An employee is paid 1.5 times the regular hourly rate for

We are given a complicated equation (IF I understood it correctly):

We are given: 40*x + 1.5*(y - 40) + 2x*Z = Salary last week

Where x is his regular hourly rate, y is total time worked and z is hours worked on sunday.

1) Solves for x, we still have 3 unknowns (y, z, salary)
2) gives us y, and gives us a weak restriction for z, but this is clearly not sufficient

1 + 2: We now have x and y, and just a vague restriction for z (z < 8), and given that he worked 54 hours in total, and an hour can be divided into fractions of an hour, we have different possibilities for z. And thus, we cannot solve for total salary.

So we go with E.

An employee is paid 1.5 times the regular hourly rate for each hour worked in excess of 40 hours per week, excluding Sunday, and 2 times the regular hourly rate for each hour worked on Sunday. How much was the employee paid last week?

If x is the hourly rate, H is the number of hours worked in excess of 40, and H' is the number of hours in excess of 40 and on Sunday,
the pay is 40x + 1.5x(H) + 2x(H')
(1) The employee's regular hourly rate is $10. This says x=10. Without knowing H and H' we can't calculate the pay.
(2) Last week the employee worked a total of 54 hours but did not work more than 8 hours on any day.
This says that 40+ H + H' = 54. Still, since we don't know x or the number of hours for H and H,' we can' calculate pay.

We don't get any new information by combining the statements, since we still don't know the number of hours worked H and H'.

E

Given: An employee is paid 1.5 times the regular hourly rate for each hour worked in excess of 40 hours per week, excluding Sunday, and 2 times the regular hourly rate for each hour worked on Sunday.

Target question: How much was the employee paid last week?

Statement 1: The employee's regular hourly rate is $10.
This statement is not sufficient. We still need to know the total number of hours worked from Monday to Saturday, AND we need to know the number of hours worked on Sunday.
Statement 1 is NOT SUFFICIENT

Statement 2: Last week the employee worked a total of 54 hours but did not work more than 8 hours on any day
Since we don't know the employee's hourly rate, there's no way to determine how much the employee was paid last week
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
The two statements COMBINED still do not provide enough information to answer the target question.
Here are two possible cases that satisfy BOTH statements:

Case a: The employee worked 8 hours each day from Monday to Saturday, for a total of 48 hours (to earn $520), AND the employee worked 6 hours on Sunday (to earn $120). In this case, the answer to the target question is the amount the employee was paid last week = $520 + $120 = $640
Case b: The employee worked a total of 46 hours from Monday to Saturday (8+8+8+8+8+6=46), to earn $490, AND the employee worked 8 hours on Sunday (to earn $160). In this case, the answer to the target question is the amount the employee was paid last week = $490 + $160 = $650
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

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