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M20-02. If x is a prime number, what is the greatest factor

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M20-02. If x is a prime number, what is the greatest factor [#permalink] New post 23 May 2014, 08:51
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Kudos [?]: 47250 [0], given: 7115

Re: M20-02. If x is a prime number, what is the greatest factor [#permalink] New post 23 May 2014, 08:57
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Official Solution:

If \(x\) is a prime number, what is the greatest factor of \(x^2\)?

Note that the greatest factor of a positive integer is that positive integer itself. For example the greatest factor of 10 is 10 itself. So, basically we should find the value of \(x\) to answer the question.

(1) \(x^2\) is an odd number. This statement just tells us that \(x\) could be any prime but 2, so it's clearly insufficient to determine the single numerical value of \(x\).

(2) The greatest common factor of \(x\) and 6 is 3. Since \(x\) is a prime number then \(x=3\) (no other prime can have 3 as a factor), so the greatest factor of \(x^2=9\) is 9. Sufficient,

Answer: B.
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Re: M20-02. If x is a prime number, what is the greatest factor   [#permalink] 23 May 2014, 08:57
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