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Math Expert V
Joined: 02 Sep 2009
Posts: 56261

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3
18 00:00

Difficulty:   95% (hard)

Question Stats: 55% (02:58) correct 45% (03:16) wrong based on 190 sessions

### HideShow timer Statistics It takes printer A 4 more minutes than printer B to print 40 pages. If working together, the two printers can print 50 pages in 6 minutes, how long will it take printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56261

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Official Solution:

It takes printer A 4 more minutes than printer B to print 40 pages. If working together, the two printers can print 50 pages in 6 minutes, how long will it take printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

Let the time needed to print 40 pages for printer A be $$a$$ minutes, so for printer B it would be $$a-4$$ minutes.

The rate of A would be $$rate=\frac{job}{time}=\frac{40}{a}$$ pages per minute and the rate of B $$rate=\frac{job}{time}=\frac{40}{a-4}$$ pages per minute.

Their combined rate would be $$\frac{40}{a}+\frac{40}{a-4}$$ pages per minute. Also as "two printers can print 50 pages in 6 minutes" then their combined rate is $$rate=\frac{job}{time}=\frac{50}{6}$$, so $$\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}$$.

$$\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}$$. Divide by 40: $$\frac{1}{a}+\frac{1}{a-4}=\frac{5}{24}$$. At this point we can either try to substitute the values from answer choices or solve quadratic equation. Remember as we are asked to find the time needed for printer A to print $$80$$ pages, then the answer would be $$2a$$ (as $$a$$ is the time needed to print $$40$$ pages).

$$2a=24$$;

$$a=12$$;

$$\frac{1}{12}+\frac{1}{8}=\frac{5}{24}$$.

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Intern  B
Joined: 04 Sep 2014
Posts: 3
Location: India
Concentration: Operations, Other

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Bunuel wrote:
Official Solution:

It takes printer A 4 more minutes than printer B to print 40 pages. If working together, the two printers can print 50 pages in 6 minutes, how long will it take printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

Let the time needed to print 40 pages for printer A be $$a$$ minutes, so for printer B it would be $$a-4$$ minutes.

The rate of A would be $$rate=\frac{job}{time}=\frac{40}{a}$$ pages per minute and the rate of B $$rate=\frac{job}{time}=\frac{40}{a-4}$$ pages per minute.

Their combined rate would be $$\frac{40}{a}+\frac{40}{a-4}$$ pages per minute. Also as "two printers can print 50 pages in 6 minutes" then their combined rate is $$rate=\frac{job}{time}=\frac{50}{6}$$, so $$\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}$$.

$$\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}$$. Divide by 40: $$\frac{1}{a}+\frac{1}{a-4}=\frac{5}{24}$$. At this point we can either try to substitute the values from answer choices or solve quadratic equation. Remember as we are asked to find the time needed for printer A to print $$80$$ pages, then the answer would be $$2a$$ (as $$a$$ is the time needed to print $$40$$ pages).

$$2a=24$$;

$$a=12$$;

$$\frac{1}{12}+\frac{1}{8}=\frac{5}{24}$$.

I tried to solve this question by considering time taken by B as "a" and that by printer A as "a+4" but was unable to solve the question. Why should B's time be "a" and A's time be "a-4" and not the other way around?
Math Expert V
Joined: 02 Aug 2009
Posts: 7764

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vdhaval wrote:
Bunuel wrote:
Official Solution:

It takes printer A 4 more minutes than printer B to print 40 pages. If working together, the two printers can print 50 pages in 6 minutes, how long will it take printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

Let the time needed to print 40 pages for printer A be $$a$$ minutes, so for printer B it would be $$a-4$$ minutes.

The rate of A would be $$rate=\frac{job}{time}=\frac{40}{a}$$ pages per minute and the rate of B $$rate=\frac{job}{time}=\frac{40}{a-4}$$ pages per minute.

Their combined rate would be $$\frac{40}{a}+\frac{40}{a-4}$$ pages per minute. Also as "two printers can print 50 pages in 6 minutes" then their combined rate is $$rate=\frac{job}{time}=\frac{50}{6}$$, so $$\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}$$.

$$\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}$$. Divide by 40: $$\frac{1}{a}+\frac{1}{a-4}=\frac{5}{24}$$. At this point we can either try to substitute the values from answer choices or solve quadratic equation. Remember as we are asked to find the time needed for printer A to print $$80$$ pages, then the answer would be $$2a$$ (as $$a$$ is the time needed to print $$40$$ pages).

$$2a=24$$;

$$a=12$$;

$$\frac{1}{12}+\frac{1}{8}=\frac{5}{24}$$.

