Hi,
I purchased the Full set of MGMAT books, and it looks like some of the problems in the Number Properties set do not consider 0 as a multiple of all numbers.
Is there a specific reason for this?
Thanks,
G
GMAT Forum
4 postsPage 1 of 1
- Genie
- MIT_Aspirant
Are you sure that the problems that you are referring to are not talking about "0 being a factor of any number". Do you have an example?
Zero is a multiple of every number, but no other number is a multiple of 0. In other words 0 is not a factor of any number.
What it means for x to be a multiple of y:
There exists some integer z such that x=y*z.
If x=0 and y is any arbitrary integer, we can take z=0, so then 0 (or x) is a multiple of any integer.
However, if we assume y=0, we *must* have x=0 (since number properties specify any number multiplied by 0 is 0 ), so no nonzero integers can be a multiple of 0.
Zero is a multiple of every number, but no other number is a multiple of 0. In other words 0 is not a factor of any number.
What it means for x to be a multiple of y:
There exists some integer z such that x=y*z.
If x=0 and y is any arbitrary integer, we can take z=0, so then 0 (or x) is a multiple of any integer.
However, if we assume y=0, we *must* have x=0 (since number properties specify any number multiplied by 0 is 0 ), so no nonzero integers can be a multiple of 0.
- Genie
Yup
I do understand the concept of Factors and Multiples, and thanks for the elaboration on the concept of X vs Y as a factor, but my question still stays good. I dont have an example off the top of my head. Maybe I'll post something tomorrow.
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
FACTS:
(1) 0 is technically a multiple of every positive integer. specifically, every positive integer goes into 0, exactly zero times.
(2) 0 is NOT a factor of anything.
(3) the question of whether 0 is a multiple / factor of 0 itself is open to multiple interpretations in the mathematical community; rest assured that you will not have to deal with this issue.
COMMENT:
i have never seen an official problem, whether from og or gmatprep, dealing with the question of whether 0 (or a negative number) should be regarded as a multiple of some other integer. the official problems tend to limit their discussion of factors and multiples to POSITIVE factors and multiples of POSITIVE integers, so i would place a rather large wager that you will not be required to know the above facts.
but but BUT,
if you plug in your own numbers on a question dealing with factors and multiples, then it's quite possible that you might have to use the above facts to answer the problem once you've restated the problem in terms of your numbers. so it won't hurt to know the facts, and you may even need them. so know them.
(1) 0 is technically a multiple of every positive integer. specifically, every positive integer goes into 0, exactly zero times.
(2) 0 is NOT a factor of anything.
(3) the question of whether 0 is a multiple / factor of 0 itself is open to multiple interpretations in the mathematical community; rest assured that you will not have to deal with this issue.
COMMENT:
i have never seen an official problem, whether from og or gmatprep, dealing with the question of whether 0 (or a negative number) should be regarded as a multiple of some other integer. the official problems tend to limit their discussion of factors and multiples to POSITIVE factors and multiples of POSITIVE integers, so i would place a rather large wager that you will not be required to know the above facts.
but but BUT,
if you plug in your own numbers on a question dealing with factors and multiples, then it's quite possible that you might have to use the above facts to answer the problem once you've restated the problem in terms of your numbers. so it won't hurt to know the facts, and you may even need them. so know them.
4 posts Page 1 of 1