Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 18 Nov 2010
Posts: 10

Machine A can process 6000 envelopes in 3 hours. Machines B [#permalink]
Show Tags
25 Nov 2010, 08:25
1
This post received KUDOS
19
This post was BOOKMARKED
Question Stats:
83% (02:15) correct 17% (02:35) wrong based on 771 sessions
HideShow timer Statistics
Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 12000 envelopes. A. 2 B. 3 C. 4 D. 6 E. 60/7 I got this far:
Machine C = 6 hours for 6000 envelopes
Then (1/T) = (1/b) +(1/c)
1/2.5 = (1/b) + (1/6) b= (30/7) for 6000 envelopes or (60/7) for 12000 envelopes.
Why isnt the answer coming up to exactly 8? EDITED THE OPTIONS
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 06 Jun 2013, 00:42, edited 2 times in total.
Edited the options.



Math Expert
Joined: 02 Sep 2009
Posts: 44290

Re: Rate Problem [#permalink]
Show Tags
25 Nov 2010, 10:08
2
This post received KUDOS
Expert's post
3
This post was BOOKMARKED
shash wrote: Machine A can process 6000 envelopes in 3 hours. MAchines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 12000 envelopes.
2 3 4 6 8  Correct Answer
I got this far:
Machine C = 6 hours for 6000 envelopes
Then (1/T) = (1/b) +(1/c)
1/2.5 = (1/b) + (1/6) b= (30/7) for 6000 envelopes or (60/7) for 12000 envelopes.
Why isnt the answer coming up to exactly 8? I think you did everything right. Let the time needed for A, B and C working individually to process 6,000 envelopes be \(a\), \(b\) and \(c\) respectively. Now, as "A can process 6,000 envelopes in 3 hours" then \(a=3\); As "B and C working together but independently can process the same number ( 6,000) of envelopes in 2.5 hours" then \(\frac{1}{b}+\frac{1}{c}=\frac{1}{2.5}=\frac{2}{5}\); Also, as "A and C working together but independently process 3000 envelopes in 1 hour", then A and C working together but independently process 2*3,000= 6,000 envelopes in 2*1=2 hours: \(\frac{1}{a}+\frac{1}{c}=\frac{1}{2}\) > as \(a=3\) then \(c=6\); So, \(\frac{1}{b}+\frac{1}{6}=\frac{2}{5}\) > \(b=\frac{30}{7}\), which means that B produces 6,000 envelopes in 30/7 hours, thus it produces 12,000 envelopes in 60/7 hours. Answer: E.
_________________
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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7988
Location: Pune, India

Re: Rate Problem [#permalink]
Show Tags
25 Nov 2010, 21:11
13
This post received KUDOS
Expert's post
4
This post was BOOKMARKED
shash wrote: Machine A can process 6000 envelopes in 3 hours. MAchines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 12000 envelopes.
2 3 4 6 8  Correct Answer
I got this far:
Machine C = 6 hours for 6000 envelopes
Then (1/T) = (1/b) +(1/c)
1/2.5 = (1/b) + (1/6) b= (30/7) for 6000 envelopes or (60/7) for 12000 envelopes.
Why isnt the answer coming up to exactly 8? In work rate questions, generally different people have to complete the same amount of work. In this question, to make it a little tricky, they have given varying amount of work done by the machines. To make the question straight forward, first thing you can do is make the work the same for all: Machine A processes 12000 envelopes in  6 hrs Machines B and C process 12000 in  5 hrs Machines A and C process 12000 in  4 hrs I chose to get them all to 12000 since my question has 12000 in it. Also, I easily get rid of all decimals. Now, I just find 1/6 + 1/c = 1/4 and get c = 12 and 1/b + 1/12 = 1/5 so b = 60/7 hrs
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 30 Aug 2010
Posts: 91
Location: Bangalore, India

Re: Rate Problem [#permalink]
Show Tags
26 Nov 2010, 04:20
14
This post received KUDOS
1
This post was BOOKMARKED
forget abt the variables a,b,c,d.....in this simple problem
A  6000 in 3 hrs ==> 2000 in 1 hr BC 6000  in 2.5 hrs == 2400 in 1 hr AC  3000 in 1 hr
take AC 3000 in 1 hr , in which A's contribution is 2000 in 1 hr, hence C's contribution is 1000 in 1 hr take BC 2400 , in which C's contribution is 1000 in 1 hr, hence B's contribution is 1400 in 1 hr.
B  1400  1 hr ==> 12000 in 12000/1400 hrs = 60/7
Regards, Murali.



