Sam, Mark and Joe work every day of the week, and each works

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

Sam, Mark and Joe work every day of the week, and each works

by BTGmoderatorRO » Sun Mar 25, 2018 7:55 am

Sam, Mark and Joe work every day of the week, and each works the same number of hours as he did the day before. In 7 days, they earn $252 in total. If each receives the same rate per person per hour, and Mark worked twice as many hours as Sam and Joe worked three times as many hours as Mark, how much money does Mark earn in 5 days?

A. $24
B. $30
C. $36
D. $40
E. $50
OA is d
what mathematical approach can I apply here to get the correct answer to this question? Can anyone help me out here?
Thanks

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Source: Beat The GMAT — Problem Solving | Sun Mar 25, 2018 7:55 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Sun Mar 25, 2018 10:38 pm

Roland2rule wrote:Sam, Mark and Joe work every day of the week, and each works the same number of hours as he did the day before. In 7 days, they earn $252 in total. If each receives the same rate per person per hour, and Mark worked twice as many hours as Sam and Joe worked three times as many hours as Mark, how much money does Mark earn in 5 days?

A. $24
B. $30
C. $36
D. $40
E. $50
OA is d
what mathematical approach can I apply here to get the correct answer to this question? Can anyone help me out here?
Thanks

Say Sam earns $x per day, thus Mark earns 2*x = $2x and Joe earns 3*2x = $6x per day.

Total earning in 7 days = 7*(x + 2x + 6x) = 63x

We are given that 63x = 252 => x = $4

Thus, Mark earns 2*4 = $8 per day or 5*8 = $40 in 5 days

The correct answer: D

Hope this helps!

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

by GMATGuruNY » Mon Mar 26, 2018 3:25 am

Roland2rule wrote:Sam, Mark and Joe work every day of the week, and each works the same number of hours as he did the day before. In 7 days, they earn $252 in total. If each receives the same rate per person per hour, and Mark worked twice as many hours as Sam and Joe worked three times as many hours as Mark, how much money does Mark earn in 5 days?

A. $24
B. $30
C. $36
D. $40
E. $50

Alternate approach:

Mark worked twice as many hours as Sam.
Joe worked three times as many hours as Mark.
Let S = 1 hour.
Since Mark works twice as many hours as Sam, M = 2*1 = 2 hours.
Since Joe works 3 times as many hours as Mark, J = 3*2 = 6 hours.
Total work-hours = 1+2+6 = 9.
Of the 9 total work-hours, Mark works 2.
Thus, Mark earns 2/9 of the total pay:
(2/9)(252) = 56.

How much money does Mark earn in 5 days?
Since there are 7 total work-days, in 5 work-days Mark earns 5/7 of his pay:
(5/7)(56) = 40.

The correct answer is D.

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by Scott@TargetTestPrep » Wed Mar 28, 2018 10:16 am

Roland2rule wrote:Sam, Mark and Joe work every day of the week, and each works the same number of hours as he did the day before. In 7 days, they earn $252 in total. If each receives the same rate per person per hour, and Mark worked twice as many hours as Sam and Joe worked three times as many hours as Mark, how much money does Mark earn in 5 days?

A. $24
B. $30
C. $36
D. $40
E. $50

We can let x = the hourly rate for each person, s = the number of hours Sam works per day, m = the number of hours Mark works per day, and j = the number of hours Joe works per day.

We are given that m = 2s and j = 3m = 3(2s) = 6s. Thus, in terms of s and x, we can create the following equation:

7sx + 7(2s)x + 7(6s)x = 252

7sx + 14sx + 42sx = 252

63sx = 252

sx = 4

We are asked for the amount of money earned by Mark in 5 days. In 5 days, Mark earns:

5(2s)x = 10sx = 10(4) = 40 dollars

Answer: D

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