Hourly Wage

This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 98
Joined: Sat May 31, 2014 8:29 pm
Thanked: 1 times
Followed by:2 members

Hourly Wage

by RiyaR » Wed Sep 24, 2014 7:52 am
. John and Mary were each paid x dollars in advance to do a certain job together, John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance ?
(A) 4y (B) 5y (C) 6y
(D) 8y (E) 9y

User avatar
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 » Wed Sep 24, 2014 7:58 am
John and Mary were each paid x dollars in advance to do a certain job together, John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance ?
(A) 4y (B) 5y (C) 6y
(D) 8y (E) 9y
We can plug in a value for the hourly rate.

Let hourly rate = $1.
Since John works 10 hours, he earns 10*1 = $10.
Since Mary works 10-2=8 hours, she earns 8*1 = $8.
Thus, the total advance payment to John and Mary = 10+8 = $18.
Since each receives x dollars in advance, x = 18/2 = $9.

John is given x=9 in advance but must earn $10.
Mary is given x=9 in advance but must earn $8.
Thus, Mary gives John y=1.

The question asks for the amount that John is paid in advance: $9.
This is our target.
Now we plug y=1 into the answers to see which yields our target of 9.

Only answer choice E works:
9y = 9*1 = 9.

The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Sep 24, 2014 9:45 am
John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?
(A) 4y
(B) 5y
(C) 6y
(D) 8y
(E) 9y
Another approach:

Salary
Mary's NET salary was x - y dollars (because Mary gave John y dollars)
John's NET salary was x + y dollars

Hours worked
Mary worked 8 hours
John worked 10 hours


In the end, John and Mary received the SAME hourly wage.
So, John's hourly wage = Mary's hourly wage
Hourly wage = (total salary)/(hours worked)
So, (x + y)/10 = (x - y)/8

In terms of y, that John was paid in advance?
In other words, what is the value of x (in terms of y)
So, we'll solve our equation for x.

Take (x + y)/10 = (x - y)/8 and cross multiply to get:
10(x - y) = 8(x + y)
Expand: 10x - 10y = 8x + 8y
Rearrange: 2x = 18y
Divide by 2: x = 9y
So, John's advance payment = [spoiler]x = 9y = E[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image