If it takes 50 workers 8 hours to build . . .

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

If it takes 50 workers 8 hours to build . . .

by M7MBA » Tue Nov 14, 2017 6:26 am

If it takes 50 workers 8 hours to build a log cabin, how long would it have taken 30 workers to build the same cabin?

A) 9 hrs 36 min.

B) 10 hrs 24 min.

C) 12 hrs 24 min.

D) 12 hrs 40 min.

E) 13 hrs 20 min.

The OA is E.

Experts, how can I calculate the answer here? What formula should I state?

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Source: Beat The GMAT — Problem Solving | Tue Nov 14, 2017 6:26 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 am; Location: Boston, MA; Thanked: 1153 times; Followed by:128 members; GMAT Score:770

by DavidG@VeritasPrep » Tue Nov 14, 2017 9:03 am

M7MBA wrote:If it takes 50 workers 8 hours to build a log cabin, how long would it have taken 30 workers to build the same cabin?

A) 9 hrs 36 min.

B) 10 hrs 24 min.

C) 12 hrs 24 min.

D) 12 hrs 40 min.

E) 13 hrs 20 min.

The OA is E.

Experts, how can I calculate the answer here? What formula should I state?

If it takes 50 workers 8 hours to build a cabin, it takes a total of 50*8 = 400 worker-hours to complete the job. In other words, if # workers * # hours worked = 400, we've got ourselves a cabin.

If there are 30 workers, we just need to solve 30 * # hours worked = 400 ---> # hours worked = 400/30 = 40/3 = 13 1/3 hours. The answer is E

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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 am; Location: Boston, MA; Thanked: 1153 times; Followed by:128 members; GMAT Score:770

by DavidG@VeritasPrep » Tue Nov 14, 2017 9:05 am

M7MBA wrote:If it takes 50 workers 8 hours to build a log cabin, how long would it have taken 30 workers to build the same cabin?

A) 9 hrs 36 min.

B) 10 hrs 24 min.

C) 12 hrs 24 min.

D) 12 hrs 40 min.

E) 13 hrs 20 min.

The OA is E.

Experts, how can I calculate the answer here? What formula should I state?

Alternatively, the # of workers and # of hours worked will have a reciprocal relationship. (If we doubled the number of workers, they'd do the job in 1/2 the time, etc.)

If we started with 50 workers, then 30 workers would mean we'd have 30/50 = 3/5 the number of workers. So 3/5 the number of workers will do the job in 5/3 the time, which was initially 8 hours. (5/3) * 8 = 40/3 = 13 1/3. The answer is E

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Tue Nov 14, 2017 1:14 pm

Hi M7MBA,
Let's take a look at your question.

The question states:
"If it takes 50 workers 8 hours to build a log cabin, how long would it have taken 30 workers to build the same cabin? "

50 workers build a log cabin = 8 hours

If we want to calculated how many hours will one worker take to build that cabin, we will be using the multiplication, since one worker will have to work more than 50 workers. Therefore,
1 worker will build the log cabin = 50 x 8 = 400 hours

Now, we need to find out how many hours 30 workers will take to build the same log cabin. Since 30 workers are more than 1 worker, so they will take less time and hence we will be using the division to find the number of hours.

30 workers will build the log cabin = 400/30 = 13.33 hours.

Therefore 30 workers will take 13.33 hours which means 13 complete hours and some more minutes. Let's see in the given options to find out the closest value to 13.33 hours i.e. 13 hours and 20 minutes.

Therefore, Option E is correct.

Hope it helps.
I am available, if you'd like any follow up.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Jul 28, 2019 9:19 am

M7MBA wrote:If it takes 50 workers 8 hours to build a log cabin, how long would it have taken 30 workers to build the same cabin?

A) 9 hrs 36 min.

B) 10 hrs 24 min.

C) 12 hrs 24 min.

D) 12 hrs 40 min.

E) 13 hrs 20 min.

The OA is E.

Experts, how can I calculate the answer here? What formula should I state?

The rate for 50 workers is 1/8. The rate for 1 worker is (1/8)/50 = 1/400, and the rate for 30 workers is 30/400 = 3/40.

Thus it takes 30 workers 1/(3/40) = 40/3 = 13 â…“ hours = 13 hours 20 minutes.

Alternate Solution:

The total number of hours needed to build the cabin is 50 x 8 = 400 hours. So if there are 30 workers, it will take 400/30 = 13.333 hours = 13 â…“ hours = 13 hours, 20 minutes.

Answer: E

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