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

Question

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

(A) 4y
(B) 5y
(C) 6y
(D) 8y
(E) 9y

Bunuel · Accepted Answer

The amount Mary has in the end is x-y dollars and she worked for 8 hours;
The amount John has in the end is x+y dollars and he worked for 10 hours;;

We are told that in this case their hourly wage was the same:  hourly \ wage=\frac{wage}{number \ of \ hours \ worked}=\frac{x-y}{8}=\frac{x+y}{10} , from  \frac{x-y}{8}=\frac{x+y}{10}  we get that  x=9y .

Answer: E.

KarishmaB · Answer

Number plugging could work like this:

John worked on the job for 10 hours and Mary worked for 8 hours. They were both paid an equal amount but Mary gave John some of her amount so that they both get the same hourly wage. We can easily imagine this by assuming that they both got $9 each initially and Mary gave $1 to John so that Mary got $8 (@$1 per hr) and John got $10 (@ $1 per hr). 
So x could be $9
and y could be $1.
We need x in terms of y which is x = 9y

runningguy · Answer

Could someone also do this problem plugging numbers. I tried but it is not working.

re4Bschool11 · Answer

I had trouble coming up with the above approach so i tried plugging numbers.

You are told John worked 10 hrs and Mary worked 8, and they are EACH paid x dollars for their work. I chose 80 for x since it's a multiple of 
8 and 10. In this case, John is paid 8/hr and Mary is paid 10/hr. Since they have to be paid the same amount, Mary gives $1 to John (remember, y represents the amount of money she gives to John, so here y = 1). John now earns $9/hr or 9y.

theGame001 · Answer

I tried this but I am not getting the answer.

Lets assume Both John and Mary got 8 and 8 advance. 
Mary gave john $2 as she worked 2 hour less.
So y=2.
Answer: a.

Where am I going wrong?

Bunuel · Answer

We are told that after Mary gave John y dollars they received the same hourly wage. Your example does not provide that. Try using $9 advance pay instead or check Karishma's post for number plugging here: john-and-mary-were-each-paid-x-dollars-in-advance-to-do-a-144782.html#p1294268 or algebraic approach here: john-and-mary-were-each-paid-x-dollars-in-advance-to-do-a-144782.html#p1161559 Hope this helps.

arunspanda · Answer

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

(A) 4y
(B) 5y
(C) 6y
(D) 8y
(E) 9y
 
John worked 10 hours and paid x dollars
Mary worked 8 hours and paid x dollars

John and Mary together worked:  10 + 8 = 18 hours 
John and Mary together paid : x + x = 2x

Hence, hourly wage or wage/hour  = 2x/18  or  x/9

As per hourly wage, john is paid less by an amount  (x/9)*10 - x  Or,  x/9 
Or, Mary is paid more by an amount  x - (x/9)*10  or  x/9

Or,  x/9  is the amount Mary gave John so that they would have received the same hourly wage.
Or,  x/9 = y 
Or,  x = 9y

Hence, answer (E)

PerfectScores · Answer

Let us say that both got $ 40 for the job, x = 40

John --- 10 hours ---- $ 40 ----- After paying ---- 40 + y
Mary --- 8 hours ------ $ 40 ----- After paying ----- 40 - y

Now the rate is same: (40 + y)/10 = (40 - y)/8
160 + 4y = 200 - 5y
9y = 40
y = 40/9

By putting y = 40/9 we should get x = 40 which is answer option E.

russ9 · Answer

Hi Karishma,

I actually tried the number approach as well and did EXACTLY that, with those same exact numbers, but for some reason, didn't think that the answer was the right answer.

Mary worked 8 hours.
John worked 10 hours.

Let's say they both earned 80 dollars, which would make:

Mary's hourly wage: $10/hr
John's hourly wage: $8/hr

To get the same wage, lets say 9, mary would earn $9/hr and John would earn $11/hr. But doing so, the total gets misaligned. Now, Mary's total wage will be (9$/hr)(8hr) = $72 and John's will be (11$/hr)(10hr) = $110. Don't they need to earn the same TOTAL money? How can this work if they need to earn the same total?

Thanks!

