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RT=W Report (m07q03)

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RT=W Report (m07q03) [#permalink] New post 14 Nov 2007, 10:16
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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, 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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 [#permalink] New post 14 Nov 2007, 10:28
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Let time taken by 'j' to type be 'j'.

We know that 1/m + 1/j = 1/12.5

i.e. 1/30 + 1/j = 1/12.5

i.e. (30+j)/30j = 1/12.5

i.e. 375 = 30j-12.5j=17.5j

i.e. j = 375/17.5=150/7

Let time taken by 'm' to edit be 'x' and that by 'j' be 'y'.

We know that 1/x + 1/y = 1/7.5

i.e. 1/x + 1/12 = 1/7.5

i.e. (12+x)/12x = 1/7.5

i.e. 90 = 12x-7.5x=4.5x

i.e. x = 90/4.5 = 20


Therefore answer = 150/7+20 = 41.4
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Re: RT=W Report (m07q03) [#permalink] New post 16 Dec 2010, 05:11
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bmwhype2 wrote:
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, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

* 41.4
* 34.1
* 13.4
* 12.4
* 10.8

[Reveal] Spoiler: OA
A

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Well, this is how I figured a shorter solution:

M takes 30 hrs, two cons of equal cap take 12.5 *2 = 25 hrs each. Hence J will take less than 25 hrs (how much less --> guess above 20 at least?)
J takes 12 hrs, two cons of equal cap take 7.5 * 2 = 15 hrs each. Hence M will take more than 15 hrs (how much greater --> guess around 18)
Add them = GT20 + GT 15 = 35 . Only one option is above 35
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Re: RT=W Report (m07q03) [#permalink] New post 20 Dec 2012, 05:19
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bmwhype2 wrote:
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, 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

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions


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 = 1/30 job/hour;
"Mary and Jim can type up a report in 12.5" and --> 1/30+1/x=1/12.5=2/25, where x is the time needed for Jim to type the report alone --> x=150/7;

"Jim needs 12 hours to edit the report" --> Jim's editing rate = 1/12 job/hour;
"Mary and Jim can edit a report in 7.5" and --> 1/y+1/12=1/7.5=2/15, where y is the time needed for Mary to edit the report alone --> y=20;

"How many hours will it take if Jim types the report and Mary edits it immediately after he is done" --> x+y=150/7+20=~41.4

Answer: A.

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Re: plz provide your explanations [#permalink] New post 20 Dec 2012, 20:16
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david1983 wrote:
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, 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


Given:
\frac{1}{M_{edit}}+\frac{1}{J_{edit}}=\frac{1}{7.5}=\frac{2}{15}
\frac{1}{M_{type}}+\frac{1}{J_{type}}=\frac{1}{12.5}=\frac{2}{25}
\frac{1}{M_{type}}=\frac{1}{30}
\frac{1}{J_{edit}}=\frac{1}{12}

Solve for M_{edit} + J_{edit}:

\frac{1}{M_{edit}}+\frac{1}{J_{edit}} - \frac{1}{J_{edit}}=\frac{2}{15}-\frac{1}{12}=\frac{1}{20}

\frac{1}{M_{type}}+\frac{1}{J_{type}}-\frac{1}{M_{type}}=\frac{2}{25}-\frac{1}{30}=\frac{7}{150}

M_{edit} + J_{type} = 20 + 21.4=41.4

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Re: RT=W Report (m07q03) [#permalink] New post 20 Dec 2011, 20:36
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Here is my answer:

Since there two consultants, one consultant can type in 12.5*2=25 hours, and edit in 7.5*2=15 hours. To type and edit for one consultant it will take 25+15=40 hours.

Mary can type in 30 hours, which is 20% slower than let's say average.
Jim can edit in 12 hours, which is 20% faster than average.

If Jim types, it will take for Jim 25*0.8%=20 hours.
If Mary edits, it will take for Mary 15*1.2%=18 hours.

Together 38 hours, which is closer to A. Therefore the correct answer is A.
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Re: plz provide your explanations [#permalink] New post 20 Dec 2012, 18:06
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david1983 wrote:
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, 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


This is a very hard question, in part because it is not phrased particularly well. In particular, I believe the question wants us to understand that the "two consultant" mentioned in the first sentence are not two consultants in general, but rather, quite specifically, Mary & Jim.

Let's consider the typing rates.
Mary's rate = 1/30 (papers per hour)
Jim's rate = 1/X ----- where X = the hours it would take Jim to type one paper
Combined rate = 1/12.5 = 2/25
Big Idea: We can always add rates.
(Mary's rate) + (Jim's rate) = (combined rate)
(1/30) + (1/X) = 2/25
1/X = 2/25 - 1/30 = 12/150 - 5/150 = 7/150

X = 150/7 = 21 3/7

Now, let's consider the editing rates:
Mary's rate = 1/Y ------ where Y = the hours it would take Mary to edit one paper
Jim's rate = 1/12
Combined rate = 1/7.5 = 2/15
(Mary's rate) + (Jim's rate) = (combined rate)
1/Y + 1/12 = 2/15
1/Y = 2/15 - 1/12 = 8/60 - 5/60 = 3/60 = 1/20
Y = 20

Combined time = X + Y = 21 3/7 + 20 = 41 3/7 = 41.42857
Answer = A

Here's a related blog you may find helpful:
http://magoosh.com/gmat/2012/gmat-work-rate-questions/

Does all this make sense?

