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# A group of 10 workers can plough a field in 20 days. This group starts

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Intern
Joined: 25 May 2020
Posts: 15
A group of 10 workers can plough a field in 20 days. This group starts  [#permalink]

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25 May 2020, 07:26
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Difficulty:

65% (hard)

Question Stats:

47% (02:35) correct 53% (02:36) wrong based on 32 sessions

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A group of 10 workers can plough a field in 20 days. This group starts the work and after every 2 days, 2 additional workers join the group. The efficiency of each worker is the same. On which day do the workers finish ploughing the field?

A. 7
B. 8
C. 13
D. 10
E. 11
GMAT Tutor
Joined: 16 Sep 2014
Posts: 523
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
A group of 10 workers can plough a field in 20 days. This group starts  [#permalink]

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Updated on: 30 May 2020, 10:02
1
itachiuchiha wrote:
A group of 10 workers can plough a field in 20 days. This group starts the work and after every 2 days, 2 additional workers join the group. The efficiency of each worker is the same. On which day do the workers finish ploughing the field?

A. 7
B. 8
C. 13
D. 10
E. 11

Here it may be easier to use percentages to compute the amount of days. A single worker would need 200 days to complete the job, so the rate of a single worker is 1/200 = 0.5%.

The combined rate in the beginning would be 5% per day, and we add 1% every two days since we get 2 more workers every day.

Then we can start adding two days at a time until we reach 100%: 10% + 12% + 14% + 16% + 18% = 70%. Add another 20% and the next day of 11% to reach 100%.

In total that took 2*5 + 2 + 1 = 13 days.

Ans: C
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Originally posted by TestPrepUnlimited on 25 May 2020, 07:40.
Last edited by TestPrepUnlimited on 30 May 2020, 10:02, edited 1 time in total.
Intern
Joined: 17 Feb 2017
Posts: 10
Location: India
WE: Consulting (Consulting)
Re: A group of 10 workers can plough a field in 20 days. This group starts  [#permalink]

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28 May 2020, 11:29
TestPrepUnlimited wrote:
itachiuchiha wrote:
A group of 10 workers can plough a field in 20 days. This group starts the work and after every 2 days, 2 additional workers join the group. The efficiency of each worker is the same. On which day do the workers finish ploughing the field?

A. 7
B. 8
C. 13
D. 10
E. 11

Here it may be easier to use percentages to compute the amount of days. A single worker would need 200 days to complete the job, so the rate of a single worker is 1/200 = 0.5%.

The combined rate in the beginning would be 5% per day, and we add 1% every two days since we get 2 more workers every day.

Then we can start adding two days at a time until we reach 100%: $$10% + 12% + 14% + 16% + 18% = 70%.$$ Add another 20% and the next day of 11% to reach 100%.

In total that took 2*5 + 2 + 1 = 13 days.

Ans: C

Unsure how you came to that number from the last bit (highlighted in red). Could you please help TestPrepUnlimited?
Intern
Joined: 26 Mar 2020
Posts: 10
Re: A group of 10 workers can plough a field in 20 days. This group starts  [#permalink]

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28 May 2020, 23:28
1
2
Total work: 10*20 = 200
Ist two day= 10*2 = 20
Next two day: 12*2= 24
So 20+24+28+32+36+40= 180
So upto 12 days 180 work completed. Next i.e. 13th day= 180+44= 204. Hence on 13th day work completed.

Posted from my mobile device
GMAT Tutor
Joined: 16 Sep 2014
Posts: 523
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
A group of 10 workers can plough a field in 20 days. This group starts  [#permalink]

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30 May 2020, 09:58
1
TestPrepUnlimited wrote:
itachiuchiha wrote:
A group of 10 workers can plough a field in 20 days. This group starts the work and after every 2 days, 2 additional workers join the group. The efficiency of each worker is the same. On which day do the workers finish ploughing the field?

A. 7
B. 8
C. 13
D. 10
E. 11

Here it may be easier to use percentages to compute the amount of days. A single worker would need 200 days to complete the job, so the rate of a single worker is 1/200 = 0.5%.

The combined rate in the beginning would be 5% per day, and we add 1% every two days since we get 2 more workers every day.

Then we can start adding two days at a time until we reach 100%: $$10% + 12% + 14% + 16% + 18% = 70%$$ Add another 20% and the next day of 11% to reach 100%.

In total that took 2*5 + 2 + 1 = 13 days.

Ans: C

Unsure how you came to that number from the last bit (highlighted in red). Could you please help TestPrepUnlimited?

Sure, remember that our rate increases every two days.

Our first two days would be 5% + 5%, of the entire task. The next two days would complete 6% + 6% of the entire task.

I am grouping these rates two days at a time now to speed up our calculations, so let's just focus on hitting 100% first. Then we need 5% + 5% + 6% + 6% + 7% .... and I did 10% + 12% + 14% + 16% + 18% = 70% to start off, we're still missing 30%.

The next days will complete 10%, 10%, 11%, 11% 12% ..... so I need three more days of work to finish off the missing 30%.

Now finally if we start counting the number of days used, 10%, 12%, 14%, 16%, 18%, and 20%, each of these percentages represents two days of work. That's 12 days which completes 90% of the work in total, and we need one more day of work so 13 days in total would be enough.

Feel free to ask any more questions!
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to reach out!
A group of 10 workers can plough a field in 20 days. This group starts   [#permalink] 30 May 2020, 09:58