Bunuel,

I can completely follow the logic below but I had no idea that we were solving for x. How did you come up with the concept, albeit correct, that we were solving for x?

Thanks!

KarishmaB · Answer

The numbers I have assumed are that Mary and John got a TOTAL of $9 each initially (same total wage received). Then Mary gave John $1 so that Mary got a total of $8 and John got a total of $10. They hourly wages are $1/hour (same for both). This gives x = $9 and y = $1.

deliverance · Answer

Hi Bunuel,

Could you please let me know where I went wrong in my approach?

I assumed that that the advance amount given to each person was 40 $. (X=40).

As John worked 10 hours and Mary worked 8 hours,

John's hourly rate = 40/10=4$/hr
Mary's houry rate = 40/8=5/hr

For Mary to receive the same hourly rate as John (4$/hr), she would have had to earn only 4*8 = 32$

Hence the amount to be given to John = 40-32=8 (i.e y = 8 in this case)

In this case 40=5(8) i.e. x=5y (option B)

Bunuel · Answer

The point is that when Mary gives John y dollars of her payment, Mary's hourly wage will decrease and John's hourly wage will increase. In your case Mary's hourly wage is $4 while John's hourly wage becomes 48/10=$4.8. As you can see the hourly wages are not equal.

ScottTargetTestPrep · Answer

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 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 hourly wages of John and Mary equal to each other.

(x + y)/10 = (x – y)/8

We can cross multiply and we get:

8x + 8y = 10x – 10y

-2x = -18y

x = 9y

Answer is E.

chetan2u · Answer

Hi,
 A simple way to look at the problem is .. 
they were paid x for equal hours..
so the time was supposed to be \frac{10+8}{2} = 9  hr..
  M gives y dollar to J since she worked one hour less and J worked 1 hr more than 9.. so hourly wage is y.. 
for 9 hours wage = 9y = x 
E

BrentGMATPrepNow · Answer

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

EMPOWERgmatRichC · Answer

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

egmat · Answer

Here's how to think about this problem:

Step 1: Translate what you know 
Both John and Mary initially received  x  dollars each. John worked for 10 hours, and Mary worked for 8 hours (that's 2 hours less than John). After the work was done, Mary gave John  y  dollars so their hourly wages would be equal.

Step 2: Set up the final payment scenario 
This is where you need to be careful. After Mary gives John  y  dollars:
 
 John's final payment:  x + y  dollars (he received  y  from Mary) 
 Mary's final payment:  x - y  dollars (she gave away  y )

Step 3: Apply the equal hourly wage condition 
Here's the key insight that makes everything click:  hourly wage = total payment ÷ hours worked

Since their hourly wages are now equal:
 \frac{x+y}{10} = \frac{x-y}{8}

Step 4: Solve for x 
Cross-multiply to eliminate the fractions:
 8(x + y) = 10(x - y)

Expand both sides:
 8x + 8y = 10x - 10y

Rearrange to group like terms:
 8y + 10y = 10x - 8x 
 18y = 2x

Therefore:
 x = 9y

Answer: (E) 9y

Quick verification: If John initially got  9y  dollars and received  y  more, he ends up with  10y  dollars for 10 hours =  y  per hour. Mary ends up with  8y  dollars for 8 hours =  y  per hour. Perfect! ✓

Now, while this solution gets you to the right answer, there's a deeper systematic framework for tackling all payment redistribution problems that you'll find incredibly useful. You can check out the  complete step-by-step solution on Neuron by e-GMAT  to understand the broader patterns and process skills (like TRANSLATE, INFER, MANIPULATE) that make these problems much easier to recognize and solve systematically. You can also explore detailed solutions for  other GMAT official questions on Neuron  for structured practice with comprehensive analytics.

Hope this helps! 🎯

Amity007 · Answer

I had a query about this question, when we are adding the IF condition in the sentence then do we have to calculate the equal amount of share after mary gave her share to john or the original one before the if condition.
Coz if we are going to take if condition hypothetically then we need to calculate the john share in terms of y which is 1x, that would be 8y.
And the same after the condition it's 9y.

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=87771 --- Harsha GMAT-Club-Forum-uwroq6nk.png

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