Mike :-)

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Re: RT=W Report (m07q03) [#permalink] New post 09 Dec 2009, 06:16
Right, and once you solve for either 150/7 or 20, you can immediately eliminate all possibilities other than A and B. This would give you a 50% guess for half the work if you're low on time.
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Re: RT=W Report (m07q03) [#permalink] New post 09 Dec 2009, 11:24
Hi
I think the question should be re-written as a "which is the closest" or "approximately how long" question since 150/7 doesn't exactly equal 21.4... It's close to it: 21.42857...
There would never be an approximate right answer on the GMAT on a question which asks for a specific quantity
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Re: RT=W Report (m07q03) [#permalink] New post 16 Dec 2010, 05:02
A.

This is calculation intensive. What would be a shorter solution?
I solved like this:
1/30 + 1/x = 1/12.5 => x = 21.4
1/12+1/y = 1/7.5 => y = 20

Total = 21.4 + 20 = 41.4
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Re: RT=W Report (m07q03) [#permalink] New post 16 Dec 2010, 11:28
sleekmover wrote:
bmwhype2 wrote:
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, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

* 41.4
* 34.1
* 13.4
* 12.4
* 10.8

[Reveal] Spoiler: OA
A

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Well, this is how I figured a shorter solution:

M takes 30 hrs, two cons of equal cap take 12.5 *2 = 25 hrs each. Hence J will take less than 25 hrs (how much less --> guess above 20 at least?)
J takes 12 hrs, two cons of equal cap take 7.5 * 2 = 15 hrs each. Hence M will take more than 15 hrs (how much greater --> guess around 18)
Add them = GT20 + GT 15 = 35 . Only one option is above 35


why you dont guess 18 (< than 25) for J and 16,1 (> than 15) for M, and therefore you get 18+16,1=34,1 and get B??

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Re: RT=W Report (m07q03) [#permalink] New post 16 Dec 2010, 12:20
noboru wrote:
sleekmover wrote:
bmwhype2 wrote:
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, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

* 41.4
* 34.1
* 13.4
* 12.4
* 10.8

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions


Well, this is how I figured a shorter solution:

M takes 30 hrs, two cons of equal cap take 12.5 *2 = 25 hrs each. Hence J will take less than 25 hrs (how much less --> guess above 20 at least?)
J takes 12 hrs, two cons of equal cap take 7.5 * 2 = 15 hrs each. Hence M will take more than 15 hrs (how much greater --> guess around 18)
Add them = GT20 + GT 15 = 35 . Only one option is above 35


why you dont guess 18 (< than 25) for J and 16,1 (> than 15) for M, and therefore you get 18+16,1=34,1 and get B??


Vaild question noburo: Here is the explanation->
J = 12, with same cap cons 1 = 15 and cons 2 = 15, Hence M needs to compensate for less hrs of J. at least 3 needs to be added to common hrs (assuming we are looking at Arithmetic mean)
M = 30, with same cap Cons 1 = 25 and Cons 2 = 25, , Hence J needs to compensate for more hrs of M. At lease 5 needs to be subtracted from common hrs (assuming we are looking at Arithmetic Mean)

We should also understand a bit about harmonic and arithmentic, a concept illustrated here: http://en.wikipedia.org/wiki/Harmonic_mean
Some points from the above post to consider:
For all positive data sets containing at least one pair of nonequal values, the harmonic mean is always the least of the three means, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between
Since the harmonic mean of a list of numbers tends strongly toward the least elements of the list

In certain situations, especially many situations involving rates and ratios, the harmonic mean provides the truest average. For instance, if a vehicle travels a certain distance at a speed x (e.g. 60 kilometres per hour) and then the same distance again at a speed y (e.g. 40 kilometres per hour), then its average speed is the harmonic mean of x and y (48 kilometres per hour), and its total travel time is the same as if it had traveled the whole distance at that average speed

Hope this explains
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Re: RT=W Report (m07q03) [#permalink] New post 20 Dec 2012, 07:57
I got the correct answer, but it took me >5 minutes! Did any of you solve it in 2 or less?

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Re: RT=W Report (m07q03) [#permalink] New post 20 Dec 2012, 08:01
Also, I don't believe this question is GMAT quality. It took me a few minutes to figure out what they were asking and that the two consultants were Mary and Jim since it wasn't stated. A correction is in order.

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plz provide your explanations [#permalink] New post 20 Dec 2012, 15:28
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, 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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Re: RT=W Report (m07q03) [#permalink] New post 20 Dec 2012, 21:11
The question was not really difficult.....But lot of calculation involved...Can anyone suggest a shorter method
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Re: plz provide your explanations [#permalink] New post 21 Dec 2012, 02:06
Expert's post
david1983 wrote:
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, 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


Merging similar topics. Please refer to the solutions above.

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Re: RT=W Report (m07q03) [#permalink] New post 16 Dec 2013, 11:35
Yes, this question isn't hard, it's just phrased poorly. The most difficult part is understanding that Jim and Mary themselves are indeed the two consultants.
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Re: RT=W Report (m07q03) [#permalink] New post 24 Dec 2013, 01:50
Archit143 wrote:
The question was not really difficult.....But lot of calculation involved...Can anyone suggest a shorter method


Let us assume typing to be a work of 750 units (a common multiple of 25/2 and 30).
So, in one day both Jim and Mary type 60 units (750/12.5) and Mary alone types 25 units (750/30).
Thus, Jim types 35 units (60-35) per day or takes approximately 21.4 days (=750/35)......(1)

Let us assume editing to be a work of 60 units (a common multiple of 15/2 and 12).
So, in one day both Jim and Mary edit 8 units (60/7.5) and Jim alone edits 5 units (60/12).
Thus, Mary edits 3 units (8 - 5) per day or takes 20 days (=60/3)................................ (2)

Combining (1) and (2), we get 21.4 + 20 or 41.4 days.
Hence, answer is Option (A)
Re: RT=W Report (m07q03)   [#permalink] 24 Dec 2013, 01:50
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