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# There is a total of 1,800 pages that needs to be typed. If it takes 90

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5839
GMAT 1: 760 Q51 V42
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There is a total of 1,800 pages that needs to be typed. If it takes 90 [#permalink]

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27 Jul 2017, 17:58
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Difficulty:

15% (low)

Question Stats:

81% (01:21) correct 19% (01:07) wrong based on 89 sessions

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There is a total of 1,800 pages that needs to be typed. If it takes 90 minutes when a types alone, 45 minutes when b types alone, and 30 minutes when c types alone. How many minutes does it take if 3 of them work together?

A. 10min
B. 12min
C. 15min
D. 18min
E. 20min

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 04 Dec 2015 Posts: 700 Location: India Concentration: Technology, Strategy Schools: ISB '19, IIMA , IIMB, XLRI WE: Information Technology (Consulting) There is a total of 1,800 pages that needs to be typed. If it takes 90 [#permalink] ### Show Tags 27 Jul 2017, 19:05 1 MathRevolution wrote: There is a total of 1,800 pages that needs to be typed. If it takes 90 minutes when a types alone, 45 minutes when b types alone, and 30 minutes when c types alone. How many minutes does it take if 3 of them work together? A. 10min B. 12min C. 15min D. 18min E. 20min It takes $$90$$ minutes when "$$a$$" types alone to complete the work. Rate of work of "$$a$$" $$= \frac{1}{90}$$ It takes $$45$$ minutes when "$$b$$" types alone to complete the work. Rate of work of "$$b$$" $$= \frac{1}{45}$$ It takes $$30$$ minutes when "$$c$$" types alone to complete the work. Rate of work of "$$c$$" $$= \frac{1}{30}$$ Rate of work of "$$a$$$$,$$$$b$$ and $$c$$" combined is; $$\frac{1}{90} + \frac{1}{45} + \frac{1}{30}$$ $$=>$$ $$\frac{1 + 2 + 3}{90} = \frac{6}{90} = \frac{1}{15}$$ Therefore time taken to complete the job when $$3$$ of them work together $$= \frac{1}{(1/15)} = 15$$ mins. Answer (C)... _________________ Please Press "+1 Kudos" to appreciate. SC Moderator Joined: 22 May 2016 Posts: 1827 There is a total of 1,800 pages that needs to be typed. If it takes 90 [#permalink] ### Show Tags 28 Jul 2017, 08:56 MathRevolution wrote: There is a total of 1,800 pages that needs to be typed. If it takes 90 minutes when a types alone, 45 minutes when b types alone, and 30 minutes when c types alone. How many minutes does it take if 3 of them work together? A. 10min B. 12min C. 15min D. 18min E. 20min Another way: calculate rates using 1800 as $$Work$$, then divide by time $$t$$ = number of minutes it takes each person to complete all 1800 pages. $$r= W/t$$ a = 1800 p/90 mins is $$(\frac{20p}{1 min})$$ b = 1800 p/45 min is $$(\frac{40p}{1 min})$$ c = 1800 p/30 min is $$(\frac{60p}{1 min})$$ In one minute, the three together can type 20 + 40 + 60 = 120 pages, i.e., $$(\frac{120p}{1 min})$$ 1800 pages/120 pages in 1 minute = 15 minutes to finish when working together Answer C _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Manager Joined: 02 Nov 2015 Posts: 171 GMAT 1: 640 Q49 V29 Re: There is a total of 1,800 pages that needs to be typed. If it takes 90 [#permalink] ### Show Tags 28 Jul 2017, 11:16 Total To be typed divided by individual capacity of each. A can type 1800/90 i.e 20 per minute . Similarly B can type 1800/45 and C can type 1800/30 per minute. Therefore together they take 1800/(20+40+60)= 1800/120 = 15. C is answer Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5839 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: There is a total of 1,800 pages that needs to be typed. If it takes 90 [#permalink] ### Show Tags 30 Jul 2017, 18:58 ==> For work rate questions, if there is a “together and alone”, you need to solve the question reciprocally. In other words, A: 1,800pg/90mins, B:1,800pg/45mins, C: 1,800pg/30mins, and if you assume A&B&C:1,800pg/t mins, you get (1/90)+(1/45)+(1/30)=(1/t), and from (1+2+3)/90=1/t, you get t=15. The answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: There is a total of 1,800 pages that needs to be typed. If it takes 90 [#permalink]

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01 Aug 2017, 17:22
MathRevolution wrote:
There is a total of 1,800 pages that needs to be typed. If it takes 90 minutes when a types alone, 45 minutes when b types alone, and 30 minutes when c types alone. How many minutes does it take if 3 of them work together?

A. 10min
B. 12min
C. 15min
D. 18min
E. 20min

The combined rate of typists a, b, and c is:

1800/90 + 1800/45 + 1800/30 = 20 + 40 + 60 = 120 pages per minute.

Thus, when working together, the typists complete the job in 1800/120 = 15 minutes.

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Re: There is a total of 1,800 pages that needs to be typed. If it takes 90   [#permalink] 01 Aug 2017, 17:22
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