Company Training

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A company offered a training program to all of its 120 employees. How many employees completed the training?

(1) Of all employees, 30 percent completed more than half of the training.

(2) Of all employees, 30 percent of those who began the training completed it.

Review: Company Training




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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