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Properties of Zero
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aditikedia
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VP_Tatiana
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Zero is considered an even integer. However, there are 3 distinct classes of integers: positive, negative, and 0. 0 is not positive.
Tatiana
Tatiana
Tatiana Becker | GMAT Instructor | Veritas Prep
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
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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Ian Stewart
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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: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.
...(-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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