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Lesson: Data Sufficiency Challenging - 23t05

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.

 = 

Review Statement 1 below. Is it sufficient or insufficient? Select the correct answer and then click Continue.

1) x2 has exactly 3 distinct integer factors.

  Sufficient Insufficient    

Review Statement 2 below. Is it sufficient or insufficient? Select the correct answer and then click Continue.

2) x is prime.

  Sufficient Insufficient    

If x is prime, then x must have only 2 factors: itself and the number 1. Since the average of those two factors is 6, again we know that: . Statement (2) is sufficient.

Having two statements give the same information in different ways is not such a rare occurrence in Data Sufficiency. When you recognize that such is the case, you know that the correct answer has to be either (D) or (E), since the information duplicated in the statements must be either sufficient or insufficient on its own. So in this question, for example, even if you got only as far as recognizing that both statements were saying that x is prime, without knowing where to go from there, you’d know that the correct answer had to be (D) or (E). This is a great advantage if you get stuck on the math or concepts.

So now we’ve seen two very tough questions that combined concepts in surprising ways. The key to these questions was to think carefully about the initial information before heading into the statements, and to deal with the concepts separately at first.

Next to display next topic in the chapter.

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