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Re M17-20 [#permalink]
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 16 Sep 2014, 01:01
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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Re: M17-20 [#permalink]
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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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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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04 Aug 2016, 05:15
1
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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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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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Math Expert
Joined: 02 Sep 2009
Posts: 44588
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Re: M17-20 [#permalink]
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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
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Intern
Joined: 01 Oct 2014
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Re: M17-20 [#permalink]
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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#p1663300Yeah got it,Thanks a lot..! lol ,major silly mistake!
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Re: M17-20 [#permalink]
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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]
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09 Nov 2017, 13:20
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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, \(A[40], = B+4\) minutes
Thus, to do 80 pages as question asks, \(A[80], = 2(B+4)\) 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 \(A[80] = 2(8+4) = 24\) minutes
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Re: M17-20 [#permalink]
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04 Jan 2018, 02:04
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
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