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?
1) x2 has exactly 3
distinct integer factors.
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Sufficient |
 |
Insufficient |
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2) x is prime.
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Sufficient |
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Insufficient |
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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.
Test Prep Lessons With Video Lessons and Explained MCQ