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Lesson: Data Sufficiency Challenging - 23t01

Unexpected Combinations: Example 2

[Page 23 of 24]

If the factors of the positive integer x have an average (arithmetic mean) of 6, what is the value of x?


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?

Fill in the textboxes with information provided in the question stem, and then click Continue.

 = 

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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