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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 [?]: 9283 [6], given: 1168 Director Status: Tutor - BrushMyQuant Joined: 05 Apr 2011 Posts: 618 Kudos [?]: 795 [2], given: 59 Location: India Concentration: Finance, Marketing Schools: XLRI (A) GMAT 1: 700 Q51 V31 GPA: 3 WE: Information Technology (Computer Software) Re: P and Q are the only two applicants qualified for a short-te [#permalink] ### Show Tags 19 Sep 2012, 03:06 2 This post received KUDOS 2 This post was BOOKMARKED 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 Hope it helps! _________________ Ankit Check my Tutoring Site -> Brush My Quant GMAT Quant Tutor How to start GMAT preparations? How to Improve Quant Score? Gmatclub Topic Tags Check out my GMAT debrief How to Solve : Statistics || Reflection of a line || Remainder Problems || Inequalities Kudos [?]: 795 [2], given: 59 Math Expert Joined: 02 Sep 2009 Posts: 42247 Kudos [?]: 132683 [3], given: 12331 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, 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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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 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. Kudos [?]: 14 [0], given: 8 Math Expert Joined: 02 Sep 2009 Posts: 42247 Kudos [?]: 132683 [1], given: 12331 Re: P and Q are the only two applicants qualified for a short-te [#permalink] ### Show Tags 28 Sep 2012, 02:35 1 This post received KUDOS 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.

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. _________________ Kudos [?]: 132683 [1], given: 12331 Director Status: Final Countdown Joined: 17 Mar 2010 Posts: 534 Kudos [?]: 360 [0], given: 75 Location: India GPA: 3.82 WE: Account Management (Retail Banking) Re: P and Q are the only two applicants qualified for a short-te [#permalink] ### Show Tags 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 _________________ " Make more efforts " Press Kudos if you liked my post Kudos [?]: 360 [0], given: 75 Senior Manager Joined: 23 Oct 2010 Posts: 381 Kudos [?]: 403 [0], given: 73 Location: Azerbaijan Concentration: Finance Schools: HEC '15 (A) GMAT 1: 690 Q47 V38 Re: P and Q are the only two applicants qualified for a short-te [#permalink] ### Show Tags 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 _________________ Happy are those who dream dreams and are ready to pay the price to make them come true I am still on all gmat forums. msg me if you want to ask me smth Kudos [?]: 403 [0], given: 73 Senior Manager Joined: 13 Aug 2012 Posts: 458 Kudos [?]: 557 [0], given: 11 Concentration: Marketing, Finance GPA: 3.23 Re: P and Q are the only two applicants qualified for a short-te [#permalink] ### Show Tags 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 _________________ Impossible is nothing to God. Kudos [?]: 557 [0], given: 11 Intern Joined: 02 Mar 2015 Posts: 32 Kudos [?]: 5 [0], given: 8 Re: P and Q are the only two applicants qualified for a short-te [#permalink] ### Show Tags 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? Kudos [?]: 5 [0], given: 8 Manager Joined: 10 Jun 2015 Posts: 126 Kudos [?]: 30 [0], given: 0 Re: P and Q are the only two applicants qualified for a short-te [#permalink] ### Show Tags 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 [#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

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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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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.

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