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# M07-03

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Math Expert
Joined: 02 Sep 2009
Posts: 50007

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16 Sep 2014, 00:34
00:00

Difficulty:

55% (hard)

Question Stats:

75% (02:51) correct 25% (03:24) wrong based on 60 sessions

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Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, approximately how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

A. 41.4
B. 34.1
C. 13.4
D. 12.4
E. 10.8

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Math Expert
Joined: 02 Sep 2009
Posts: 50007

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16 Sep 2014, 00:34
Official Solution:

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, approximately how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

A. 41.4
B. 34.1
C. 13.4
D. 12.4
E. 10.8

Break down the problem into two pieces: typing and editing.

"Mary needs 30 hours to type the report": Mary's typing rate $$= \frac{1}{30}$$ job/hour;

"Mary and Jim can type up a report in 12.5": $$\frac{1}{30} + \frac{1}{x}= \frac{1}{12.5}=\frac{2}{25}$$, where $$x$$ is the time needed for Jim to type the report alone. Solving gives $$x=\frac{150}{7}$$;

"Jim needs 12 hours to edit the report": Jim's editing rate $$= \frac{1}{12}$$ job/hour;

"Mary and Jim can edit a report in 7.5": $$\frac{1}{y}+\frac{1}{12}=\frac{1}{7.5}=\frac{2}{15}$$, where $$y$$ is the time needed for Mary to edit the report alone. Solving gives $$y=20$$;

"How many hours will it take if Jim types the report and Mary edits it immediately after he is done": $$x+y= \frac{150}{7}+20 \approx 41.4$$

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Current Student
Joined: 06 Mar 2014
Posts: 247
Location: India
GMAT Date: 04-30-2015

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12 Oct 2014, 15:16
Most of the work/rate problems are causing trouble to me. Is there any thread dedicated to breaking down the common types and tricks, dealing with work/rate problems.

Something Similar to the distance speed time one: distance-speed-time-word-problems-made-easy-87481.html
Math Expert
Joined: 02 Sep 2009
Posts: 50007

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12 Oct 2014, 15:18
1
earnit wrote:
Most of the work/rate problems are causing trouble to me. Is there any thread dedicated to breaking down the common types and tricks, dealing with work/rate problems.

Something Similar to the distance speed time one: distance-speed-time-word-problems-made-easy-87481.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
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Current Student
Joined: 06 Mar 2014
Posts: 247
Location: India
GMAT Date: 04-30-2015

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24 Feb 2015, 05:31
Bunuel wrote:
Official Solution:

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, approximately how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

A. 41.4
B. 34.1
C. 13.4
D. 12.4
E. 10.8

Break down the problem into two pieces: typing and editing.

"Mary needs 30 hours to type the report": Mary's typing rate $$= \frac{1}{30}$$ job/hour;

"Mary and Jim can type up a report in 12.5": $$\frac{1}{30} + \frac{1}{x}= \frac{1}{12.5}=\frac{2}{25}$$, where $$x$$ is the time needed for Jim to type the report alone. Solving gives $$x=\frac{150}{7}$$;

"Jim needs 12 hours to edit the report": Jim's editing rate $$= \frac{1}{12}$$ job/hour;

"Mary and Jim can edit a report in 7.5": $$\frac{1}{y}+\frac{1}{12}=\frac{1}{7.5}=\frac{2}{15}$$, where $$y$$ is the time needed for Mary to edit the report alone. Solving gives $$y=20$$;

"How many hours will it take if Jim types the report and Mary edits it immediately after he is done": $$x+y= \frac{150}{7}+20 \approx 41.4$$

My approach is the same except that in the end, i calculate the combined Rate for Mary and Jim after having found their new rates of editing and typing respectively.

So that in the end, the time taken would be the reciprocal of the Total Rate. But then with this approach my answer changes.

Please tell me what am i doing wrong here?
Math Expert
Joined: 02 Sep 2009
Posts: 50007

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24 Feb 2015, 06:03
earnit wrote:
Bunuel wrote:
Official Solution:

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, approximately how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

A. 41.4
B. 34.1
C. 13.4
D. 12.4
E. 10.8

Break down the problem into two pieces: typing and editing.

"Mary needs 30 hours to type the report": Mary's typing rate $$= \frac{1}{30}$$ job/hour;

"Mary and Jim can type up a report in 12.5": $$\frac{1}{30} + \frac{1}{x}= \frac{1}{12.5}=\frac{2}{25}$$, where $$x$$ is the time needed for Jim to type the report alone. Solving gives $$x=\frac{150}{7}$$;

"Jim needs 12 hours to edit the report": Jim's editing rate $$= \frac{1}{12}$$ job/hour;

"Mary and Jim can edit a report in 7.5": $$\frac{1}{y}+\frac{1}{12}=\frac{1}{7.5}=\frac{2}{15}$$, where $$y$$ is the time needed for Mary to edit the report alone. Solving gives $$y=20$$;

"How many hours will it take if Jim types the report and Mary edits it immediately after he is done": $$x+y= \frac{150}{7}+20 \approx 41.4$$

My approach is the same except that in the end, i calculate the combined Rate for Mary and Jim after having found their new rates of editing and typing respectively.