I tried to solve this question by considering time taken by B as "a" and that by printer A as "a+4" but was unable to solve the question. Why should B's time be "a" and A's time be "a-4" and not the other way around?

hi,
printer A= a, B=a-4..
OR
printer B=a and A= a+4..

both the above cases are same and if you have taken the second case, be careful in that you are getting a as value of B and you will have to convert to A's time..
You could be going wrong there, otherwise you should get the answer either way

_________________
Senior Manager  Joined: 31 Mar 2016
Posts: 376
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34 GPA: 3.8
WE: Operations (Commercial Banking)

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1
I think this is a high-quality question and I agree with explanation.
Intern  B
Joined: 01 Oct 2014
Posts: 39
Schools: DeGroote'21 (A)

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Bunuel wrote:
Official Solution:

It takes printer A 4 more minutes than printer B to print 40 pages. If working together, the two printers can print 50 pages in 6 minutes, how long will it take printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

Let the time needed to print 40 pages for printer A be $$a$$ minutes, so for printer B it would be $$a-4$$ minutes.

The rate of A would be $$rate=\frac{job}{time}=\frac{40}{a}$$ pages per minute and the rate of B $$rate=\frac{job}{time}=\frac{40}{a-4}$$ pages per minute.

Their combined rate would be $$\frac{40}{a}+\frac{40}{a-4}$$ pages per minute. Also as "two printers can print 50 pages in 6 minutes" then their combined rate is $$rate=\frac{job}{time}=\frac{50}{6}$$, so $$\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}$$.

$$\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}$$. Divide by 40: $$\frac{1}{a}+\frac{1}{a-4}=\frac{5}{24}$$. At this point we can either try to substitute the values from answer choices or solve quadratic equation. Remember as we are asked to find the time needed for printer A to print $$80$$ pages, then the answer would be $$2a$$ (as $$a$$ is the time needed to print $$40$$ pages).

$$2a=24$$;

$$a=12$$;

$$\frac{1}{12}+\frac{1}{8}=\frac{5}{24}$$.

why do we have to take 40/a+40/a−4 and not 40/a+40/a+4 why is my answer not coming right?
Math Expert V
Joined: 02 Sep 2009
Posts: 56261

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Bunuel wrote:
Official Solution:

It takes printer A 4 more minutes than printer B to print 40 pages. If working together, the two printers can print 50 pages in 6 minutes, how long will it take printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

Let the time needed to print 40 pages for printer A be $$a$$ minutes, so for printer B it would be $$a-4$$ minutes.

The rate of A would be $$rate=\frac{job}{time}=\frac{40}{a}$$ pages per minute and the rate of B $$rate=\frac{job}{time}=\frac{40}{a-4}$$ pages per minute.

Their combined rate would be $$\frac{40}{a}+\frac{40}{a-4}$$ pages per minute. Also as "two printers can print 50 pages in 6 minutes" then their combined rate is $$rate=\frac{job}{time}=\frac{50}{6}$$, so $$\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}$$.

$$\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}$$. Divide by 40: $$\frac{1}{a}+\frac{1}{a-4}=\frac{5}{24}$$. At this point we can either try to substitute the values from answer choices or solve quadratic equation. Remember as we are asked to find the time needed for printer A to print $$80$$ pages, then the answer would be $$2a$$ (as $$a$$ is the time needed to print $$40$$ pages).

$$2a=24$$;

$$a=12$$;

$$\frac{1}{12}+\frac{1}{8}=\frac{5}{24}$$.

why do we have to take 40/a+40/a−4 and not 40/a+40/a+4 why is my answer not coming right?

Please check the discussion above. For example, this post: m17-184126.html#p1663300
_________________
Intern  B
Joined: 01 Oct 2014
Posts: 39
Schools: DeGroote'21 (A)

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Bunuel wrote:
Bunuel wrote:
Official Solution:

It takes printer A 4 more minutes than printer B to print 40 pages. If working together, the two printers can print 50 pages in 6 minutes, how long will it take printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

Let the time needed to print 40 pages for printer A be $$a$$ minutes, so for printer B it would be $$a-4$$ minutes.

The rate of A would be $$rate=\frac{job}{time}=\frac{40}{a}$$ pages per minute and the rate of B $$rate=\frac{job}{time}=\frac{40}{a-4}$$ pages per minute.

Their combined rate would be $$\frac{40}{a}+\frac{40}{a-4}$$ pages per minute. Also as "two printers can print 50 pages in 6 minutes" then their combined rate is $$rate=\frac{job}{time}=\frac{50}{6}$$, so $$\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}$$.

$$\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}$$. Divide by 40: $$\frac{1}{a}+\frac{1}{a-4}=\frac{5}{24}$$. At this point we can either try to substitute the values from answer choices or solve quadratic equation. Remember as we are asked to find the time needed for printer A to print $$80$$ pages, then the answer would be $$2a$$ (as $$a$$ is the time needed to print $$40$$ pages).

$$2a=24$$;

$$a=12$$;

$$\frac{1}{12}+\frac{1}{8}=\frac{5}{24}$$.

why do we have to take 40/a+40/a−4 and not 40/a+40/a+4 why is my answer not coming right?

