OG 11 - Question No. 220

[mehravikas]

Mary and John were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hrs and Mary worked on the job for 2 hrs less than John. If Mary, gave John y dollars of her payment so that they would have recieved the same hourly wage rate 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


OA is: E, not satisfied with the explanation in OG

Can someone please explain?

[VP_Jim]

I'd plug in a number. Let's say each of them was paid $9 in advance, so x=$9.

Hence, John got paid $9 to work 10 hours and Mary got paid $9 to work 8 hours.

To make their hourly rates the same, Mary would give John $1. Then, John would have $10 for 10 hours and Mary would have $8 for 8 hours.

So, Y=$1 given these numbers. Now we just have to find the answer choice that gives us $9 (the amount they were paid in advance) when we plug in $1 for Y, so E.

The numbers don't work so nicely if x is not divisible by 9. However, part of being a good GMAT taker is recognizing what numbers are good to plug in. In this problem, I saw that 9 was a good number because we have 10 (John's hours) and 8 (Mary's hours) and we want to equalize them (at 9).

Hope this helps!

[mehravikas]

It is actually confusing. Here is what I did -

Amount of advance - 100
John worked for 10 hours, so his hourly rate would be 10 p/h
Mary's hour rate - 12.5 p/h
Therefore, mary has to give $20 to john for an equal hourly pay rate.
Y = 20 and 5Y = 100 (the amount john had as an advance)

I'd plug in a number. Let's say each of them was paid $9 in advance, so x=$9.

Hence, John got paid $9 to work 10 hours and Mary got paid $9 to work 8 hours.

To make their hourly rates the same, Mary would give John $1. Then, John would have $10 for 10 hours and Mary would have $8 for 8 hours.

So, Y=$1 given these numbers. Now we just have to find the answer choice that gives us $9 (the amount they were paid in advance) when we plug in $1 for Y, so E.

The numbers don't work so nicely if x is not divisible by 9. However, part of being a good GMAT taker is recognizing what numbers are good to plug in. In this problem, I saw that 9 was a good number because we have 10 (John's hours) and 8 (Mary's hours) and we want to equalize them (at 9).

Hope this helps!

[dmateer25]

(X + Y)/10 - John's hourly rate after getting Y dollars from Mary

(X - Y)/8 - Mary's hourly rate after giving Y dollars to John

Because we know the hourly rates are equal after Mary gives John Y dollars we can set them equal and isolate X.

(X + Y)/10 = (X - Y)/8

10X - 10Y = 8X + 8Y

2X = 18Y

X = 9Y

[rohangupta83]

if you don't want to solve the problem:

total number of hours worked = 10+8 = 18
J worked 10 hrs
M worked 8 hrs
wage / hr = x/18

but they should have worked 9 hrs each as they were paid equally. This means that Mary gave 1 hr worth of salary to John
or
x/18 = y or x = 18y

John was paid half x = x/2 or 18y/2 = 9y