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

Question

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

A) $10
B) $15
C) $20
D) $25
E) $30

Bunuel · Accepted Answer

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.

BrushMyQuant · Answer

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!

Carcass · Answer

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

Bunuel · Answer

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.

honggil · Answer

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.

Bunuel · Answer

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.

thevenus · Answer

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

LalaB · Answer

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

mbaiseasy · Answer

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

jimwild · Answer

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?

mathivanan · Answer

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

wolves5 · Answer

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

susheelh · Answer

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

ScottTargetTestPrep · Answer

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 = 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

EMPOWERgmatRichC · Answer

Hi All,

This question gives us a number of facts to work with: 
1) The project pays 600 dollars in total. 
2) Candidate P would be paid 50 percent more per hour than candidate Q would be paid. 
3) Candidate Q would require 10 hours more than candidate P to do the job.

With this information, we can create two equations and solve using "system Algebra." We're asked for the difference between Candidate P’s hourly wage and candidate Q’s hourly wage.

X = pay per hour 
T = number of hours

Candidate P = ($1.5X)(T) = 600 
Candidate Q = ($X)(T+10) = 600

(1.5)(X)(T) = 600 
XT + 10X = 600

In the first equation, we can divide both sides by 1.5, which gives us: 
XT = 600/1.5 = 400 
We can then substitute this value into the second equation: 
400 + 10X = 600 
10X = 200 
X = 20

Since X = $20, 1.5X = $30 and the difference is $10

Final Answer:  A

GMAT assassins aren't born, they're made, 
Rich

GyMrAT · Answer

Let  x  be the # of hours required for P to do the job, then

(x + 10)  is the # of hours required for Q to do the same job.

Given that the hourly wage of P is 50% more than that of Q.

Hence, we have  \frac{600}{x}  =  \frac{1.5*600}{(x + 10)}

solving we get  x = 20

Hence hourly wage for P =  600/20 = 30

& hourly wage for Q =  600/30 = 20

Thus, P has a hourly wage greater by $10 than that of Q.

Answer A.

Thanks,
GyM

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