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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-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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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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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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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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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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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


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

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New post 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.

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

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New post 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 (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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New post 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

Answ is A
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New post 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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New post 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 short-te [#permalink]

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New post 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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New post 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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New post 19 Oct 2017, 04:56
A good question with quite a lot of learning. Here are few things would be nice to know when answering question such as this

  • Wages are distributed based on work efficiency. A person whose rate is more (Read, more efficient) gets paid more
  • A person whose rate is better takes less time to complete a task whereas a person who is less efficient takes more time
  • Mathematically we can say that Work efficiency of a person/salary paid is inversely proportional to the time taken.
  • Simply put, faster a person finishes a task, higher he gets paid per hour and Vice-Versa


Let

\(Time \ taken \ by \ P \ to \ finish \ the \ task = t\)

\(Time \ taken \ by \ Q \ to \ finish \ the \ task = t+10.\)

From the points mentioned above, we get

\(=>\frac{(salary \ paid \ to \ P)}{(Salary \ Paid \ to \ Q)} = \frac{150}{100}= \frac{3}{2} = \frac{(t+10)}{t}\)

Solving, we get t = 20

Therefore, (Salary Paid to P) - (Salary Paid to Q) = (20+10) - (20) = 10

Answer = A
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