Let p+5 be the number of pages produced by B.

\(24(p + p+5) = 60(p)==> p=10pages\)

Answer: 60(p)=600pages
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When working together, printers A and B can finish printing the entire 04 Mar 2013, 00:40
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gauravnagpal
Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A ?

A. 600
B. 800
C. 1000
D. 1200
E. 1500

Show Spoiler
I know this question is relatively symol if make an equation in one vaibale ...
I tried to do it by applying the fundamental of A = Jobs per min * time ( the way we typically solve the work problems ) and i was stuck

I did jobs per minute A , 1/60
combined rate = 1/24

so rate of b = 1/24 - 1/60 = 1/40

but could not arrive at the solution ... i tried to form the equation by assuming x as the total numbe of pages So x/60+ x+5/40 = cld nt take ot forward from here
kindly see where am I losing the track !
Show more

total time taken by B = 24 * 60 / (60 -24) = 40 min.

A take 60 min. B takes 40 min to complete a task.

Now, divide the values given in option (in Ans) to get the rate per min.

option A: 600 / 10 = 60 & 600/40 = 15...> this satisfies the condition given in question stem that printer B prints 5 pages a minute more than printer A ?
. therefore A
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When working together, printers A and B can finish printing the entire 18 Mar 2014, 07:00
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Rate A= X
Rate B= X+5

Work(A)=> X * 60 = 60X

Rate(A+B) * 24 = Work

(2X+5) * 24 = 60X

X=10
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When working together, printers A and B can finish printing the entire 15 May 2014, 11:02
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Easiest way to do this: Machine A and B can do the task in 24 minutes thus Rate of A and B = 1/24. Now given A can do the task in 60 minutes therefore Rate of A= 1/60. We know that Rate of A and B = Rate of A + Rate of B therefore Rate of B= Rate of A and B - Rate of A = 1/24-1/60= 1/40. Now we know that Rate of B = 1/40 thus B can do the work in 40 minutes.

Let pages printed per minute by A = x, given that pages printed by B per minute is 5 more than that of A
Pages printed by B per minute = x+5
Now Complete task is done by A in 60 minutes therefore total number of pages printed by A = x * 60
Also Complete task is done by B in 40 minutes therefore total number of pages printed by B = (x+5) * 40
therefore x * 60 = (x+5) * 40
therefore x=10
thus the total number of pages in task = x*60 = 10*60 = 600 :-D
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When working together, printers A and B can finish printing the entire 18 Jul 2016, 05:29
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gauravnagpal
Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A ?

A. 600
B. 800
C. 1000
D. 1200
E. 1500

Show Spoiler
I know this question is relatively symol if make an equation in one vaibale ...
I tried to do it by applying the fundamental of A = Jobs per min * time ( the way we typically solve the work problems ) and i was stuck

I did jobs per minute A , 1/60
combined rate = 1/24

so rate of b = 1/24 - 1/60 = 1/40

but could not arrive at the solution ... i tried to form the equation by assuming x as the total numbe of pages So x/60+ x+5/40 = cld nt take ot forward from here
kindly see where am I losing the track !
Show more


Okay..this is how I did it..
Let the task(number of pages) be 120x(LCM of all numbers given in the problem)..

A and B take 24 minutes to complete it..thus, pages per min = 5x
A's pages per minute = 2x
B's pages per minute = 3x

Difference
3x - 2x = 5
=> x = 5
Thus, 120x = 600..(A)
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When working together, printers A and B can finish printing the entire 26 Jul 2020, 15:47
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gauravnagpal
Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A ?

A. 600
B. 800
C. 1000
D. 1200
E. 1500

Show more
Solution:

We can let x = the number of minutes it takes printer B to finish the task by itself and create the equation:

1/60 + 1/x = 1/24

Multiplying both sides of the equation by 120x, we have:

2x+ 120 = 5x

120 = 3x

40 = x

Now, if we let n = the total number of pages the task has and since printer B prints 5 pages a minute more than printer A, we can recreate the equation:

n/60 + 5 = n/40

Multiplying both sides of the equation by 120, we have:

2n + 600 = 3n

600 = n

Answer: A
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When working together, printers A and B can finish printing the entire 23 May 2022, 19:43
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gauravnagpal
Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A ?

A. 600
B. 800
C. 1000
D. 1200
E. 1500

Show Spoiler
I know this question is relatively symol if make an equation in one vaibale ...
I tried to do it by applying the fundamental of A = Jobs per min * time ( the way we typically solve the work problems ) and i was stuck

I did jobs per minute A , 1/60
combined rate = 1/24

so rate of b = 1/24 - 1/60 = 1/40

but could not arrive at the solution ... i tried to form the equation by assuming x as the total numbe of pages So x/60+ x+5/40 = cld nt take ot forward from here
kindly see where am I losing the track !
Show more


Why on earth would we not use PITA (Plugging In The Answers) rather than doing the algebra?!?! You get zero bonus points for doing the "real" math. The GMAT is not a math test. It is a test of whether you can get the right answers quickly, efficiently, without causing yourself fatigue, and without setting yourself up to make careless mistakes.

We know we need to be a multiple of 24 and of 60. B, C, and E are wrong. Cool, down to A and D. A looks easier to work with, so let's try that.

If the task is to print 600 pages and A can finish in 60 minutes, A prints 10 pages per minute. B prints 5 pages per minute more than A, so B prints 15 pages per minute. Together, they print 25 pages per minute. If they work together for 24 minutes, will they finish the 600 pages? Yep.

Answer choice A.


ThatDudeKnowsPITA
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When working together, printers A and B can finish printing the entire 28 Nov 2023, 22:51
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Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A ?

A. 600
B. 800
C. 1000
D. 1200
E. 1500

For A: W = W | R = W/60 | T = 60 mins
For B: W = W | R = (W/60)+5 | T = t

Combined W rate = 24 mins
W = [W/60 + (W/60)+5]*24 (W=RT)

Upon simplifying we get,

60W = [(2W + 300)/60]*24
12W = 7200
W = 600 pages
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When working together, printers A and B can finish printing the entire 20 Dec 2024, 23:30
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it can be done in like this way to : take lcm of of 60 and 34 which is 120 page total work done by both printer in 18 minutes. simply since a print rate is same and only b prints 5 more pages than A and A has fixed printing rate which is 120/60 2 page/minute only the b printing rate is changes so just multiply by 5 because addition 5 pages are printed in the previous work, total work = 120*5 which is 600 pages
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When working together, printers A and B can finish printing the entire 21 Dec 2024, 05:17
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Given when both printers work together they finish the document in 24 min
and a takes 60 min individualy

therefore 1/a + 1/b = 1/60 + 1/b = 1/24
==> b = 40

the difference in page printed is 5
taking 'x' as total number of pages'
1/b - 1/a = 5/x ==> 1/40 - 1/60 = 5/x
==> x=600 (Option A)
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