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# If a group of five Democrats take 3 hours to write a proposal, how lon

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Math Expert
Joined: 02 Sep 2009
Posts: 57229
If a group of five Democrats take 3 hours to write a proposal, how lon  [#permalink]

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11 Aug 2019, 05:53
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25% (medium)

Question Stats:

86% (01:31) correct 14% (00:59) wrong based on 36 sessions

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If a group of five Democrats take 3 hours to write a proposal, how long will it take a group of 4 Republicans to write the same proposal?

(1) A Republican writes at 2/3 the rate of a Democrat
(2) 5 Democrats and 4 Republicans writing together will take $$1 \frac{9}{10}$$ hours to finish the proposal

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Joined: 23 Jul 2014
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Re: If a group of five Democrats take 3 hours to write a proposal, how lon  [#permalink]

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11 Aug 2019, 06:36
Bunuel wrote:
If a group of five Democrats take 3 hours to write a proposal, how long will it take a group of 4 Republicans to write the same proposal?

(1) A Republican writes at 2/3 the rate of a Democrat
(2) 5 Democrats and 4 Republicans writing together will take $$1 \frac{9}{10}$$ hours to finish the proposal

What we need is the work rate per hour of a Republican to write a proposal. Note this is a DS question; so, we needn't actually solve it. As long as we can frame a linear equation, we should be good.

Group of 5 democrats takes 3 hours to write a proposal.

So, the work rate of a Democrat: 1/D = 1/3*1/5 = 1/15. (It takes one democrat 15 hours to complete the proposal.)

Statement 1:
R = 2/3 rate of a Democrat -> 2/3 * 1/15 = 2/45 (It takes one Republican 22.5 hours to complete the proposal). We can hence find how much time it will take 4 Republicans. Sufficient.

Statement 2:
5 Democrats + 4 Republicans take 1 9/10 hours to complete the proposal/
We know the work rate of a democrat. We have the combined time on the other side. So, we can find the work rate of 4 republicans. Sufficient.

Hence: D

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Joined: 18 Dec 2017
Posts: 166
Re: If a group of five Democrats take 3 hours to write a proposal, how lon  [#permalink]

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11 Aug 2019, 12:28
Bunuel wrote:
If a group of five Democrats take 3 hours to write a proposal, how long will it take a group of 4 Republicans to write the same proposal?

(1) A Republican writes at 2/3 the rate of a Democrat
(2) 5 Democrats and 4 Republicans writing together will take $$1 \frac{9}{10}$$ hours to finish the proposal

My Approach:
5 D take 3 hours to complete 1 unit of work. So I can calculate value for 1 D.
Question: 4 R for 1 unit of work?

Statement 1 : R=2/3D. I can calculate 1 R. And hence 4 R. Sufficient
Statement 2 : 5 D + 4 R take 1.9 hours. I know 5D take 3 hours. I can calculate 4R. Sufficient.

IMO D
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Re: If a group of five Democrats take 3 hours to write a proposal, how lon   [#permalink] 11 Aug 2019, 12:28
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