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M17-20

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M17-20 [#permalink]

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New post 16 Sep 2014, 01:01
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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
[Reveal] Spoiler: OA

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Re M17-20 [#permalink]

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New post 16 Sep 2014, 01:01
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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).

Answer D works:

\(2a=24\);

\(a=12\);

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


Answer: D
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Collection of Questions:
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DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M17-20 [#permalink]

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New post 22 Mar 2016, 22:08
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).

Answer D works:

\(2a=24\);

\(a=12\);

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


Answer: D


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?

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Re: M17-20 [#permalink]

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New post 22 Mar 2016, 22:16
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).

Answer D works:

\(2a=24\);

\(a=12\);

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


Answer: D


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

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Re M17-20 [#permalink]

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New post 04 Aug 2016, 05:15
I think this is a high-quality question and I agree with explanation.

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Re: M17-20 [#permalink]

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New post 26 Aug 2016, 03:18
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).

Answer D works:

\(2a=24\);

\(a=12\);

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


Answer: D



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?

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Re: M17-20 [#permalink]

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New post 26 Aug 2016, 04:01
89renegade 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).

Answer D works:

\(2a=24\);

\(a=12\);

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


Answer: D



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
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128980 [0], given: 12185

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Re: M17-20 [#permalink]

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New post 26 Aug 2016, 04:06
Bunuel wrote:
89renegade 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).

Answer D works:

\(2a=24\);

\(a=12\);

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


Answer: D



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!

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Re: M17-20 [#permalink]

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New post 22 Aug 2017, 13:13
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.

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Re: M17-20   [#permalink] 22 Aug 2017, 13:13
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