January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52144

Question Stats:
53% (02:33) correct 47% (03:09) wrong based on 220 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 52144

Re M1720
[#permalink]
Show Tags
16 Sep 2014, 00:01
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 \(a4\) minutes. The rate of A would be \(rate=\frac{job}{time}=\frac{40}{a}\) pages per minute and the rate of B \(rate=\frac{job}{time}=\frac{40}{a4}\) pages per minute. Their combined rate would be \(\frac{40}{a}+\frac{40}{a4}\) 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 \(\frac{40}{a}+\frac{40}{a4}=\frac{50}{6}\). \(\frac{40}{a}+\frac{40}{a4}=\frac{50}{6}\). Divide by 40: \(\frac{1}{a}+\frac{1}{a4}=\frac{5}{24}\). 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
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 04 Sep 2014
Posts: 4
Location: India
Concentration: Operations, Other

Re: M1720
[#permalink]
Show Tags
22 Mar 2016, 21:08
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 \(a4\) minutes. The rate of A would be \(rate=\frac{job}{time}=\frac{40}{a}\) pages per minute and the rate of B \(rate=\frac{job}{time}=\frac{40}{a4}\) pages per minute. Their combined rate would be \(\frac{40}{a}+\frac{40}{a4}\) 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 \(\frac{40}{a}+\frac{40}{a4}=\frac{50}{6}\). \(\frac{40}{a}+\frac{40}{a4}=\frac{50}{6}\). Divide by 40: \(\frac{1}{a}+\frac{1}{a4}=\frac{5}{24}\). 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 "a4" and not the other way around?



Math Expert
Joined: 02 Aug 2009
Posts: 7200

Re: M1720
[#permalink]
Show Tags
22 Mar 2016, 21:16
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 \(a4\) minutes. The rate of A would be \(rate=\frac{job}{time}=\frac{40}{a}\) pages per minute and the rate of B \(rate=\frac{job}{time}=\frac{40}{a4}\) pages per minute. Their combined rate would be \(\frac{40}{a}+\frac{40}{a4}\) 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 \(\frac{40}{a}+\frac{40}{a4}=\frac{50}{6}\). \(\frac{40}{a}+\frac{40}{a4}=\frac{50}{6}\). Divide by 40: \(\frac{1}{a}+\frac{1}{a4}=\frac{5}{24}\). 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 "a4" and not the other way around? hi, printer A= a, B=a4.. 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
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Senior Manager
Joined: 31 Mar 2016
Posts: 384
Location: India
Concentration: Operations, Finance
GPA: 3.8
WE: Operations (Commercial Banking)

Re M1720
[#permalink]
Show Tags
04 Aug 2016, 04:15
I think this is a highquality question and I agree with explanation.



Intern
Joined: 01 Oct 2014
Posts: 23

Re: M1720
[#permalink]
Show Tags
26 Aug 2016, 02:18
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 \(a4\) minutes. The rate of A would be \(rate=\frac{job}{time}=\frac{40}{a}\) pages per minute and the rate of B \(rate=\frac{job}{time}=\frac{40}{a4}\) pages per minute. Their combined rate would be \(\frac{40}{a}+\frac{40}{a4}\) 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 \(\frac{40}{a}+\frac{40}{a4}=\frac{50}{6}\). \(\frac{40}{a}+\frac{40}{a4}=\frac{50}{6}\). Divide by 40: \(\frac{1}{a}+\frac{1}{a4}=\frac{5}{24}\). 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?



Math Expert
Joined: 02 Sep 2009
Posts: 52144

Re: M1720
[#permalink]
Show Tags
26 Aug 2016, 03:01
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 \(a4\) minutes. The rate of A would be \(rate=\frac{job}{time}=\frac{40}{a}\) pages per minute and the rate of B \(rate=\frac{job}{time}=\frac{40}{a4}\) pages per minute. Their combined rate would be \(\frac{40}{a}+\frac{40}{a4}\) 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 \(\frac{40}{a}+\frac{40}{a4}=\frac{50}{6}\). \(\frac{40}{a}+\frac{40}{a4}=\frac{50}{6}\). Divide by 40: \(\frac{1}{a}+\frac{1}{a4}=\frac{5}{24}\). 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: m17184126.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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 01 Oct 2014
Posts: 23

Re: M1720
[#permalink]
Show Tags
26 Aug 2016, 03:06
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 \(a4\) minutes. The rate of A would be \(rate=\frac{job}{time}=\frac{40}{a}\) pages per minute and the rate of B \(rate=\frac{job}{time}=\frac{40}{a4}\) pages per minute. Their combined rate would be \(\frac{40}{a}+\frac{40}{a4}\) 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 \(\frac{40}{a}+\frac{40}{a4}=\frac{50}{6}\). \(\frac{40}{a}+\frac{40}{a4}=\frac{50}{6}\). Divide by 40: \(\frac{1}{a}+\frac{1}{a4}=\frac{5}{24}\). 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: m17184126.html#p1663300Yeah got it,Thanks a lot..! lol ,major silly mistake!



Senior Manager
Joined: 26 Jun 2017
Posts: 400
Location: Russian Federation
Concentration: General Management, Strategy
WE: Information Technology (Other)

Re: M1720
[#permalink]
Show Tags
22 Aug 2017, 12:13
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.



Current Student
Joined: 17 Sep 2017
Posts: 8
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: M1720
[#permalink]
Show Tags
09 Nov 2017, 12:20
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



Manager
Joined: 31 Oct 2016
Posts: 106

Re: M1720
[#permalink]
Show Tags
04 Jan 2018, 01:04
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



Manager
Joined: 20 Jan 2016
Posts: 88
Location: Canada
WE: Consulting (Other)

Re: M1720
[#permalink]
Show Tags
16 Jul 2018, 11:23
BunuelCan this be solved using weighted average?
_________________
Migatte no Gokui



Manager
Joined: 07 Feb 2017
Posts: 188

Re: M1720
[#permalink]
Show Tags
16 Jul 2018, 11:55
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^2280x960 0=5x^228x96 0=(5x+12)(x8) x=8
40/12 t = 80 t=24 min Answer D










