Explanation
The question describes a somewhat elaborate policy for the
overdue charge on a rental item. We set about to write an algebraic expression
for the overage fee in terms of how many hours late the item is, but find that
the expression would depend on when the item was due. Writing expressions would
not be entirely possible, but algebra is not our friend on this question, so we
will proceed by analysis by cases, evaluating the statements separately first.
Statement (1) gives us a piece of information that is
necessary, but not sufficient, to determine the overage fees. For all we know,
the thing could have been returned an hour late or a day late. Insufficient.
Statement (2), likewise, gives us necessary but
insufficient info. Considered independently of Statement (1), it doesn't give
us the normal hourly rate, so we can't calculate the overage fees.
Insufficient.
When the statements are combined, we seem to be in the
ballpark of sufficiency. We can be sure through case analysis. Case I: the item
was due 9:00 am on Monday. This means that it was returned
hours later,
so on Wednesday at 3:00 pm. That interval includes 8 working hours on Monday, 8
on Tuesday, and 6 hours on Wednesday, so 8 hours at the regular rate of $12 and
14 hours at the triple rate of $36, or
. We can calculate an exact value for the late
return fees. Case II: the thing was due later on Monday; say it was due 2:00 pm
on Monday. In that case it was still returned 54 = 48 + 6 hours later, on
Wednesday at 8:00 pm. The return fees add up to something different in this
case: there are only 3 hours on the first day, at $12/hour, and 16 hours at the
triple rate on Tuesday and Wednesday. Just to be quite sure, we subtract:
Yielding
Which is -12, not 0, confirming the two fees are
different. We have insufficient information to answer the question
definitively.
The correct answer is (E).
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