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# S95-18

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Math Expert
Joined: 02 Sep 2009
Posts: 49496

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16 Sep 2014, 01:49
00:00

Difficulty:

35% (medium)

Question Stats:

65% (00:59) correct 35% (01:21) wrong based on 85 sessions

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Three medical experts, working together at the same constant rate, can write an anatomy textbook in 24 days. How many additional experts, working together at this same constant rate, are needed to write the textbook in 9 days?

A. 2
B. 3
C. 5
D. 8
E. 15

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Math Expert
Joined: 02 Sep 2009
Posts: 49496

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16 Sep 2014, 01:49
Official Solution:

Three medical experts, working together at the same constant rate, can write an anatomy textbook in 24 days. How many additional experts, working together at this same constant rate, are needed to write the textbook in 9 days?

A. 2
B. 3
C. 5
D. 8
E. 15

We are asked to determine how many additional experts must be added to our team of 3 in order to decrease the time required to write an anatomy textbook from 24 days to 9 days.

We can plug in the values we are given into the work formula, $$w = rt$$, where $$w$$ is the amount of work done, $$r$$ is the rate at which the work is performed, and $$t$$ is the time it takes the work to be completed. In this case, $$w = 1$$ (since there is one textbook), $$t = 24$$, and $$r$$ is unknown. Thus, the original situation can be represented by the formula: $$1 = (3r)(24) = 72r$$. Note that we use $$3r$$ because there are 3 people working, each at the same rate of $$r$$.

We solve for $$r$$ by dividing both sides by 72, leaving $$r = \frac{1}{72}$$ book per day. This is the rate at which each expert works.

We use this value of $$r$$ to solve for $$k$$, the number of experts it would take to write a book in 9 days. In this new equation, $$w$$ will still equal 1, $$r = \frac{1}{72}k$$, and $$t = 9$$. This gives us: $$1 = (\frac{1}{72}k)(9) = \frac{1}{8}k$$. We solve for $$k$$ by multiplying both sides by $$8$$. We find that $$k = 8$$. So it will take 8 experts to finish the book in 9 days.

Remember, though, that we are looking for the number of additional experts. Since we already have 3 experts, in order to get 8, we need an additional $$8 - 3 = 5$$ experts.

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Joined: 06 Sep 2016
Posts: 2

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08 Dec 2016, 15:09
If it takes 24 days for 3 people working at the same constant rate to write a book- we can deduce 24/3= rate per writer=8days

If we double the writers 3+3 we get half of 24= 12. so we know we need more than 3 additional writers. Two additional writers to the 6 will give us 9days. so in total we have 5 additional writers.
Manager
Joined: 01 Nov 2016
Posts: 68
Concentration: Technology, Operations

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13 Apr 2017, 21:59
Sigh, I always get excited when I know how to find an answer that I forget things like additional experts. The answer 8 is a trick for people like me. You have to subtract 3 from 8 to get the real answer, 5
Intern
Joined: 05 Sep 2012
Posts: 8

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06 Jun 2017, 17:36
2
since days and medical experts are inversely proportional therefore

days*no of medical experts holds true

24*3=9*(3+x)

solve for x and its 5
Manager
Joined: 18 Mar 2015
Posts: 104
Location: India
Schools: ISB '19
GMAT 1: 600 Q47 V26
GPA: 3.59

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15 Aug 2017, 01:08
I'm always confused with questions of formula w=rt
never able to find what is W. here also how we got 1 ?
Math Expert
Joined: 02 Sep 2009
Posts: 49496

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15 Aug 2017, 01:19
r19 wrote:
I'm always confused with questions of formula w=rt
never able to find what is W. here also how we got 1 ?

I think alternative solutions from this topic should help.

Work/Rate Problems

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Intern
Joined: 05 Nov 2017
Posts: 2

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07 Nov 2017, 07:11
I thought of the question from non-algebraic standpoint. If 3 experts can put the book together in 24 days that means their rate is 8 days a piece. If you cut 24 days in half you now have 12 days which equates to 6 workers because we cut time in half by doubling the amount of workers. As of now you have added 3 workers. The question asks for 9 days so adding 3 more workers to the 6 that we currently have is too many. It would cut 24 days into 1/3 that time which is 8. SO it has to be a number a little less that 6 which is 5.
Re: S95-18 &nbs [#permalink] 07 Nov 2017, 07:11
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# S95-18

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