Target question: What is the value of y?For a week Raymond is paid at the rate of x dollars per hour for the first 40 hours he works and y dollars per hour for the hours worked in excess of 40 hours. What is the value of y?
(1) If Raymond works 46 hours in one week, he will earn $416.50.
(2) Raymond's hourly rate for the hours worked in excess of 40 hours per week is 1.5 times his hourly rate for the first 40 hours.
Given: Raymond is paid at the rate of x dollars per hour for the first 40 hours he works and y dollars per hour for the hours worked in excess of 40 hours.
Statement 1: If Raymond works 46 hours in one week, he will earn $416.50.
Here, Raymond works 40 hours at a rate of x dollars per hour, and he works an additional 6 hours at y dollars per hour. His total salary is $416.50
So, we can write: 40x + 6y = 416.50
We have one equation with two variables, which can't be solved for y.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Raymond's hourly rate for the hours worked in excess of 40 hours per week is 1.5 times his hourly rate for the first 40 hours
In other words, y = 1.5x
Since we're not told anything about any wages, we can't determine the value of y.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that 40x + 6y = 416.50
Statement 2 tells us that y = 1.5x
Now that we have TWO unique equations with TWO variables, we have enough information to determine the value of y. Of course, we're not going to waste time doing so. We need only recognize that we have enough information to do so.
Since we could answer the target question with certainty, the combined statements are SUFFICIENT
Aside: If we solve the above system, we get y = 12.75
Answer = C
Cheers,
Brent
