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S95-18

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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
[Reveal] Spoiler: OA

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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.


Answer: C
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New post 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.

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New post 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

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New post 06 Jun 2017, 17:36
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

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Re: S95-18 [#permalink]

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New post 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 ?

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Re: S95-18 [#permalink]

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New post 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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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 129056 [0], given: 12187

Re: S95-18   [#permalink] 15 Aug 2017, 01:19
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