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P and Q are the only two applicants qualified for a shortte [#permalink]
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19 Sep 2012, 02:33
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P and Q are the only two applicants qualified for a shortterm 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
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Re: P and Q are the only two applicants qualified for a shortte [#permalink]
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P and Q are the only two applicants qualified for a shortterm 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. => 600 /(1.5x) + 10 = 600 /x = > x = 20 P's hourly wage is 1.5x  x $ greater = .5x $ greater = .5 * 20 = 10$ So, Answer will be A Hope it helps!
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Re: P and Q are the only two applicants qualified for a shortte [#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 shortterm 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 t10 hours to do the job. Since they both are paid equal total amount of $600, then x*t=1.5x*(t10) > 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/(t10)=$30, therefore the difference in hourly wages is $30$20=$10. Answer: A.
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Re: P and Q are the only two applicants qualified for a shortte [#permalink]
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19 Sep 2012, 04:39
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I think 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 set 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 problems one key could be to set equal D ( W or other output) ??? Thanks
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Last edited by carcass on 19 Sep 2012, 05:36, edited 2 times in total.



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Re: P and Q are the only two applicants qualified for a shortte [#permalink]
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19 Sep 2012, 04:49
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.
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Re: P and Q are the only two applicants qualified for a shortte [#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 shortterm 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 t10 hours to do the job. Since they both are paid equal total amount of $600, then x*t=1.5x*(t10) > 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/(t10)=$30, therefore the difference in hourly wages is $30$20=$10. Answer: A. When it says, "a shortterm 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.



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Re: P and Q are the only two applicants qualified for a shortte [#permalink]
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28 Sep 2012, 02:35
honggil wrote: Bunuel wrote: carcass wrote: P and Q are the only two applicants qualified for a shortterm 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 t10 hours to do the job. Since they both are paid equal total amount of $600, then x*t=1.5x*(t10) > 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/(t10)=$30, therefore the difference in hourly wages is $30$20=$10. Answer: A. When it says, "a shortterm 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. Hope it's clear.
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Re: P and Q are the only two applicants qualified for a shortte [#permalink]
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25 Oct 2012, 06:54
Let P & Q be the hourly wages of P & Q candidates resp. Let "x" be the hours worked by P scope of silly mistake: we need to find (PQ) NOT P or Q  so be careful Formula; No.of hrs * hourly wage= total wage Given; P=1.5 Q P's total earning; x * 1.5Q =600(i) Q=600/(x * 1.5 ) Q's total earning; (x+10) * Q =600(ii) Putting Q from (i) we'll get; (x+10) * 600/(x * 1.5) =600 x=20 putting x in (i) or (ii) we'll get; Q=20 putting Q=20 in (i) or (ii) we'll get P=30 (PQ)=3020= 10 Answer : A
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Re: P and Q are the only two applicants qualified for a shortte [#permalink]
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28 Oct 2012, 09:24
we know that RateP/RateQ=3/2 and TimeQTimeP=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 PRateQ=3020=10 Answ is A
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Re: P and Q are the only two applicants qualified for a shortte [#permalink]
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14 Nov 2012, 05:31
\(P = 1.5d x h = 600\) \(Q = d x (h + 10) = dh + 10d = 600\) \(Eq1: 1.5dh = 600\) \(dh = 6000/15 = 400\) Substitute dh = 400 to Eq 2: \(400 + 10d = 600 ==> 10d = 200 ==> d=20\) \(400 = 20h => h=20\) P hourly rate = 600 / 20 = 30 dollars Q hourly rate = 600 / 30 = 20 dollars Answer: 10
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Re: P and Q are the only two applicants qualified for a shortte [#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?



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Re: P and Q are the only two applicants qualified for a shortte [#permalink]
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13 Aug 2015, 09:08
carcass wrote: P and Q are the only two applicants qualified for a shortterm 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 shortte [#permalink]
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04 Dec 2016, 21:31
Total pay = $600 P: gets paid (1.5 per hour)(Q) Q: 10 + P hours to get the job done P’s hourly wage is how much greater than Q’s hourly wage?
Total Salary Rate Hours P $600 1.5Q P Q $600 Q P+10
Set total equal to each other. (1.5Q)(P) = (Q)(P+10) 1.5QP = 1QP + 10Q 0.5QP = 10Q → Divide and cross out Q's to get 20 = P.
Find hourly rate. 600 = (Q)(30) → 20 = Q gets paid $20 per hour. P gets paid 1.5 times more than Q. (20)(1.5) = $30 per hour.
$30$20 = $10 Answer: A




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