Intern
Joined: 03 Jun 2009
Posts: 49

Re: Rate Problem [#permalink]
Show Tags
27 Nov 2010, 11:07
1
This post was BOOKMARKED
muralimba wrote: forget abt the variables a,b,c,d.....in this simple problem
A  6000 in 3 hrs ==> 2000 in 1 hr BC 6000  in 2.5 hrs == 2400 in 1 hr AC  3000 in 1 hr
take AC 3000 in 1 hr , in which A's contribution is 2000 in 1 hr, hence C's contribution is 1000 in 1 hr take BC 2400 , in which C's contribution is 1000 in 1 hr, hence B's contribution is 1400 in 1 hr.
B  1400  1 hr ==> 12000 in 12000/1400 hrs = 60/7
Regards, Murali. Adding to Murali's approach.... A = 2000 B+C = 2400 A+C = 3000 => C = 30001 = 30002000 = 1000 => B = 2400 C =24001000 =1400 hence B can process 1400 Envelopes in 1hour...how much time wud it take B to process 12000 Envelopes = 12000/1400 = 60/7



Manager
Joined: 01 Nov 2010
Posts: 166
Location: Zürich, Switzerland

Re: Rate Problem [#permalink]
Show Tags
27 Nov 2010, 18:58
1
This post was BOOKMARKED
For 1 hour
Machine A rate 2000 envelopes Machine B+C rate 2400 envelopes Since A + C = 3000 envelopes A's rate is 2000 envelopes as above, C has a rate of 1000 envelopes per hour. Which makes machine B's rate as 1400 envelopes per hour.
Thus, it will take 8 hours to manufacture 12000 envelopes.
Answer:E



Math Expert
Joined: 02 Sep 2009
Posts: 44290

Re: Machine A can process 6000 envelopes in 3 hours. Machines B [#permalink]
Show Tags
30 May 2013, 05:09



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 624

Re: Machine A can process 6000 envelopes in 3 hours. Machines B [#permalink]
Show Tags
30 May 2013, 10:50
1
This post received KUDOS
shash wrote: Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 12000 envelopes.
A. 2 B. 3 C. 4 D. 6 E. 8
Machine A takes 3 hours for 6000 envelopes. Thus, Machine A would take exactly 6 hours for 12000 envelopes. Also, we know that machines B and C, working together, can produce the same no of envelopes in 2.5 hours. Thus, if\(r_B\) and\(r_C\) are the rates respectively , we know that\((r_B+r_C)*\frac{5}{2}\) = 6000 > \((r_B+r_C) = 2400\). Thus, even if we assume that \(r_B\) = 2000 (which is the same rate as that of Machine A), Machine B would again need 6 hours. However, as\(r_C\)= 1000, we know for sure that\(r_B\) <2000. Thus, the only option more than 6 hours is E(Assuming that the correct OA is provided with the question).
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Intern
Joined: 30 May 2013
Posts: 15

Re: Rate Problem [#permalink]
Show Tags
05 Jun 2013, 15:36
Sarang wrote: For 1 hour
Machine A rate 2000 envelopes Machine B+C rate 2400 envelopes Since A + C = 3000 envelopes A's rate is 2000 envelopes as above, C has a rate of 1000 envelopes per hour. Which makes machine B's rate as 1400 envelopes per hour.
Thus, it will take 8 hours to manufacture 12000 envelopes.
Answer:E I did this but shouldn't the work take 9 hours instead? In 8 hours machine B would have made 1400 * 8 = 11200 envelopes. In order to make 12000 it would require a fraction of an hour to create 200 more envelopes. Am I mistaken?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7988
Location: Pune, India

Re: Rate Problem [#permalink]
Show Tags
06 Jun 2013, 00:14
PKPKay wrote: Sarang wrote: For 1 hour
Machine A rate 2000 envelopes Machine B+C rate 2400 envelopes Since A + C = 3000 envelopes A's rate is 2000 envelopes as above, C has a rate of 1000 envelopes per hour. Which makes machine B's rate as 1400 envelopes per hour.
Thus, it will take 8 hours to manufacture 12000 envelopes.
Answer:E I did this but shouldn't the work take 9 hours instead? In 8 hours machine B would have made 1400 * 8 = 11200 envelopes. In order to make 12000 it would require a fraction of an hour to create 200 more envelopes. Am I mistaken? As mentioned above, the OA is incorrect. In fact, the options are incorrect since none of them is 60/7 hrs (which is the answer).
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Math Expert
Joined: 02 Sep 2009
Posts: 44290

Re: Rate Problem [#permalink]
Show Tags
06 Jun 2013, 00:44



Intern
Joined: 18 Mar 2013
Posts: 3

Re: Machine A can process 6000 envelopes in 3 hours. Machines B [#permalink]
Show Tags
07 Jun 2013, 05:35
How much time should one take in solving these kind of questions which involves though simple yet a lot of calculations?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7988
Location: Pune, India

