primE

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu Mar 19, 2009 3:28 am

Is x a prime number?

1. x is an even number.

2. x can not be divided evenly by an odd number other than 1.

OA E

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Source: Beat The GMAT — Data Sufficiency | Thu Mar 19, 2009 3:28 am

scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Thu Mar 19, 2009 3:37 am

x prime?

1) x=even, x can be 0, 2, 4, 6......
x is prime only if x=2. cant say if x is prime definitely

2) this statement means x=even in other words. just like statement 1.

combining doesnt add extra info
hence E

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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

by Stuart@KaplanGMAT » Thu Mar 19, 2009 3:46 pm

scoobydooby wrote:x prime?

1) x=even, x can be 0, 2, 4, 6......
x is prime only if x=2. cant say if x is prime definitely

2) this statement means x=even in other words. just like statement 1.

combining doesnt add extra info
hence E

Statement (2) doesn't mean "x = even". It means "x has no odd factors other than 1". For this to be true, x must be a power of 2.

For example, "6" has a factor of 3, so it doesn't fit statement (2).

However, even though your reasoning isn't perfect, your answer is correct.

From (2), x could be any power of 2, i.e. 2, 4, 8, 16, 32, ...; since it could be 2 (prime) or any other power of 2 (not prime), it's insufficient.

Since (2) gives us numbers that are all a subset of (1) (i.e. every number that fits (2) also fits (1)), combining doesn't help us at all: choose (E).

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Thu Mar 19, 2009 4:12 pm

Just one exception to add to Stuart's excellent explanation - from Statement 2, x could also be equal to 1, so there is one number which satisfies Statement 2 but not Statement 1. That doesn't affect the answer in any way, however.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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