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'Work' Word Problems Made Easy

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Re: 'Work' Word Problems Made Easy [#permalink] New post 11 Aug 2013, 00:09
Hi,

Can sombody please solve this wit solution for this question.

It takes Printer A 4 more minutes than printer B to print 40 pages. 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

Regards,
Rrsnathan.
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Re: 'Work' Word Problems Made Easy [#permalink] New post 11 Aug 2013, 00:14
Expert's post
rrsnathan wrote:
Hi,

Can sombody please solve this wit solution for this question.

It takes Printer A 4 more minutes than printer B to print 40 pages. 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

Regards,
Rrsnathan.


Check here: it-takes-printer-a-4-more-minutes-than-printer-b-to-print-98479.html

Hope it helps.
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Re: 'Work' Word Problems Made Easy [#permalink] New post 02 Sep 2013, 12:18
Just 3 hours back, literally I was at zero confidence to start with work rate problems, but after going through your notes and solving 5 or 6 problems, I have solved 80 to 90% difficulty level problems like a pro, solutions are also matching closely to Bunuel's. Really work rate is not that as much tough as I was thinking before. Reciprocate the hours to find the rate of work per day or per minute that's it half battle won-> "master key to every work rate problem".

Thanks allot.
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Re: 'Work' Word Problems Made Easy [#permalink] New post 16 Sep 2013, 22:46
Bunuel wrote:
resh924 wrote:
Bunuel,

Can you help me with this question?

A group of 5 craftsmen, working together at the same rate, can finish a job in 3 hours. How long will it take a group of 4 apprentices working together to do the same job?
(1) Each apprentice works at 2/3 the rate of a craftsman.
(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job.

Answer choice seems to be D.


Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.

time*speed=distance <--> time*rate=job \ done.

So, if we say that the rate of a craftsmen is x job/hours and the rate of an apprentice is y job/hour then we'll have (5x)*3=job=(4y)*t --> (5x)*3=(4y)*t. Question: t=\frac{15x}{4y}=?

(1) Each apprentice works at 2/3 the rate of a craftsman --> y=\frac{2}{3}x --> \frac{x}{y}=\frac{3}{2} --> t=\frac{15x}{4y}=\frac{45}{8} hours. Sufficient.

(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job --> as the 5 craftsmen need 3 hours to do the job then in 45/23 hours they'll complete (45/23)/3=15/23 rd of the job (15 parts out of 23) so the rest of the job, or 1-15/23=8/23 (8 parts out of 23) is done by the 4 apprentices in the same amount of time (45/23 hours): \frac{5x}{4y}=\frac{15}{8} --> \frac{x}{y}=\frac{3}{2}, the same info as above. Sufficient.

Answer: D.


Hi Bunuel,

For #2, I set-up my equation as:

1/3 + 1/A = 1/(45/23)

Since we already know the rate of the 5 craftsmen and the total hours needed for the 2 groups to finish the job. However, I arrived at a different answer for A (45/8). I can't seem to figure out where it went wrong, hope you can help.

Thanks.
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Re: 'Work' Word Problems Made Easy [#permalink] New post 16 Sep 2013, 23:43
Expert's post
pauc wrote:
Bunuel wrote:
resh924 wrote:
Bunuel,

Can you help me with this question?

A group of 5 craftsmen, working together at the same rate, can finish a job in 3 hours. How long will it take a group of 4 apprentices working together to do the same job?
(1) Each apprentice works at 2/3 the rate of a craftsman.
(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job.

Answer choice seems to be D.


Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.

time*speed=distance <--> time*rate=job \ done.

So, if we say that the rate of a craftsmen is x job/hours and the rate of an apprentice is y job/hour then we'll have (5x)*3=job=(4y)*t --> (5x)*3=(4y)*t. Question: t=\frac{15x}{4y}=?

(1) Each apprentice works at 2/3 the rate of a craftsman --> y=\frac{2}{3}x --> \frac{x}{y}=\frac{3}{2} --> t=\frac{15x}{4y}=\frac{45}{8} hours. Sufficient.

