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An employee is paid 1.5 times the regular hourly rate for

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Manager
Joined: 02 Dec 2012
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An employee is paid 1.5 times the regular hourly rate for  [#permalink]

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14 Dec 2012, 05:09
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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?

(1) The employee's regular hourly rate is $10. (2) Last week the employee worked a total of 54 hours but did not work more than 8 hours on any day. Math Expert Joined: 02 Sep 2009 Posts: 60687 Re: An employee is paid 1.5 times the regular hourly rate for [#permalink] Show Tags 14 Dec 2012, 05:15 2 2 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? (1) The employee's regular hourly rate is$10. No information about the number of hours the employee worked last week and what was the distribution of these hours. Not sufficient.

(2) Last week the employee worked a total of 54 hours but did not work more than 8 hours on any day. We don't know what is the regular hourly rate and the distribution of these 54 hours. Not sufficient.

(1)+(2) If the employee worked 40 hours from Monday to Friday (8 hours per day), 7 hours on Saturday and 7 hours on Sunday, then the employee was paid 40*10+7*15+7*20. But if the employee worked 40 hours from Monday to Friday (8 hours per day), 8 hours on Saturday and 6 hours on Sunday, then the employee was paid 40*10+8*15+6*20. Not sufficient.

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Re: An employee is paid 1.5 times the regular hourly rate for  [#permalink]

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13 Sep 2013, 22:26
1
Same answer as above, but expanding on the algebra if we're trying to evaluate option (C)

• $$R=$$Regular Rate (Mon - Sat)
• $$N=$$Hours worked (Mon - Sat)
• $$N_s=$$Hours worked Sunday
• $$R_s=2R=$$Sunday Rate

The total hours worked are 54($$N+N_s=54$$), this could mean the employee worked 8 hours per day Monday - Saturday ($$N=48$$) and 6 hours Sunday ($$N_s=6$$), in which case

$$Total Pay = 40R+\frac{3}{2}R(8)+R_s6=40R+\frac{3}{2}R(8)+2R6=40R+12R+12R=64R$$

OR the employee could have worked 8 hours per day for 5 weekdays, 6 hours for the remaining weekday ($$N=46$$) and 8 hours on Sunday ($$N_s=8$$), in this case,

$$Total Pay = 40R+\frac{3}{2}R(6)+R_s8=40R+\frac{3}{2}R(6)+2R8=40R+9R+16R=65R$$

In one scenario Total Pay is $$65R$$, in the other Total Pay is $$64R$$ therefore statements (1) and (2) are jointly insufficient.
Manager
Joined: 12 Jan 2013
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Re: An employee is paid 1.5 times the regular hourly rate for  [#permalink]

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10 Jan 2014, 09:29
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?

(1) The employee's regular hourly rate is $10. (2) Last week the employee worked a total of 54 hours but did not work more than 8 hours on any day. 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. Manager Joined: 21 Oct 2013 Posts: 175 Location: Germany GMAT 1: 660 Q45 V36 GPA: 3.51 Re: An employee is paid 1.5 times the regular hourly rate for [#permalink] Show Tags 12 Jun 2014, 03:35 (1) We don't know how many hours were worked. IS (2) we don't know if he maybe wokred 8 hours from monday to friday and 8 hours on saturday and 6 on sunday or in another distribution. IS (1) + (2) we still don't know the distribution. IS. SVP Joined: 06 Nov 2014 Posts: 1868 Re: An employee is paid 1.5 times the regular hourly rate for [#permalink] Show Tags 01 Jul 2015, 00:05 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
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Joined: 12 Sep 2015
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Re: An employee is paid 1.5 times the regular hourly rate for  [#permalink]

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25 Nov 2019, 08:31
Top Contributor
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?

(1) The employee's regular hourly rate is $10. (2) Last week the employee worked a total of 54 hours but did not work more than 8 hours on any day. 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

Cheers,
Brent
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Re: An employee is paid 1.5 times the regular hourly rate for   [#permalink] 25 Nov 2019, 08:31
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