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Is Zero to be considered a multiple of all the numbers?

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by g_beatthegmat » Thu Aug 02, 2007 4:26 am
Hello,

Is Zero considered a multiple of all the numbers? I came across question # 13 in the Full-Length Practice Test of Kaplan which says-
Ques: If x is a prime number, what is the value of x?
(1) x < 15
(2) (x - 2) is a multiple of 5.
Now here (1) and (2) separately aren't enough. (1) could be 2, 3, 5, 7, 11, 13. And (2) could be 7, 17, 37... this is where I'm corrected by the book, which says 0 also needs to be considered as a factor of a number- which would make the possible vales for (2) as 2, 7, 17, 37...

So considering 0 would change the answer of this question to (E)-both not sufficient from (C)-statement 1 & 2 together are sufficient.

If zero is a multiple of all the numbers, then shouldn't it be considered for calculating the LCM & GCM of all the numbers as well? :roll:

Thanks in advance
Last edited by g_beatthegmat on Thu Aug 02, 2007 11:25 pm, edited 1 time in total.
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by beny » Thu Aug 02, 2007 5:43 pm
0 is not considered a multiple of all numbers.

Either way, as you stated, with statement 2, the answer could be 7, 12, 17, 22, ... therefore, B is insufficient byitself.

I think the answer should be C, which would narrow the answer to 7 (since 12 is not a prime).
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by lalitgmat » Thu Aug 02, 2007 8:26 pm
In this case also, only prime multiple of 5 and less than 15 is 5 itself only.
Hence, both statements ensure we have unique answer.
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by g_beatthegmat » Thu Aug 02, 2007 11:36 pm
thanks benny and lalitgmat!

So the conclusion: Zero is NOT to be considered a factor of numbers. We can then define factor as:
Factor is a +ve number that completely divides into another +ve integer.

Thanks.
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by ash g » Fri Mar 07, 2008 7:03 pm
Guys,
Just wanted to reopen this old thread. Is what is concluded in this thread correct ?
So the conclusion: Zero is NOT to be considered a factor of numbers.
This would also mean Kaplan explanation is incorrect which I dont think so.

I happen to believe that - All numbers divide zero and hence zero is a multiple of all numbers.

The example of LCM used to contradict above I think is incorrect.
The wiki definition of LCM is:
In arithmetic and number theory, the least common multiple or lowest common multiple (lcm) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b. Since it is a multiple, it can be divided by a and b without a remainder. If there is no such positive integer, e.g., if a = 0 or b = 0, then lcm(a, b) is defined to be zero.

Any thoughts ??
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by Stuart@KaplanGMAT » Sat Mar 08, 2008 7:01 am
0 is a multiple of all numbers; 0 is a factor of no number.

Negative numbers are also multiples. For example, the set of all multiples of 5 is:

{..., -15, -10, -5, 0, 5, 10, 15, ...}

However, when we talk about the lowest common multiple, we're always referring to the smallest positive multiple of the numbers involved.

So, to review this particular question:

If x is prime, what's the value of x?

(1) x < 15

x could be 2, 3, 5, 7, 11, 13: insufficient

(2) (x - 2) is a multiple of 5

x could be billions and billions of different numbers: insufficient

Together:

If we look at our list from statement (1), (2-2)=0 which IS a multiple of 5 and (7-2)=5 which is ALSO a multiple of 5. Hence, x could still be either 2 or 7: choose (e).
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by Atul Sharma » Mon Nov 16, 2009 3:16 am
Dear all

here it is not the question that who is right or Kaplan has given the explanation so it must be right

If you read the question stem, the very first line says x is a prime.
0 is not a prime so the answer should be C to the question (no need to consider 0 as multiple of any integer or whatso ever)
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by Atul Sharma » Mon Nov 16, 2009 3:17 am
Dear all

here it is not the question that who is right or Kaplan has given the explanation so it must be right

If you read the question stem, the very first line says x is a prime.
0 is not a prime so the answer should be C to the question (no need to consider 0 as multiple of any integer or whatso ever)
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by Stuart@KaplanGMAT » Mon Nov 16, 2009 10:44 am
Atul Sharma wrote:Dear all

here it is not the question that who is right or Kaplan has given the explanation so it must be right

If you read the question stem, the very first line says x is a prime.
0 is not a prime so the answer should be C to the question (no need to consider 0 as multiple of any integer or whatso ever)
You're correct, 0 is not prime; however, that's irrelevant to the question.

Statement (2) says that (x-2) is a multiple of 5, not that x is a multiple of 5.

To satisfy (2), we can choose x=2 (which is prime), since 2-2=0 which is a multiple of 5.
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by hongwang9703 » Tue Apr 13, 2010 12:33 pm
the one law immutable laws of the universe is you do not EVER doubt the accuracy of Mr. Stuart!!
i got utterly defeated by the gmat.
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by Laetitia » Wed Mar 28, 2012 7:59 am
I'm trying different GMAT tests at the moment and I am stuck with this question:
If x, y, z are three integers, are they consecutive integers?
1) z=x+2
2) None of the three integers are multiples of 3.

If we consider 0 as a multiple of 3, then there is one consecutive suite: 0, 1, 2 without any element being a multiple of 3 and then both statements together are insufficient. However, if we consider that 0 is a multiple of 3 then the second statement is sufficient
What do you think ? My book says that the statement 2) is enough.

Thank you for your help
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by Bill@VeritasPrep » Sat Mar 31, 2012 10:38 pm
Since 0 is a multiple of 3 (and of every other integer), 0-1-2 is not a possible set of values for x, y, and z.

For any set of 3 consecutive integers, 1 integer will be a multiple of 3. Thus, we know from Statement 2 that x, y, and z, CANNOT be consecutive integer
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by Mathsbuddy » Fri Nov 08, 2013 7:28 am
Indeed,

Zero is a multiple of all numbers. The question did not limit the answer to positive multiples.
So the answer is 2 or 7 because both correctly match the criteria.
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