Who is hired?

[gmat6087]

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

OA A

This question is from gmat club but to solve this question the assumption taken is only one candidate can be hired for 600$. how does this assumption come into picture?

[anuprajan5]

Hi,

In either case P or Q will be paid only 600 dollars

Assume n is the number of hours

Assume q is the hourly rate for Q

for P - n*1.5q = 600
and for Q - (n+10) *q = 600

Subtracting we get q*(n+10) = n*1.5q

Simplifying we get n = 20 which makes q = 20

[spoiler]we need to find out p's hourly wage - Q's hourly wage which equals 1.5q-q = 0.5q. Therefore 0.5*20 =10. Hence Answer A[/spoiler]

[Brent@GMATPrepNow]

This question is from gmat club but to solve this question the assumption taken is only one candidate can be hired for 600$. how does this assumption come into picture?

I don't think we're making that assumption here. The entire question is hypothetical. If P is hired then here's how things would be, and if Q is hired then here's how things would be.

Cheers,
Brent

[Brent@GMATPrepNow]

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

anuprajan5's solution is great. I thought I'd fill in a few steps though.

Hourly wages:
Let Q = Candidate Q's hourly wage
If Candidate P's wage is 50% more, then 1.5Q = Candidate P's hourly wage

Time required:
Let T = Number of hours for Candidate P to complete the job
If Candidate Q requires 10 extra hours, then T+15 = number of hours for Candidate Q to complete the job

(hourly wage)(time to complete job) = Total cost

Candidate Q: (Q)(T+10) = 600
Candidate P: (1.5Q)(T) = 600

We have a 2 equation with 2 unknowns.

Expand to get:
QT + 10Q = 600
1.5QT = 600

Multiply top equation by 1.5 to get:
1.5QT + 15Q = 900
1.5QT = 600

Subtract bottom equation from top equation to get:
15Q = 300
So, Q = 20

Q = 20 = Candidate Q's hourly wage
1.5Q = 1.5(20) = 30 = Candidate P's hourly wage

So, the difference in hourly wages is [spoiler]30 - 20 = 10 = A[/spoiler]

Cheers,
Brent

[GMATGuruNY]

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

OA A

An alternate approach is to plug in the answers, which represent the difference between P's hourly wage and Q's hourly wage -- in other words, 50% of Q's hourly wage, since P earns 50% more per hour than Q.
When the correct answer choice is plugged in, P and Q will each earn $600.

Answer choice C: 20
Since $20 is 50% of Q's hourly wage, Q's hourly wage = 2*20 = 40.
Since Q earns $600, the number of hours worked by Q = 600/40 = 15.
Since Q works 10 more hours than P, the number of hours worked by P = 15-10 = 5.
Since P makes $20 more per hour than Q -- for a total of $60 per hour -- the amount earned by P in 5 hours = 60*5 = 300.
Here, Q earns $600, while P earns $300.
To decrease the difference between their earnings, the difference between their hourly wages must decrease.

Answer choice B: 15
Since $20 is 50% of Q's hourly wage, Q's hourly wage = 2*15 = 30.
Since Q earns $600, the number of hours worked by Q = 600/30 = 20.
Since Q works 10 more hours than P, the number of hours worked by P = 20-10 = 10.
Since P makes $15 more per hour than Q -- for a total of $45 per hour -- the amount earned by P in 10 hours = 45*10 = 450.
Here, Q earns $600, while P earns $450.
To decrease the difference between their earnings, the difference between their hourly wages must decrease.

The correct answer is A.

[thevenus]

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