So that in the end, the time taken would be the reciprocal of the Total Rate. But then with this approach my answer changes.

Please tell me what am i doing wrong here?

The point is that typing and editing are two separate actions: Jim types the report and Mary edits it immediately after he is done. Hence you cannot use combined rate for those two actions.

Hope it's clear.
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Joined: 18 Aug 2014
Posts: 324

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03 May 2016, 13:14
Bunuel wrote:

"Jim needs 12 hours to edit the report": Jim's editing rate $$= \frac{1}{12}$$ job/hour;

"Mary and Jim can edit a report in 7.5": $$\frac{1}{y}+\frac{1}{12}=\frac{1}{7.5}=\frac{2}{15}$$, where $$y$$ is the time needed for Mary to edit the report alone. Solving gives $$y=20$$;

Can someone please break this out by step? I got here (as well the other step before this that is the same style of equation) during the problem but I got stuck proceeding on the math. Am I supposed to find the LCM for 7.5 and 12, add them then cross multiply? Do I just have to multiply 12 by 7.5 to quickly come up with a workable denominator?
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04 May 2016, 06:54
redfield wrote:
Bunuel wrote:

"Jim needs 12 hours to edit the report": Jim's editing rate $$= \frac{1}{12}$$ job/hour;

"Mary and Jim can edit a report in 7.5": $$\frac{1}{y}+\frac{1}{12}=\frac{1}{7.5}=\frac{2}{15}$$, where $$y$$ is the time needed for Mary to edit the report alone. Solving gives $$y=20$$;

Can someone please break this out by step? I got here (as well the other step before this that is the same style of equation) during the problem but I got stuck proceeding on the math. Am I supposed to find the LCM for 7.5 and 12, add them then cross multiply? Do I just have to multiply 12 by 7.5 to quickly come up with a workable denominator?

$$\frac{1}{y}+\frac{1}{12}=\frac{1}{7.5}=\frac{2}{15}$$

$$\frac{1}{y}=\frac{2}{15}-\frac{1}{12}=\frac{8}{60}-\frac{5}{60}=\frac{3}{60}=\frac{1}{20}$$
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Joined: 06 Feb 2016
Posts: 48
Location: Poland
Concentration: Finance, Accounting
GMAT 1: 730 Q49 V41
GPA: 3.5

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23 Sep 2017, 08:28
I think the part "immediately after he is done" is the key to answer this question. It means they are not working simultaneously.
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Joined: 31 Oct 2016
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26 Oct 2017, 11:36
How did I solve? Estimation approach.
Disadvantage: there is more logic than math and it won't give you the exact number. Only range

But I think that, if you are not math-genius and you can't solve that kind of problems for 2 minutes, you can try this approach.

Typing a report:
Mary and Jim together: 12.5 hours.
Only Mary: 30 hours
Mary and Mary together: 30/2 = 15 hours. So, it means that Jim is typing faster.
Jim and Jim together: less than 12.5 hours. About 12.5-(15-12.5) = 10 hours (since it is just approximation we can consider 10-11 hours).
It means that Jim working alone can type a report for about 20-22 hours.

Editing a report:
Mary and Jim together: 7.5 hours
Only Jim: 12 hours
Jim and Jim together: 12/2 = 6 hours. So, it means that Jim is editing also faster (good Jim)
Mary and Mary together: more than 7.5 hours. About (7.5-6)+7.5 = 9 hours (since it is just approximation we can consider 9-10 hours)
It means that Mary working alone can edit a report for about 18-20 hours.

Let's sum up. Our range is about (20+18) - (22+20) hours. Or about 38-42 hours ("-" do not read as "minus" here. It is a range).

Only A falls into this range.

Again - the official solution is much better and accurate. Use the official solution approach whenever is possible, but if you want to little bit save your time taking some risk, you can use approximation approach.
Manager
Joined: 26 Feb 2018
Posts: 79
Location: United Arab Emirates
GMAT 1: 710 Q47 V41
GMAT 2: 770 Q49 V47

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10 Mar 2018, 13:25
This question is not mathematically difficult but it is time consuming.

The best approach is to guess. You know that working together they would to the typing and the editing in 20hrs. That means C, D and E can immediately be eliminated. B is still on the low side, too - why? We know that Mary takes 30 hrs alone to type and Mary + Jim take 12.5hrs. If Jim was the same speed as Mary, they would take 15hrs together - 12.5hrs isn't that much lower so we know that Jim isn't that much faster than Mary. So estimate a number in the mid 20s for Jim alone (say 25) Similarly, if Jim takes 12hrs to edit alone, Mary and Jim at the same rate would take 6hrs. 7.5 isn't that far away, so we know Mary is slower at editing but not by much. Estimate a number in the mid teens for Mary alone (say 16) and add - around 40.

A good example where quick educated guessing can save you a lot of time to use on questions
Re: M07-03 &nbs [#permalink] 10 Mar 2018, 13:25
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# M07-03

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