Is a a prime number

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catchdharani: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Tue Nov 03, 2009 11:14 am

by catchdharani » Tue Nov 03, 2009 11:16 am

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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Source: Beat The GMAT — Data Sufficiency | Tue Nov 03, 2009 11:16 am

mp2437: Master | Next Rank: 500 Posts; Posts: 177; Joined: Thu Aug 14, 2008 11:59 am; Thanked: 25 times

by mp2437 » Tue Nov 03, 2009 12:10 pm

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@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: Is a a prime number

by Stuart@KaplanGMAT » Tue Nov 03, 2009 1:48 pm

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.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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chipbmk: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Mon Oct 05, 2009 9:33 am

by chipbmk » Wed Nov 04, 2009 3:30 pm

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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