John and Marry were each paid x dollars in advance...

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

John and Marry were each paid x dollars in advance...

by BTGmoderatorLU » Mon Mar 12, 2018 2:19 pm

John and Mary were 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

The OA is E.

I'm really confused by this PS question. Experts, any suggestion?

I tried to solve it as follow,

x/10 johns wage
x/8 mary wage

x/8-y=x/10+y

x= 80y

80y/10= 8y so my answer was D.

However, it is wrong. I don't get it. Where is the mistake? I need your help, please! Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Mon Mar 12, 2018 2:19 pm

GMAT/MBA Expert

Brent@GMATPrepNow: 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 » Tue Mar 13, 2018 6:21 am

LUANDATO wrote:John and Mary were 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

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 = x = 9y = E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Quote

GMAT/MBA Expert

Brent@GMATPrepNow: 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 » Tue Mar 13, 2018 6:25 am

LUANDATO wrote:John and Mary were 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

The OA is E.

I'm really confused by this PS question. Experts, any suggestion?

I tried to solve it as follow,

x/10 johns wage
x/8 mary wage

x/8-y=x/10+y

x= 80y

80y/10= 8y so my answer was D.

However, it is wrong. I don't get it. Where is the mistake? I need your help, please! Thanks in advance.

The problem with your solution is highlighted above in green

In order for their hourly wages to be the same, we need (x - y)/8 = (x + y)/10
We need this because hourly wage = (total $ received)/(total hours worked)

For more on this, see my solution below.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Mar 14, 2018 3:29 pm

LUANDATO wrote:John and Mary were 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 are first given that John worked for 10 hours, and that Mary worked for 2 hours less than John. So we can say:

John's hours = 10

Mary's hours = 8

We are also given that John and Mary were each given x dollars in advance. We can use this to determine the hourly wage for both Mary and John.

Since (hourly wage)(# of hours) = total paid, we can say that:

hourly wage = (total paid)/(# of hours)

John's hourly wage = x/10

Mary's hourly wage = x/8

We are also told that Mary gave John y dollars of her payment so that they would have an equal hourly wage. This means that Mary actually made (x - y) dollars. Since John received y dollars he now makes (x + y) dollars. Using this information, the revised hourly wages of John and Mary are:

Mary's wage = (x - y)/8

John's wage = (x + y)/10

Since we are told that the two hourly wages are the same, we can set the revised hourly wages of John and Mary equal to each other.

(x + y)/10 = (x - y)/8

We cross multiply and obtain:

8x + 8y = 10x - 10y

-2x = -18y

x = 9y

Answer: E

Scott Woodbury-Stewart
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