Is X a multiple and factor of itself

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wilderness: Master | Next Rank: 500 Posts; Posts: 102; Joined: Sat Mar 15, 2008 4:03 am; Thanked: 4 times

by wilderness » Tue Jul 08, 2008 6:27 am

On GMAT when calculating factors and multiple of an integer X, should X be considered a factor and a multiple of itself.

Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Jul 08, 2008 6:27 am

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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 » Tue Jul 08, 2008 8:12 am

If X is a positive integer, then yes. As an example, if X = 12, the multiples of X are ...-24, -12, 0, 12, 24, ... and the positive divisors of X are 1, 2, 3, 4, 6, and 12.

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wilderness: Master | Next Rank: 500 Posts; Posts: 102; Joined: Sat Mar 15, 2008 4:03 am; Thanked: 4 times

by wilderness » Tue Jul 08, 2008 8:23 am

Ian Stewart wrote:If X is a positive integer, then yes .

Hi Ian,

Thanks for the answer. Regarding the comment about if X is +ve,

1) do we really talk about factors of a -ve number ?

2) If yes, then why does this rule not apply to that case. Afterall just like 2/2 = 1 and -2/-2 = 1 and 2*1=2 and -2*1 = 2.

Thanks in advance.

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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 » Tue Jul 08, 2008 3:02 pm

wilderness wrote: 1) do we really talk about factors of a -ve number ?

2) If yes, then why does this rule not apply to that case. Afterall just like 2/2 = 1 and -2/-2 = 1 and 2*1=2 and -2*1 = 2.

Thanks in advance.

Re 1), not in any GMAT question I've ever seen. I've only ever seen GMAT questions that ask about 'positive divisors', and divisibility questions seem to always be restricted to positive integers.

The rules are, as you point out, the same for negatives and positives- when I was restricting things to positives in my first post, I was actually only trying to exclude zero (zero is a bit of an exception- zero is a multiple of itself, but not a divisor of itself- that's not a technicality you need to be concerned about for the GMAT). And, of course, I was limiting the discussion to the case that's relevant on the GMAT.

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wilderness: Master | Next Rank: 500 Posts; Posts: 102; Joined: Sat Mar 15, 2008 4:03 am; Thanked: 4 times

by wilderness » Wed Jul 09, 2008 12:37 am

Thanks !

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