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OG 12th Edition- SD 118

by nikee » Fri Sep 02, 2011 6:57 am
What am I missing here?

Question
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 45 hours but did not work more than 8 hours on any day

Answer
E

The answer explanation in the back for #2 says "From this, the employee worked a total of 54-40= 14 hours..."

What am I missing? How is the total number of hours worked 14 and NOT 54, like it is stated in #2?
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by knight247 » Fri Sep 02, 2011 7:06 am
I just checked the OG...Statement 2 specifically says

Last week the employee worked a total of 54 hours but did not work more than 8 hours on any day

You've written it as 45 in your question. Anyway, if he has worked 54 hours in the last week and never more than 8 hours a day, we don't know if he worked 6 days or 7 days and if yes then how many hours on each day, because the Sunday rates are higher.
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by nikee » Fri Sep 02, 2011 7:47 am
Thanks for the quick reply.

After re-reading the question and reviewing my notes, I noticed I wrote down 56 work hours, not 54. The misprint on my part was throwing me off.

Thanks again for your help!
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by armandolatigo » Mon Aug 31, 2015 6:17 pm
I saw the strange explanation for #2 and I can't wrap my head around it either. The employee worked a total of 54 hours and the explanation says no, he actually worked a total of 14 hours. What? Huh? Why? (2) also states he did not work more than 8 hours on any day, I concluded that on one day he could've worked 7 hours on two different days (not knowing if that could've been on a Sunday), or one day worked 6 hours (possibly on Sunday or not), all of it totals 54 hours. Do they really mean 14 overtime hours? It really doesn't make any sense. I'm just as confused as I would be if my boss suddenly deducted 40 hours from my paycheck :|
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by Max@Math Revolution » Fri Sep 04, 2015 3:14 am
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.


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 45 hours but did not work more than 8 hours on any day

==> by using variable approach method we transform the original condition and the question. we have regular hourly rate:r, weekend hours:a, sunday hours :b and thus there are 3 variables (r,a,b). In order to match the number of variables and equations we need 3 equations, and since there is 1 each in 1) and 2), we need 1 equation more. Therefore E is likely the answer, and it turns out that E actually is the answer since we can't find the value for sunday hours even with both 1) and 2).

The answer explanation in the back for #2 says "From this, the employee worked a total of 54-40= 14 hours..."

What am I missing? How is the total number of hours worked 14 and NOT 54, like it is stated in #2?
==> It seems like someone made a mistake and wrote 54 instead of 45. 54 - 40 is probably used to find out the excess hours...



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by gmatdriller » Fri Sep 04, 2015 3:21 am
armandolatigo wrote:I saw the strange explanation for #2 and I can't wrap my head around it either. The employee worked a total of 54 hours and the explanation says no, he actually worked a total of 14 hours. What? Huh? Why? (2) also states he did not work more than 8 hours on any day, I concluded that on one day he could've worked 7 hours on two different days (not knowing if that could've been on a Sunday), or one day worked 6 hours (possibly on Sunday or not), all of it totals 54 hours. Do they really mean 14 overtime hours? It really doesn't make any sense. I'm just as confused as I would be if my boss suddenly deducted 40 hours from my paycheck :|
The 14hrs should refer to total OT hours worked.
Since we do not know how many regular OT(1.5) or Sunday(2) worked,
we cannot conclude on the total package... So, E.
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by Matt@VeritasPrep » Fri Sep 04, 2015 6:15 pm
armandolatigo wrote:I saw the strange explanation for #2 and I can't wrap my head around it either. The employee worked a total of 54 hours and the explanation says no, he actually worked a total of 14 hours. What? Huh? Why? (2) also states he did not work more than 8 hours on any day, I concluded that on one day he could've worked 7 hours on two different days (not knowing if that could've been on a Sunday), or one day worked 6 hours (possibly on Sunday or not), all of it totals 54 hours. Do they really mean 14 overtime hours? It really doesn't make any sense. I'm just as confused as I would be if my boss suddenly deducted 40 hours from my paycheck :|
Let's say the employee is paid $x per hour for regular time, $1.5x per hour for non-Sunday overtime, and $2x per hour on Sunday.

S1 tells us x = $10, so we know how much he's paid each day, but not how many hours he worked on each day.

S2 tells us that the employee worked 54 hours that week, but only (at most) 8 hours per day. This gives us at least scenarios: 8 hours every day except Sunday, and 6 hours on Sunday OR 8 hours every day except Saturday, and 6 hours on Saturday.

Taking the two together, in the first case, the employee would make 40*$10 + 8*$15 + 6*$20. In the second case, the employee would make 40*$10 + 6*$15 + 8*$20. So we can't say how much he made, and the answer is E.
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