1) x2 has exactly 3 distinct integer factors.
2) x is a prime number.
This question stem is testing both the average formula
and factor knowledge. We'll need to consider both concepts in answering
the question. The average formula appears below. How might we use it to
answer the question?
The Exam rarely tests averages directly, because the concept is pretty
straightforward and there isn’t a lot of room for conceptual confusion
or even calculation errors. So instead the Exam tends to use average in
combination with other concepts as a roundabout way to provide basic information.
What kind of info? Well, in this question, if we knew how many factors
x had, we could use the average of those factors to figure out
their sum, since:
Note that this question is also a "value" question, which means
that the only way to have sufficiency is to find the precise value of
x. Of course, we can assume that there must be more than one positive
integer whose factors average to 6, otherwise this wouldn’t make a very
good Data Sufficiency question. So what we’re going to have to do is see
whether the statements narrow the possibilities down to just one.
Let’s look at Statement 1.
Countinue
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