Working together, Joe and Joanne

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Mon Nov 20, 2017 4:41 am

Working together, Joe and Joanne finish a job in 2 hours. How long will it take Jeremy and Joe to finish the job?

(1) Working alone and without breaks Joe takes 5 hours to finish the job, which is 400% as long as the time it takes Jeremy to finish the job.

(2) Working alone and without breaks Joanne takes 10 hours to finish 3 times the job.

Which of the statements is the correct answer?

OA A

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Source: Beat The GMAT — Data Sufficiency | Mon Nov 20, 2017 4:41 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Nov 20, 2017 1:11 pm

lheiannie07 wrote:Working together, Joe and Joanne finish a job in 2 hours. How long will it take Jeremy and Joe to finish the job?

(1) Working alone and without breaks Joe takes 5 hours to finish the job, which is 400% as long as the time it takes Jeremy to finish the job.

(2) Working alone and without breaks Joanne takes 10 hours to finish 3 times the job.

Statement 1:
Since Joe's time of 5 hours is equal to 400% of Jeremy's time, we get:
5 = (400/100)(Jeremy's time)
5 = (4)(Jeremy's time)
5/4 = Jeremy's time.

Case 1: Job = 5 widgets
Since Joe's time = 5 hours, Joe's rate = w/t = 5/5 = 1 widget per hour.
Since Jeremy's time = 5/4 hours, Jeremy's rate = w/t = 5/(5/4) = (5)(4/5) = 4 widgets per hour.
Combined rate for Joe and Jeremy together = 1+4 = 5 widgets per hour.
Since their combined rate = 5 widgets per hour, the time for Joe and Jeremy together to complete the 5-widget job = w/r = 5/5 = 1 hour.

Case 2: Job = 10 widgets
Since Joe's time = 5 hours, Joe's rate = w/t = 10/5 = 2 widgets per hour.
Since Jeremy's time = 5/4 hours, Jeremy's rate = w/t = 10/(5/4) = (10)(4/5) = 8 widgets per hour.
Combined rate for Joe and Jeremy together = 2+8 = 10 widgets per hour.
Since their combined rate = 10 widgets per hour, the time for Joe and Jeremy together to complete the 10-widget job = w/r = 10/10 = 1 hour.

In each case, the time for Joe and Jeremy together is THE SAME (1 hour).
SUFFICIENT.

Statement 2:
No information about Jeremy.
INSUFFICIENT.

The correct answer is A.

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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

by Mo2men » Tue Nov 21, 2017 10:00 am

GMATGuruNY wrote:
lheiannie07 wrote:Working together, Joe and Joanne finish a job in 2 hours. How long will it take Jeremy and Joe to finish the job?

(1) Working alone and without breaks Joe takes 5 hours to finish the job, which is 400% as long as the time it takes Jeremy to finish the job.

(2) Working alone and without breaks Joanne takes 10 hours to finish 3 times the job.
Statement 1:
Since Joe's time of 5 hours is equal to 400% of Jeremy's time, we get:
5 = (400/100)(Jeremy's time)
5 = (4)(Jeremy's time)
5/4 = Jeremy's time.

Case 1: Job = 5 widgets
Since Joe's time = 5 hours, Joe's rate = w/t = 5/5 = 1 widget per hour.
Since Jeremy's time = 5/4 hours, Jeremy's rate = w/t = 5/(5/4) = (5)(4/5) = 4 widgets per hour.
Combined rate for Joe and Jeremy together = 1+4 = 5 widgets per hour.
Since their combined rate = 5 widgets per hour, the time for Joe and Jeremy together to complete the 5-widget job = w/r = 5/5 = 1 hour.

Case 2: Job = 10 widgets
Since Joe's time = 5 hours, Joe's rate = w/t = 10/5 = 2 widgets per hour.
Since Jeremy's time = 5/4 hours, Jeremy's rate = w/t = 10/(5/4) = (10)(4/5) = 8 widgets per hour.
Combined rate for Joe and Jeremy together = 2+8 = 10 widgets per hour.
Since their combined rate = 10 widgets per hour, the time for Joe and Jeremy together to complete the 10-widget job = w/r = 10/10 = 1 hour.

In each case, the time for Joe and Jeremy together is THE SAME (1 hour).
SUFFICIENT.

Statement 2:
No information about Jeremy.
INSUFFICIENT.

The correct answer is A.

Dear Mitch,

How come you reach 1 hour in statement A, while its mentioned in the stem that both together will finish a job in 2 hrs, I highlighted it above.
Also I do understand what the question real asks if is every one alone.

Thanks

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Nov 21, 2017 10:05 am

Mo2men wrote:Dear Mitch,

How come you reach 1 hour in statement A, while its mentioned in the stem that both together will finish a job in 2 hrs, I highlighted it above.
Also I do understand what the question real asks if is every one alone.

Thanks

Read carefully.
The prompt indicates that the time Joe and JOANNE = 2 hours.
My work in Statement 1 indicates that the time for Joe and JEREMY = 1 hour.
Joe and JOANNE â‰ Joe and JEREMY.

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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

by Mo2men » Tue Nov 21, 2017 10:07 am

GMATGuruNY wrote:
Mo2men wrote:Dear Mitch,

How come you reach 1 hour in statement A, while its mentioned in the stem that both together will finish a job in 2 hrs, I highlighted it above.
Also I do understand what the question real asks if is every one alone.

Thanks
Read carefully.
The prompt indicates that the time Joe and JOANNE = 2 hours.
My work in Statement 1 indicates that the time for Joe and JEREMY = 1 hour.
Joe and JOANNE â‰ Joe and JEREMY.

Thanks Mitch,
I did not take care while I was reading quickly, The names are all close.

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Jan 17, 2018 9:26 pm

GMATGuruNY wrote:
lheiannie07 wrote:Working together, Joe and Joanne finish a job in 2 hours. How long will it take Jeremy and Joe to finish the job?

(1) Working alone and without breaks Joe takes 5 hours to finish the job, which is 400% as long as the time it takes Jeremy to finish the job.

(2) Working alone and without breaks Joanne takes 10 hours to finish 3 times the job.
Statement 1:
Since Joe's time of 5 hours is equal to 400% of Jeremy's time, we get:
5 = (400/100)(Jeremy's time)
5 = (4)(Jeremy's time)
5/4 = Jeremy's time.

Case 1: Job = 5 widgets
Since Joe's time = 5 hours, Joe's rate = w/t = 5/5 = 1 widget per hour.
Since Jeremy's time = 5/4 hours, Jeremy's rate = w/t = 5/(5/4) = (5)(4/5) = 4 widgets per hour.
Combined rate for Joe and Jeremy together = 1+4 = 5 widgets per hour.
Since their combined rate = 5 widgets per hour, the time for Joe and Jeremy together to complete the 5-widget job = w/r = 5/5 = 1 hour.

Case 2: Job = 10 widgets
Since Joe's time = 5 hours, Joe's rate = w/t = 10/5 = 2 widgets per hour.
Since Jeremy's time = 5/4 hours, Jeremy's rate = w/t = 10/(5/4) = (10)(4/5) = 8 widgets per hour.
Combined rate for Joe and Jeremy together = 2+8 = 10 widgets per hour.
Since their combined rate = 10 widgets per hour, the time for Joe and Jeremy together to complete the 10-widget job = w/r = 10/10 = 1 hour.

In each case, the time for Joe and Jeremy together is THE SAME (1 hour).
SUFFICIENT.

Statement 2:
No information about Jeremy.
INSUFFICIENT.

The correct answer is A.

Thanks a lot!

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