Is zero an even divisor?

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rahulvsd: Master | Next Rank: 500 Posts; Posts: 184; Joined: Tue Sep 07, 2010 9:43 amFollowed by: 1 member; Thanked: 6 times

by rahulvsd » Sun May 13, 2012 4:46 am

If x = 3y, where y is a prime number greater than 2 how many positive even divisors does x have including x ?

A. 0
B. 1
C. 2
D. 3
E. Cannot be determined from information above

[spoiler]OA: A. Source: Veritas Prep. I have a doubt here, From the info we know that x will be an odd number. I have only one thing to confirm here, zero cannot be a factor here right? This is because a number P will be a factor of Q only if Q/P is an integer. Since Q/0 is undefined we can say that 0 is not a factor of P. Hence 0 cannot be a factor of any number by this logic.

[/spoiler]

Source: Beat The GMAT — Problem Solving | Sun May 13, 2012 4:46 am

sam2304: Legendary Member; Posts: 1239; Joined: Tue Apr 26, 2011 6:25 amFollowed by: 26 members; Thanked: 233 times; GMAT Score:680

by sam2304 » Sun May 13, 2012 5:07 am

You are right. 0 cannot divide any number and hence cannot be a factor of any number. Moreover its given as 'positive' even divisor and 0 is neither positive nor negative. So you can eliminate with that as well if you are confused.

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Bill@VeritasPrep: GMAT Instructor; Posts: 1248; Joined: Thu Mar 29, 2012 2:57 pmFollowed by: 192 members; Location: Everywhere; Thanked: 503 times; GMAT Score:780

by Bill@VeritasPrep » Sun May 13, 2012 8:40 am

Zero is a factor of nothing and a multiple of everything.

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hey_thr67: Master | Next Rank: 500 Posts; Posts: 299; Joined: Tue Feb 15, 2011 10:27 amFollowed by: 2 members; Thanked: 9 times

by hey_thr67 » Mon May 14, 2012 2:01 am

how many multiples 340 has ?

Bill@VeritasPrep: GMAT Instructor; Posts: 1248; Joined: Thu Mar 29, 2012 2:57 pmFollowed by: 192 members; Location: Everywhere; Thanked: 503 times; GMAT Score:780

by Bill@VeritasPrep » Mon May 14, 2012 7:23 am

hey_thr67 wrote:how many multiples 340 has ?

Infinite. 340*1, 340*2, 340*3...340*1000...340*10000..340*100000...and so on, as well as 340 multiplied by infinite negative integers. Oh, and 340*0 of course.

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