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John and Mary were each paid x dollars in advance to do a

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by M7MBA » Fri Apr 05, 2019 11:11 am

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Answers

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E

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Difficulty—

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

[spoiler]OA=E[/spoiler]

Source: Official Guide
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by Brent@GMATPrepNow » Fri Apr 05, 2019 1:39 pm
M7MBA wrote: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

[spoiler]OA=E[/spoiler]

Source: Official Guide
One 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 = x = 9y = E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Thu Sep 26, 2019 12:49 pm
Hi All,

This question can be solved by TESTing VALUES. Here's how to do so:

In the second sentence, we're told that John worked for 10 hours and Mary worked for 8 hours... thus, 18 total hours were worked. We have to do a little more work before we pick a value for X though...

For the sake of using a nice, "round" number, let's say that the hourly pay for BOTH John and Mary should be $10/hour. This means that the entire 18-hour job should cost...

(18)($10) = $180.

The first sentence tells us that John and Mary were paid the SAME X-Dollar payment in advance though, so that $180 was split in HALF.... $90 for John and $90 for Mary.

At this point, John worked 10 hours for $90....
and Mary worked 8 hours for $90.

Mary gives John enough of her money ($Y) so that they both have the same hourly pay (the $10/hour that we chose earlier). Thus, Mary would have to give John $10. Now, the totals would be....

John worked 10 hours for $90 + $10 = $100 (re: $10/hour)
and Mary worked 8 hours for $90 - $10 = $80 (re: $10/hour)

So Y = 10 and we're looking for an answer that equals 90. That result is actually really easy to spot...

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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by Scott@TargetTestPrep » Sun Sep 29, 2019 6:18 pm
M7MBA wrote: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

[spoiler]OA=E[/spoiler]

Source: Official Guide
We are first given that John worked for 10 hours and that Mary worked for 2 hours less than John. It follows that:

John's hours = 10

Mary's hours = 8

We are also given that John and Mary were each given x dollars in advance. We are also told that Mary gave John y dollars of her payment so that they would have an equal hourly wage. It follows that Mary actually made (x - y) dollars. Since John received y dollars from Mary, he now made (x + y) dollars. Using this information, the hourly wages of John and Mary are:

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

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 hourly wages of John and Mary equal to each other.

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

We can cross multiply and solve:

8x + 8y = 10x - 10y

-2x = -18y

x = 9y

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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