Is a a prime number

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catchdharani
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Topic: Is a a prime number
PostTue Nov 03, 2009 11:16 am Reply with quote
Is integer a a prime number

1) 2a has exactly 3 factors

2) a is an even number

Wy shud I not be tempted to select D as my answer. A is the correct answer but I am not satisfied with the explanation. Could someone help?
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mp2437
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PostTue Nov 03, 2009 12:10 pm Reply with quote
Statement 2 is saying that a is an even integer. Is every even integer a composite number (non-prime)?? a could be 2 (a prime number), or 12 (a non-prime).

Statement 1 says that 2a has exactly 3 factors. You should know that only perfect squares have 3 factors, so 2a is a perfect square. Since 2a is a perfect square, you know that a cannot be a perfect square, and cannot be prime as well. This statement is sufficient.

Ans: A
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Stuart Kovinsky
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PostTue Nov 03, 2009 1:48 pm Reply with quote
catchdharani wrote:
Is integer a a prime number

1) 2a has exactly 3 factors

2) a is an even number

Wy shud I not be tempted to select D as my answer. A is the correct answer but I am not satisfied with the explanation. Could someone help?
D is only correct if each statement, taken alone, is enough to answer the question.

If we look at statement (2) in a vaccuum, the only thing that we know about a is that it's even. We can pick numbers to quickly see that (2) isn't sufficient.

2 is even... is 2 a prime number? YES.
4 is even... is 4 a prime number? NO.

Since we can get both a yes and a no answer, (2) alone is insufficient.
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chipbmk
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PostWed Nov 04, 2009 3:30 pm Reply with quote
Quote:
Statement 1 says that 2a has exactly 3 factors. You should know that only perfect squares have 3 factors, so 2a is a perfect square. Since 2a is a perfect square, you know that a cannot be a perfect square, and cannot be prime as well. This statement is sufficient.

Ans: A
I agree with your answer, A is correct. However, I think your explanation is incorrect (specifically, the portion I bolded).

As you said, only perfect squares have 3 factors. Therefore, 2a is a perfect square and furthermore, a must equal 2. If a equals 2, then a IS a prime.

You may have just accidentally said "cannot" rather than "can". Just wanted to clarify.
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