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Properties of Zero

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
Expert replies
Source: — Quantitative Reasoning |

by VP_Tatiana » Mon Jul 21, 2008 7:35 am
Zero is considered an even integer. However, there are 3 distinct classes of integers: positive, negative, and 0. 0 is not positive.

Tatiana
Tatiana Becker | GMAT Instructor | Veritas Prep
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by lightbulb » Sat Aug 02, 2008 7:15 pm
I was at a Kaplan test center today to take the diagnostic test.

One of the questions (Math # 13), led me to list numbers such that:
- The number x is prime
- The number x < 15
- The quantity (x -2) is a multiple of 5

So, I got the set of prime numbers: x: {2,3,5,7,11 and 13}
The set of numbers such that (x - 2) is a multiple of 5: {7}

BUT:
According to their explanation, x = 2 is also correct, since according to them 0 is also a multiple of 5. I understand that when zero is divided by any number (other than 0), you get zero. But I am not sure if you can call zero a multiple of every number and I am wondering what GMAC's/GMAT Instructor's thought's are about this.

Here is the link to their explanation (Math, #:13)

https://www.kaptest.com/oneoff/testdrive ... ations.pdf
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by Ian Stewart » Sun Aug 03, 2008 3:54 am
lightbulb wrote: BUT:
According to their explanation, x = 2 is also correct, since according to them 0 is also a multiple of 5. I understand that when zero is divided by any number (other than 0), you get zero. But I am not sure if you can call zero a multiple of every number and I am wondering what GMAC's/GMAT Instructor's thought's are about this.
GMAC's definition of 'multiple' will be the same as that used universally in mathematics. What does it mean for 'x to be a multiple of y'? It means you can multiply y by an integer to get x. The multiples of 5 are:

...(-2)*5, (-1)*5, (0)*5, (1)*5, (2)*5, ...

i.e.

...-10, -5, 0, 5, 10, ...

In brief, zero is a multiple of every integer (and even of zero).
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
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by lightbulb » Sun Aug 03, 2008 6:09 pm
Thanks for your response.
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