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

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27 Dec 2012, 06:05

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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?

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 \(x=9y\).

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 _________________

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

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18 Nov 2013, 19:45

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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.

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

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31 Dec 2013, 08:58

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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

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, \(x = 9y\)

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

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10 Jan 2014, 04:45

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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.

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

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01 Dec 2013, 11:19

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..

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

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10 Jan 2014, 04:35

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.

Last edited by aeglorre on 10 Jan 2014, 04:47, edited 2 times in total.

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

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12 Aug 2014, 18:09

Bunuel wrote:

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

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 \(x=9y\).

Answer: E.

Hi Bunuel,

Would this fall into wordy word problems category? I would love to work on similar long wordy problems if you can link me the location to a few.

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

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28 Oct 2014, 18:46

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:

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:

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

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 \(x=9y\).

Answer: E.

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?

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

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24 Dec 2014, 08:58

Bunuel wrote:

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

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 \(x=9y\).

Answer: E.

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

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:

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:

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

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 \(x=9y\).

Answer: E.

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.

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:

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. _________________

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

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30 May 2015, 08:00

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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