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Manager  Joined: 02 Dec 2012
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Question Stats: 63% (02:22) correct 37% (02:46) wrong based on 939 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 55681
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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

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 $$x=9y$$.

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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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

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.
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Intern  Joined: 09 Sep 2013
Posts: 16
Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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Could someone also do this problem plugging numbers. I tried but it is not working.
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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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

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
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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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HCalum11 wrote:
runningguy wrote:
Could someone also do this problem plugging numbers. I tried but it is not working.

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.

Exactly!.. I picked up the same approach with 800$provided to Mary and John.. It is easier to choose the multiple of rates when picking up a number instead of a just using a 100$ approach..
Manager  Joined: 13 Jul 2013
Posts: 64
GMAT 1: 570 Q46 V24 Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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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? Math Expert V Joined: 02 Sep 2009 Posts: 55681 Re: John and Mary were each paid x dollars in advance to do a [#permalink] Show Tags 1 theGame001 wrote: 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.

Where am I going wrong?

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. _________________ Manager  Joined: 04 Oct 2013 Posts: 151 Location: India GMAT Date: 05-23-2015 GPA: 3.45 Re: John and Mary were each paid x dollars in advance to do a [#permalink] Show Tags 1 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 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) Manager  Joined: 12 Jan 2013 Posts: 145 Re: John and Mary were each paid x dollars in advance to do a [#permalink] Show Tags Walkabout 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 I did NOT solve this question correctly but I still got to the correct answer because I knew that 9 needed to be included in the correct answer because of this: Initially we are given x + x = Total Advance. Then, given that Mary gives John y USD of her payment, we have: 10(x + y) + 8(x - y) = Total Advance ----> 10x + 10y + 8x - 8y = TA ----> 18x + 2y = TA ----> 9x + y = TA.. There is no multiple of 9 in the answer other than E, thus I came to the correct answer even though I knew I hadn't done sufficient calculations to solve for the exact value of 9y. Of course, this approach is very flawed because nothing out of 9x + y tells us that the answer should be 9y.. But given that more than 40% of everyone who did this question failed it, I find it quite obvious that the "correct" approach is not intuitive to a lot of us. IMO, the GMAT is not a test where you're successful only if you know 100% of everything; a big portion of the test consists of making qualified guesses, otherwise many of us spend too much time trying to solve problems that obviously are over our heads (like this one, for me). With that in mind, I think this approach - seeing a possible pattern - is a weak but viable approach. Originally posted by aeglorre on 10 Jan 2014, 04:35. Last edited by aeglorre on 10 Jan 2014, 04:47, edited 2 times in total. Manager  Joined: 20 Dec 2013 Posts: 119 Re: John and Mary were each paid x dollars in advance to do a [#permalink] Show Tags 2 Walkabout 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 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.
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Manager  Joined: 15 Aug 2013
Posts: 241
Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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

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

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 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

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: $$hourly \ wage=\frac{wage}{# \ of \ hours \ worked}=\frac{x-y}{8}=\frac{x+y}{10}$$, from $$\frac{x-y}{8}=\frac{x+y}{10}$$ we get that $$x=9y$$.

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!
Intern  Joined: 01 Sep 2014
Posts: 2
Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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Bunuel 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

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: $$hourly \ wage=\frac{wage}{# \ of \ hours \ worked}=\frac{x-y}{8}=\frac{x+y}{10}$$, from $$\frac{x-y}{8}=\frac{x+y}{10}$$ we get that $$x=9y$$.

Hi Bunuel

My doubt is that shouldn't the amount Mary and John have in the end also contains (Hourly wage * No. of hours)?

I solved it like this :

Total revenue of John= x +10(hourly wage)+y
Similarly for Mary, it will be = x+8(hourly wage)-y

Since, Mary gives y amount to John which corresponds to extra 2 hours worked by John and 2 less hours by Mary

2 * hourly wage = y
or hourly wage = y/2

final equation to equate hourly wages
(x+(10y/2)+ y)/10 = (x+(8y/2)-y)/8

(x+6y)/10 = (x+3y)/8

hence, x=9y

Isn't this the right approach?

Thanks Math Expert V
Joined: 02 Sep 2009
Posts: 55681
Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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russ9 wrote:
VeritasPrepKarishma wrote:
runningguy wrote:
Could someone also do this problem plugging numbers. I tried but it is not working.

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

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 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

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: $$hourly \ wage=\frac{wage}{# \ of \ hours \ worked}=\frac{x-y}{8}=\frac{x+y}{10}$$, from $$\frac{x-y}{8}=\frac{x+y}{10}$$ we get that $$x=9y$$.

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!

We are told that John was paid x dollars in advance.
The question asks: what was the dollar amount, in terms of y, that John was paid in advance? So, it asks to find x (the dollar amount that John was paid in advance) in terms of y.

Hope it's clear.
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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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russ9 wrote:
VeritasPrepKarishma wrote:
runningguy wrote:
Could someone also do this problem plugging numbers. I tried but it is not working.

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

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!

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 = $1. _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Senior Manager  B Joined: 10 Mar 2013 Posts: 488 Location: Germany Concentration: Finance, Entrepreneurship GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) Re: John and Mary were each paid x dollars in advance to do a [#permalink] Show Tags John and Mary worked together 18 Hours and received (let's say) 36$ --> Wage 2$/hour John received: 18$ and worked 10 hours
Mary received: 18$and worked 8 hours --> Mary should have received 8hours*2$ =16$, so Mary must give John 2$ (our Y)
We know that John received 18$in advance which is equal to 9y (9*2$)
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GMAT 1: 640 Q39 V38 GMAT 2: 700 Q47 V38 Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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Hourly wage = x/total time worked

John works for 10 hours
Mary works of 8 hours

Hourly wage of John = (x+y)/10
Hourly wage for Mary= (x-y)/8

Since both hourly wage must be the same,
(x+y)/10=(x-y)/8
18y=2x
9y=x
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Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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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

looks more like a 600 lvl question...
each pre-paid X $we know that (x-y)/8 - hourly rate for marry is equal to (x+y)/10 - hourly rate for john. and these two are equal cross multiply and get: 10x-10y=8x+8y 2x=18y x=9y we are asked how much john was pre-paid. he received x$. but x=9y

E
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GMAT 1: 720 Q48 V41 John and Mary were each paid x dollars in advance to do a  [#permalink]

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Bunuel 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

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: $$hourly \ wage=\frac{wage}{# \ of \ hours \ worked}=\frac{x-y}{8}=\frac{x+y}{10}$$, from $$\frac{x-y}{8}=\frac{x+y}{10}$$ we get that $$x=9y$$.

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)
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Joined: 02 Sep 2009
Posts: 55681
Re: John and Mary were each paid x dollars in advance to do a  [#permalink]

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deliverance wrote:
Bunuel 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

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: $$hourly \ wage=\frac{wage}{# \ of \ hours \ worked}=\frac{x-y}{8}=\frac{x+y}{10}$$, from $$\frac{x-y}{8}=\frac{x+y}{10}$$ we get that $$x=9y$$.

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)

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.
_________________ Re: John and Mary were each paid x dollars in advance to do a   [#permalink] 28 Mar 2016, 02:14

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