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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, 02:33

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Question Stats:

70% (03:05) correct
30% (03:01) wrong based on 185 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, 03:06

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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.

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

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19 Sep 2012, 04:23

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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.

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

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19 Sep 2012, 04:49

Expert's post

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. _________________

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

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27 Sep 2012, 18:07

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.

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

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28 Sep 2012, 02:35

Expert's post

honggil wrote:

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.

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, 09:24

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

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

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27 Jun 2014, 07:48

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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, 07:05

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, 09:08

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

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Re: P and Q are the only two applicants qualified for a short-te
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13 Aug 2015, 09:08

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