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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]

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19 Sep 2012, 02:33
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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 _________________ Kudos [?]: 9290 [6], given: 1169 Math Expert Joined: 02 Sep 2009 Posts: 42280 Kudos [?]: 132893 [3], given: 12391 Re: P and Q are the only two applicants qualified for a short-te [#permalink] ### Show Tags 19 Sep 2012, 04:23 3 This post received KUDOS Expert's post 2 This post was BOOKMARKED 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.

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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) $30 Suppose Q's hourly wage is x then and P's hourly wage is 1.5x Time taken by P = 600 /(1.5x) Time taken by Q = 600 / x Candidate Q, if hired, would require 10 hours more than candidate P to do the job. => 600 /(1.5x) + 10 = 600 /x = > x = 20 P's hourly wage is 1.5x - x$ greater = .5x $greater = .5 * 20 = 10$

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

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28 Sep 2012, 02:35
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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]

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24 Oct 2017, 06:05
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Expert's post
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 _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Kudos [?]: 934 [1], given: 3 Math Expert Joined: 02 Sep 2009 Posts: 42280 Kudos [?]: 132893 [0], given: 12391 Re: P and Q are the only two applicants qualified for a short-te [#permalink] ### Show Tags 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. _________________ Kudos [?]: 132893 [0], given: 12391 Intern Joined: 31 May 2012 Posts: 11 Kudos [?]: 14 [0], given: 8 Re: P and Q are the only two applicants qualified for a short-te [#permalink] ### Show Tags 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.

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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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

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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

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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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

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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?

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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 Kudos [?]: 31 [0], given: 0 Intern Joined: 21 Jan 2015 Posts: 36 Kudos [?]: [0], given: 51 Location: United States Schools: Booth PT '20 GMAT 1: 660 Q44 V38 GPA: 3.2 Re: P and Q are the only two applicants qualified for a short-te [#permalink] ### Show Tags 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

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

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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

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