(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job --> as the 5 craftsmen need 3 hours to do the job then in 45/23 hours they'll complete (45/23)/3=15/23 rd of the job (15 parts out of 23) so the rest of the job, or 1-15/23=8/23 (8 parts out of 23) is done by the 4 apprentices in the same amount of time (45/23 hours): \frac{5x}{4y}=\frac{15}{8} --> \frac{x}{y}=\frac{3}{2}, the same info as above. Sufficient.

Answer: D.


Hi Bunuel,

For #2, I set-up my equation as:

1/3 + 1/A = 1/(45/23)

Since we already know the rate of the 5 craftsmen and the total hours needed for the 2 groups to finish the job. However, I arrived at a different answer for A (45/8). I can't seem to figure out where it went wrong, hope you can help.

Thanks.


You should get the same answer: 1/3 + 1/A = 1/(45/23) --> A=45/8.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: 'Work' Word Problems Made Easy [#permalink] New post 17 Sep 2013, 02:31
Quote:
Hi Bunuel,

For #2, I set-up my equation as:

1/3 + 1/A = 1/(45/23)

Since we already know the rate of the 5 craftsmen and the total hours needed for the 2 groups to finish the job. However, I arrived at a different answer for A (45/8). I can't seem to figure out where it went wrong, hope you can help.

Thanks.


You should get the same answer: 1/3 + 1/A = 1/(45/23) --> A=45/8.[/quote]

Oops, you're right. I was obsessing over a different value (3/2 from Statement 2). Thank you.
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Re: 'Work' Word Problems Made Easy [#permalink] New post 25 Jul 2014, 17:23
Bunuel wrote:
resh924 wrote:
Bunuel,

Can you help me with this question?

A group of 5 craftsmen, working together at the same rate, can finish a job in 3 hours. How long will it take a group of 4 apprentices working together to do the same job?
(1) Each apprentice works at 2/3 the rate of a craftsman.
(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job.

Answer choice seems to be D.


Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.

time*speed=distance <--> time*rate=job \ done.

So, if we say that the rate of a craftsmen is x job/hours andthe rate of an apprentice is y job/hour then we'll have (5x)*3=job=(4y)*t --> (5x)*3=(4y)*t. Question: t=\frac{15x}{4y}=?

(1) Each apprentice works at 2/3 the rate of a craftsman --> y=\frac{2}{3}x --> \frac{x}{y}=\frac{3}{2} --> t=\frac{15x}{4y}=\frac{45}{8} hours. Sufficient.

(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job --> as the 5 craftsmen need 3 hours to do the job then in 45/23 hours they'll complete (45/23)/3=15/23 rd of the job (15 parts out of 23) so the rest of the job, or 1-15/23=8/23 (8 parts out of 23) is done by the 4 apprentices in the same amount of time (45/23 hours): \frac{5x}{4y}=\frac{15}{8} --> \frac{x}{y}=\frac{3}{2}, the same info as above. Sufficient.

Answer: D.

Check this for more: word-translations-rates-work-104208.html


Bunuel,

I agree with the answer you got but not the logic you used to arrive at the answer. The reason that I disagree with your logic is based on my understanding that DS questions are precise in their statements and we are not supposed to assume anything outside of what is stated. Can you please care to comment on the following?

Nowhere in the question stem it is mentioned that 4 apprentices work at the same rate. So, I am not sure if the highlighted portion in your solution is valid.

Statement 1: We can deduce that 4 apprentices work at the same rate since it says "Each apprentice works at 2/3 the rate of a craftsman"
For statement 2, we cannot assume that the 4 apprentices work at the same rate. However, since the question asks us to find time taken by group of 4 apprentices and not one apprentice, this statement alone can give us the answer and hence sufficient.

Is my understanding correct or am I reading too much into this?
Re: 'Work' Word Problems Made Easy   [#permalink] 25 Jul 2014, 17:23
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