Re: Machine A can process 6000 envelopes in 3 hours. Machines B [#permalink]
Show Tags
09 Jun 2013, 20:52
samheeta wrote: How much time should one take in solving these kind of questions which involves though simple yet a lot of calculations? This can be easily done in under 2 mins. If you look at the explanation provided above: To make the question straight forward, first thing you can do is make the work the same for all: Machine A processes 12000 envelopes in  6 hrs Machines B and C process 12000 in  5 hrs Machines A and C process 12000 in  4 hrs I chose to get them all to 12000 since my question has 12000 in it. Also, I easily get rid of all decimals. Almost no calculations till hereNow, I just find 1/6 + 1/c = 1/4 and get c = 12 and 1/b + 1/12 = 1/5 so b = 60/7 hrs You should be comfortable with manipulating fractions. 1/c = 1/4  1/6 = 2/24 = 1/12 So c = 12 (Finding c should take just a few seconds)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Director
Joined: 17 Dec 2012
Posts: 635
Location: India

Re: Machine A can process 6000 envelopes in 3 hours. Machines B [#permalink]
Show Tags
09 Jun 2013, 21:56
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
shash wrote: Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 12000 envelopes.
A. 2 B. 3 C. 4 D. 6 E. 60/7
You can either take the amount of work done as the same as Karishma has done or take the work done by each in the same time. I will do the latter 1. Work done in 1 hr by A is 2000 envelopes 2. Work done in 1 hr by A and C is 3000 envelopes 3. So work done in 1 hr by C is 1000 envelopes 4. Work done in 1 hr by B and C is 2400 envelopes 5. So work done in 1 hr by B is 1400 envelopes 6. So to process 12000 envelopes B will take 12000/1400 hrs = 60/7 hrs So the answer is choice E
_________________
Srinivasan Vaidyaraman Sravna http://www.sravnatestprep.com/courses.php
Premium Material Standardized Approaches



Manager
Joined: 30 May 2012
Posts: 217
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)

Re: Machine A can process 6000 envelopes in 3 hours. Machines B [#permalink]
Show Tags
05 Dec 2014, 02:30
shash wrote: ... If Machines A and C working together but independently ... Is this a tricky way of saying "working together"? I mean, can I treat that phrase just like how you would when you combine the rates of machine A and machine C? Is there a question where GMAT asks two or more entities working together depending on each other?



Math Expert
Joined: 02 Sep 2009
Posts: 44290

Re: Machine A can process 6000 envelopes in 3 hours. Machines B [#permalink]
Show Tags
05 Dec 2014, 07:51



Intern
Joined: 23 Dec 2014
Posts: 48

Re: Machine A can process 6000 envelopes in 3 hours. Machines B [#permalink]
Show Tags
14 Feb 2015, 09:45
1
This post received KUDOS
shash wrote: Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 12000 envelopes. A. 2 B. 3 C. 4 D. 6 E. 60/7 I got this far:
Machine C = 6 hours for 6000 envelopes
Then (1/T) = (1/b) +(1/c)
1/2.5 = (1/b) + (1/6) b= (30/7) for 6000 envelopes or (60/7) for 12000 envelopes.
Why isnt the answer coming up to exactly 8? EDITED THE OPTIONS1/A = 2000 1/B+1/C = 6000/2.5=2400 (1) 1/A+ 1/C = 3000 (2) (1)  (2) 1/B1/A =24003000 > 1/B  2000 = 24003000 > 1/B = 1400 Rate = 1400 Work= 12000 Time= 12000/1400 =60/7 Feed me kudos if it is helpful for you :D



Director
Joined: 10 Mar 2013
Posts: 581
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: Machine A can process 6000 envelopes in 3 hours. Machines B [#permalink]
Show Tags
24 Dec 2015, 16:54
shash wrote: Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 12000 envelopes. A. 2 B. 3 C. 4 D. 6 E. 60/7 I got this far:
Machine C = 6 hours for 6000 envelopes
Then (1/T) = (1/b) +(1/c)
1/2.5 = (1/b) + (1/6) b= (30/7) for 6000 envelopes or (60/7) for 12000 envelopes.
Why isnt the answer coming up to exactly 8? EDITED THE OPTIONSThis is not the original question. In the original question (from Kaplan) the time given for mashines B and C working together is 2\frac{2}{5} and the correct answer choice is E, which equals to 8 and not \(\frac{60}{7}\)
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Director
Joined: 07 Dec 2014
Posts: 922

Machine A can process 6000 envelopes in 3 hours. Machines B [#permalink]
Show Tags
05 Mar 2017, 15:58
Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 12000 envelopes.
A. 2 B. 3 C. 4 D. 6 E. 60/7
let a,b,c=respective rates a=2000 (a+c)(b+c)=ab=600 b=1400 12000/1400=60/7 hours E



Intern
Joined: 04 Jul 2016
Posts: 5

Re: Machine A can process 6000 envelopes in 3 hours. Machines B [#permalink]
Show Tags
08 Mar 2018, 12:48
Instead of 2.5 hours , 2 hours and (2/5) mins then answer will be 4 hours . Correct? Posted from GMAT ToolKit




Re: Machine A can process 6000 envelopes in 3 hours. Machines B
[#permalink]
08 Mar 2018, 12:48



Go to page
1 2
Next
[ 21 posts ]



