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P and Q are the only two applicants qualified for a short-te [#permalink]

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19 Sep 2012, 01:33

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69% (02:29) correct 31% (03:16) wrong based on 312 sessions

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P and Q are the only two applicants qualified for a short-term research project that pays 600 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage?

Re: P and Q are the only two applicants qualified for a short-te [#permalink]

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19 Sep 2012, 02:06

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P and Q are the only two applicants qualified for a short-term research project that pays 600 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage? A) $10 B) $15 C) $20 D) $25 E) $30

Suppose Q's hourly wage is x then and P's hourly wage is 1.5x

Time taken by P = 600 /(1.5x) Time taken by Q = 600 / x Candidate Q, if hired, would require 10 hours more than candidate P to do the job.

P and Q are the only two applicants qualified for a short-term research project that pays 600 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage?

A) $10 B) $15 C) $20 D) $25 E) $30

Say Q's hourly wage is x, then P's hourly wage is 1.5x; Say Q needs t hours to do the job, then P needs t-10 hours to do the job.

Since they both are paid equal total amount of $600, then x*t=1.5x*(t-10) --> x cancels out and we'll get that t=30 hours.

So, Q's hourly wage is 600/t=$20 and P's hourly wage is 600/(t-10)=$30, therefore the difference in hourly wages is $30-$20=$10.

The constant here is 600 sio D = R x T (here D is some output: distance work and so on)

Q rate is 1.0 and P is 1.5 so we can ste equal 1.5T = 1.0 (T + 10) ---> T = is 20 h for P so 600/20 = 30. For Q is T + 10 = 30 ---> 600/30 = 20

So P earns 30 per h Q 20 per h, the difference is 10

What do you think Bunuel ?? and is true that in most difficult problem one key could be to set equal D ( W or other output) ???

Thanks

Your approach is correct. It's basically the same as mine. You denoted P's time as T time and I denoted Q's time as T. As a result your equation is 1.5T = 1.0 (T + 10) and mine is T = 1.5 (T - 10).

Also, you are right, in similar questions equating output/distance/pay is a good strategy to attack the problem.
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Re: P and Q are the only two applicants qualified for a short-te [#permalink]

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27 Sep 2012, 17:07

Bunuel wrote:

carcass wrote:

P and Q are the only two applicants qualified for a short-term research project that pays 600 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage?

A) $10 B) $15 C) $20 D) $25 E) $30

Say Q's hourly wage is x, then P's hourly wage is 1.5x; Say Q needs t hours to do the job, then P needs t-10 hours to do the job.

Since they both are paid equal total amount of $600, then x*t=1.5x*(t-10) --> x cancels out and we'll get that t=30 hours.

So, Q's hourly wage is 600/t=$20 and P's hourly wage is 600/(t-10)=$30, therefore the difference in hourly wages is $30-$20=$10.

Answer: A.

When it says, "a short-term research project that pays 600 dollars in total," how did you know that it was per person rather than 600 for both of them? I was confused there and was wondering if there was a quick rule of thumb to recognize such subtle, but critical difference.

P and Q are the only two applicants qualified for a short-term research project that pays 600 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage?

A) $10 B) $15 C) $20 D) $25 E) $30

Say Q's hourly wage is x, then P's hourly wage is 1.5x; Say Q needs t hours to do the job, then P needs t-10 hours to do the job.

Since they both are paid equal total amount of $600, then x*t=1.5x*(t-10) --> x cancels out and we'll get that t=30 hours.

So, Q's hourly wage is 600/t=$20 and P's hourly wage is 600/(t-10)=$30, therefore the difference in hourly wages is $30-$20=$10.

Answer: A.

When it says, "a short-term research project that pays 600 dollars in total," how did you know that it was per person rather than 600 for both of them? I was confused there and was wondering if there was a quick rule of thumb to recognize such subtle, but critical difference.

Well it's implied in the question that only one applicant can be hired for the project, so $600 that is payed for it is only for one.

Re: P and Q are the only two applicants qualified for a short-te [#permalink]

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28 Oct 2012, 08:24

we know that RateP/RateQ=3/2 and TimeQ-TimeP=10

RateP/RateQ=3/2 means that TimeP/TimeQ=2/3 since we know that the difference between times of P and Q is 10, we can think that TimeP=20 TimeQ=30 or Rate P=30 RateQ=20

Rate P-RateQ=30-20=10

Answ is A
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Re: P and Q are the only two applicants qualified for a short-te [#permalink]

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12 Aug 2015, 06:05

Bunuel wrote:

carcass wrote:

I thing also:

The constant here is 600 sio D = R x T (here D is some output: distance work and so on)

Q rate is 1.0 and P is 1.5 so we can ste equal 1.5T = 1.0 (T + 10) ---> T = is 20 h for P so 600/20 = 30. For Q is T + 10 = 30 ---> 600/30 = 20

So P earns 30 per h Q 20 per h, the difference is 10

What do you think Bunuel ?? and is true that in most difficult problem one key could be to set equal D ( W or other output) ???

Thanks

Your approach is correct. It's basically the same as mine. You denoted P's time as T time and I denoted Q's time as T. As a result your equation is 1.5T = 1.0 (T + 10) and mine is T = 1.5 (T - 10).

Also, you are right, in similar questions equating output/distance/pay is a good strategy to attack the problem.

Bunuel pls why did you choose T - 10 for candidate P instead of choosing T + 10 for candidate Q, i chose 2nd choice and end up solving quadratic equation that take lot of time, how to choose that strategic choice?

Re: P and Q are the only two applicants qualified for a short-te [#permalink]

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13 Aug 2015, 08:08

carcass wrote:

P and Q are the only two applicants qualified for a short-term research project that pays 600 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage?

A) $10 B) $15 C) $20 D) $25 E) $30

let Q works for x per hour, then P works for 1.5x per hour let P works for t hours and Q works for t+10 hours P gets 1.5tx = 600, tx = 400 also tx+ 10x = 600 10x = 200 x = 20 1.5x = 30 difference = 10

P and Q are the only two applicants qualified for a short-term research project that pays 600 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage?

A) $10 B) $15 C) $20 D) $25 E) $30

We know that hourly wage = total paid/number of hours.

If we let h = the number of hours worked by P, then h + 10 = the number of hours worked by Q. Thus:

600/h = 1.5[600/(h+10)]

600/h = 900/(h + 10)

600(h + 10) = 900h

600h + 6000 = 900h

6000 = 300h

20 = h

Thus, P’s hourly wage is 600/20 = $30 and Q’s hourly wage is 600/30 = $20. Thus, P’s hourly wage is 30 - 20 = 10 dollars greater than Q’s hourly wage.

Answer: A
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This question gives us a number of facts to work with: 1) The project pays 600 dollars in total. 2) Candidate P would be paid 50 percent more per hour than candidate Q would be paid. 3) Candidate Q would require 10 hours more than candidate P to do the job.

With this information, we can create two equations and solve using "system Algebra." We're asked for the difference between Candidate P’s hourly wage and candidate Q’s hourly wage.

In the first equation, we can divide both sides by 1.5, which gives us: XT = 600/1.5 = 400 We can then substitute this value into the second equation: 400 + 10X = 600 10X = 200 X = 20

Since X = $20, 1.5X = $30 and the difference is $10