Unitary Method Problem

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by [email protected] » Sat Oct 10, 2015 2:23 am

If 5 men working for 6 hours a day can reap a field in 20 days, in how many days will 15 men reap the field, working 8 hours a day ?

(a) 5 days

(b) 6 days

(c) 7 & 1/2 days

(d) 9 days

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Source: Beat The GMAT — Problem Solving | Sat Oct 10, 2015 2:23 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Oct 10, 2015 7:14 am

[email protected] wrote:If 5 men working for 6 hours a day can reap a field in 20 days, in how many days will 15 men reap the field, working 8 hours a day ?

(a) 5 days

(b) 6 days

(c) 7 & 1/2 days

(d) 9 days

Assign a VALUE to the number of pants a worker can reap each hour.

If 5 men working for 6 hours a day can reap a field in 20 days
Let's say that ONE worker can reap 1 PLANT EACH HOUR
So, in 6 hours, ONE worker can reap 6 PLANTS
In 20 days, ONE worker can reap 120 PLANTS
In 20 days, FIVE worker can reap 600 PLANTS
So, we can say that this field has 600 PLANTS

...in how many days will 15 men reap the field, working 8 hours a days?
If the field has 600 PLANTS, then EACH of the 15 men will be in charge of 600/15 plants.
In other words, EACH man will be in charge of 40 plants.
If ONE worker can reap 1 PLANT EACH HOUR, then it will take EACH man 40 hours to reap his assigned plants
If each man works 8 hours per day, then the number of days it take = 40/8 = 5 days

Answer: A

Brent Hanneson - Creator of GMATPrepNow.com

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