OG 11 - Question No. 220

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!

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)

VP_Jim wrote: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!

(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

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