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g_beatthegmat · Thu Aug 02, 2007 5:26 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-

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beny · Thu Aug 02, 2007 6:43 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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lalitgmat · Thu Aug 02, 2007 9:26 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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g_beatthegmat · Fri Aug 03, 2007 12:36 am

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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ash g · Fri Mar 07, 2008 8:03 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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Stuart Kovinsky · Sat Mar 08, 2008 8:01 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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Atul Sharma · Mon Nov 16, 2009 4:16 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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Atul Sharma · Mon Nov 16, 2009 4:17 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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Stuart Kovinsky · Mon Nov 16, 2009 11:44 am

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