Machine A can process 6000 envelopes in 3 hours. Machines B

Question

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)=a-b=600
b=1400
12000/1400=60/7 hours
E

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

muralimba · Accepted Answer

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.

KarishmaB · Answer

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

Bunuel · Answer

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.

krishireddy · Answer

Adding to Murali's approach....

A = 2000
B+C = 2400
A+C = 3000 => C = 3000-1 = 3000-2000 = 1000

=> B = 2400 -C =2400-1000 =1400

hence B can process 1400 Envelopes in 1hour...how much time wud it take B to process 12000 Envelopes = 12000/1400 = 60/7

Sarang · Answer

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

Bunuel · Answer

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on work/rate problems: work-word-problems-made-easy-87357.html
All DS work/rate problems to practice: search.php?search_id=tag&tag_id=46
All PS work/rate problems to practice: search.php?search_id=tag&tag_id=66

mau5 · Answer

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).

PKPKay · Answer

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?

KarishmaB · Answer

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).

Bunuel · Answer

Edited the options. Check for a solution here: machine-a-can-process-6000-envelopes-in-3-hours-machines-b-105362.html#p823509 or here: machine-a-can-process-6000-envelopes-in-3-hours-machines-b-105362.html#p823655

samheeta · Answer

How much time should one take in solving these kind of questions which involves though simple yet a lot of calculations?

KarishmaB · Answer

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 here

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

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)

SVaidyaraman · Answer

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

Blackbox · Answer

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?

Bunuel · Answer

Yes. This means that they work independently of each other but they are turned on simultaneously.

Salvetor · Answer

1/A = 2000 1/B+1/C = 6000/2.5=2400 ---------(1) 1/A+ 1/C = 3000 -----------------------(2) (1) - (2) 1/B-1/A =2400-3000 > 1/B - 2000 = 2400-3000 > 1/B = 1400 Rate = 1400 Work= 12000 Time= 12000/1400 =60/7 Feed me kudos if it is helpful for you :D :lol:

BrainLab · Answer

This 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}

gracie · Answer

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)=a-b=600
b=1400
12000/1400=60/7 hours
E

A. 2
B. 3
C. 4
D. 6
E. 60/7

let a,b,c=respective rates
a=2000
(a+c)-(b+c)=a-b=600
b=1400
12000/1400=60/7 hours
E

ptl0u1 · Answer

Instead of 2.5 hours , 2 hours and (2/5) mins then answer will be 4 hours . Correct?

https://gmatclub.com/static/posted_from.png     Posted from    GMAT ToolKit

Machine A can process 6000 envelopes in 3 hours. Machines B

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Machine A can process 6000 envelopes in 3 hours. Machines B

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards