IMO, answer is (C). I also apologize in advance for my overly wordy explanation.
In Statement (1), we're told that an additional 6 hours of work yields an additional $180 of wages. which translates to $30/hour. There are 3 scenarios to consider, however:
Scenario 1: His base rate is $30/hour
If this is the case, he has worked a total of 26 hours thus far, since (26 hours)*($30/hour) = $780.
Thus, adding 6 more hours would result in a total of 32 hours worked, and he'd thus earn (32 hours)*($30/hour) = $960.
Scenario 2: His overtime rate is $30/hour
if this is the case, he has already worked at least 40 hours, such that the 6 additional hours would be considered entirely as overtime. This would mean that his base rate is $15/hour.
Then, how do we get to his current weekly earnings of $780?
(40 hours)*($15/hour) + (? hours)*($30/hour) = $780, and we can determine that he has already worked 6 hours of overtime prior to the additional 6 hours referenced in Statement (1), or a total of 46 hours this week.
Scenario 3: $15/hour < Base Rate < $30/hour
This would mean that he has already worked fewer than 40 hours, but that the additional 6 hours would put him above 40 hours for the week. In this case, the additional $180 would come from a weighted average - say 3 hours at some base wage, and 3 hours at the overtime wage. However, we don't need to evaluate this scenario, since we've already established that, based solely on Statement (1), there is more than one possible answer to the question (26 hours or 46 hours)
So, Statement (1) is insufficient.
*******************************************************************
There are also multiple scenarios to consider in evaluating Statement (2)
Scenario 1: Number of Hours Worked <= 40
If this is the case, his base rate would be $19.50/hour ($390/20 hours).
Note that, if 20 hours of lost work translates to $390 of lost wages, 40 hours of work translates to twice that amount, or $780, which just happens to be the amount of money he has earned this week.
Using Statement (2) alone, it's possible that he has worked 40 hours this week.
It is also worth noting that, using Statement (2) alone, he could not have worked fewer than 40 hours.
Considering that ($780)/(40 hours) = $19.50/hour, his base rate would necessarily be greater than $19.50/hour if he worked fewer than 40 hours. For instance, if he worked only 20 hours, his base wage would be ($780/20 hours) = $39/hour.
In this case, losing 20 hours @ base wage would necessarily cost him more than $390, but we're told that he loses exactly $390. Thus, he could not have worked fewer than 40 hours.
Scenario 2: Number of Hours Worked >= 60
In this scenario, all 20 lost hours would be evaluated at some currently unknown overtime rate.
Thus, losing $390 would mean that the overtime rate is $19.50/hour, and the base rate is $9.75/hour.
His $780 of earnings could thus be explained as follows: (40 hours)*(9.75/hour) + (? hours)*(19.50/hour), and we can solve for the unknown amount of overtime, which happens to be 20 hours.
Thus, it's possible that he has worked 60 hours this week.
Since we have two possible answers to the question (40 hours and 60 hours), based solely on Statement (2),
Statement 2 is insufficient
*******************************************************************
Is the solution of 40 hours possible when combining statements?
If we subtract 20 hours and lose $390, the base rate is $19.50/hour, so the overtime rate would be $39/hour.
If this were true, adding 6 hours @ $39/hour would bring his weekly earnings to $780 + (6 hours)*($39/hour) = $780 + $234 = $1,014, which contradicts Statement (1).
So, 40 hours is not a solution.
Is 60 hours a solution? It works for Statement (2), but does it hold for Statement (1)? If we add 6 hours - which would be entirely at the overtime rate of $19.50/hour - the total weekly earnings would be $780 + (6 hours)*($19.50/hour) = $780 + $117 = $897, which contradicts Statement (1).
So, 60 hours is not a solution.
When the 6 hours is added to the 40 hours, weekly earnings = $1,014.
When the 6 hours is added to the 60 hours, weekly earnings = $897.
We know from Statement (1) that the final earnings will be $960, which falls between the two above values.
It's probably safe to surmise that a solution does exist, and the number of hours will fall somewhere between 40 and 60.
With this reasoning, I selected answer (C).
As proof to myself, I used the earlier "solutions" of 46 hours, which satisfied Statement (1) to test Statement (2).
Subtracting 20 hours from the 46 hours means that 6 hours @ overtime rate will be subtracted, and then 14 hours @ base rate will be subtracted.
(6 hours)*($30/hour) = $180.
(14 hours)*($15/hour) = $210.
Combining the two, the loss of 20 hours from 46 hours results in a loss of $390, which satisfies Statement (2).
46 hours satisfies both statements
Last edited by
tomada on Thu Dec 16, 2010 12:01 pm, edited 1 time in total.
I'm really old, but I'll never be too old to become more educated.
