Explanation
The question is clear enough--on to the data statements,
separately first.
Statement (1) can be analyzed by cases. It could be true
that 30 percent of employees completed more than half of the training and none
of them finished, so the overall completion was zero. The data statement also
permits the case that 30 percent of employees completed more than half the
training and in fact all finished it, leading to a completion of 30 percent.
Those cases yield different outcomes, so we have insufficient information to
answer the question in this statement.
Statement (2), also, can be analyzed by cases. We could
imagine that all of the employees began the training, and also that none of the
employees began the training. Both such cases are permitted by the data and
yield different results, so this statement is insufficient.
Combining the statements, we will again evaluate by cases.
One allowed case is that everyone began the training, 30 percent of employees
completed more than half of it, and that same 30 percent all completed it,
leading to an overall completion rate of 30 percent or
. Let's see if we can get a case with a different
result. Could it be that only 30 percent of the group even attempted the
training? In that case, all of that 30 percent could complete more than half
the training, so Statement (1) would allow that case. And possibly only 30
percent of that 30 percent complete the training, so Statement (2) would allow
that case. In this case, only 30% of 36 people would complete the training.
Actually, that's not possible, because we can't have a non-integer number of
people completing the training. But we can see that there will be an allowed
case with a different result. Therefore the statements are insufficient
together.
The correct answer is (E).
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