Please check the discussion above. For example, this post: m17-184126.html#p1663300

Yeah got it,Thanks a lot..! lol ,major silly mistake!
Senior Manager  P
Joined: 26 Jun 2017
Posts: 404
Location: Russian Federation
Concentration: General Management, Strategy
WE: Information Technology (Other)

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Bunuel wrote:
It takes printer A 4 more minutes than printer B to print 40 pages. If working together, the two printers can print 50 pages in 6 minutes, how long will it take printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

I like the solution when after we get to 1/a+1/(a−4)=5/24, we check the answer choices.

I solved the full quadr equation:
50/ (40/(t+4) + 40/t) = 6 - got pretty big numbers and although i solved it correct, it took me over 4 minutes, which is unacceptable. (We have to find 2t+8 in this case).

But then I realized, that we can simplify this equation.
It takes printer A 4 more minutes than printer B to print 40 pages = It takes printer A 1 more minute than printer B to print 10 pages
In this case we have to solve next equation:
50/(10/(t+1) + 10/t) = 6 (and to find 2t+8)- this is much faster than the first one.
Current Student B
Joined: 17 Sep 2017
Posts: 8
Concentration: Finance, Entrepreneurship
Schools: Oxford"19 (A)
GMAT 1: 730 Q48 V42 GPA: 3.8

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1
Speaking of taking 4 minutes...

Found it quicker to solve this in terms of printer B:

Time it takes printer A to do 40 pages, $$A, = B+4$$ minutes
Thus, to do 80 pages as question asks, $$A, = 2(B+4)$$ minutes

Next, $$R$$A $$+$$ $$R$$B $$=$$ $$\frac{25}{3}$$ $$=>$$ $$\frac{40}{B+4}$$ + $$\frac{40}{B}$$ = $$\frac{25}{3}$$

At this point, eyeballing is useful: $$B=10$$ or $$B=5$$ are clearly out and a little mental stretching suggests only $$B=8$$ fits the quadratic

If $$B=8$$, then $$A = 2(8+4) = 24$$ minutes
Manager  B
Joined: 31 Oct 2016
Posts: 106

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How did I solve using approximation?

Let's assume that both of them are the same printers and let's replace 40 pages by 50 pages. Together they printed 50 pages in 6 minutes. It means that 1 printer can print 50 pages in 12 minutes.
12 minutes - our average time taken by both different printers. Given that A is slower than B for 4 minutes, the only values we can get are 10 and 14 minutes (average is 12, and one is more gradual than another for 4 minutes).

Printer A can print 50 pages in 14 minutes and 100 pages in 28 minutes. Therefore, it can print 80 pages a little bit faster than 28 minutes. Answer - 24 minutes. Confidence - 80%. Time - about 1 minute
Manager  B
Joined: 20 Jan 2016
Posts: 83
Schools: HBS '18
WE: Consulting (Other)

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Bunuel

Can this be solved using weighted average?
_________________
Migatte no Gokui
Manager  S
Joined: 07 Feb 2017
Posts: 182

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Rates: 40/x
40/(x+4)

40/x*6+40/(x+4)*6=50
240/x+240/(x+4)=50
240(x+4)+240x=50x(x+4)
240x+960+240x=50x^2+200x
0=50x^2-280x-960
0=5x^2-28x-96
0=(5x+12)(x-8)
x=8

40/12 t = 80
t=24 min
Manager  S
Joined: 21 Jul 2018
Posts: 193

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Bunuel wrote:
It takes printer A 4 more minutes than printer B to print 40 pages. If working together, the two printers can print 50 pages in 6 minutes, how long will it take printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

Tried to find correct answer through POE and solved in less than 2 mins and you can also reach to correct ans if you don't have superb knowledge which required to use above described method, Following are the steps which I followed.

1) Try to plugin value of option C(medium value) 80/20 = 4 PPM (Pages Per Min), hence in 6 min A will print 24 pages hence B will print 26 pages hence B will print 26/6 PPM but calculation will get difficult if you try to prove 1st condition and GMAT never give difficult calculations as it tests your logic skills and not calculation skills.

2) Try with option B 80/18 = 40/9 PPM, hence in 6 Min A will print 40/9 * 6 = 26 pages which is not possible as A can not print more than 50% of pages in total contribution of 50 pages as it works slow than B.

3) Now You can also eliminate option A as Printer A can not take less than 18 Min. Hence Option A, B, and C is canceled and left with D and E.

4) Try with option D 80/24 = 10/3 PPM, hence in 6 min Printer A will print 10/3 * 6 = 20 pages and B will print 50-20 = 30 Pages. Hence B can print 30/6 = 5 PPM
Now plug in this value for 1st condition and you will find that A will print 40 pages in 12 min and B will print 40 pages in 8 min. Got your ans.

This looks like time consuming but it is not if you perform most of the steps in Brain and not Paper.

Hi chetan2u, Bunuel,

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Please let me know if I'm wrong somewhere and help me to learn  M17-20   [#permalink] 26 Feb 2019, 13:03
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# M17-20

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