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P and Q are the only two applicants qualified for a short-te

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P and Q are the only two applicants qualified for a short-te [#permalink] New post 19 Sep 2012, 01:33
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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
[Reveal] Spoiler: OA

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

=> 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
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Re: P and Q are the only two applicants qualified for a short-te [#permalink] New post 19 Sep 2012, 03:23
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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.

Answer: A.
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Re: P and Q are the only two applicants qualified for a short-te [#permalink] New post 19 Sep 2012, 03:39
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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, 04:36, edited 2 times in total.
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Re: P and Q are the only two applicants qualified for a short-te [#permalink] New post 19 Sep 2012, 03:49
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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 short-te [#permalink] New post 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.
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Re: P and Q are the only two applicants qualified for a short-te [#permalink] New post 28 Sep 2012, 01:35
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.

Hope it's clear.
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Re: P and Q are the only two applicants qualified for a short-te [#permalink] New post 25 Oct 2012, 05:54
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 (P-Q) 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

(P-Q)=30-20= 10

Answer : A
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Re: P and Q are the only two applicants qualified for a short-te [#permalink] New post 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] New post 14 Nov 2012, 04:31
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 short-te [#permalink] New post 27 Jun 2014, 06:48
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Re: P and Q are the only two applicants qualified for a short-te   [#permalink] 27 Jun 2014, 06:48
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