Is Zero even.

Hi All,

While this is an old post, the concepts involved are important and will play a role in several questions on Test Day (especially DS questions).

Here are the 'essentials' that you need to know about the number 0.

1) 0 is an EVEN INTEGER. On a number line, integers follow a pattern: odd-even-odd-even-etc. -2 is even, -1 is odd, 0 is even, 1 is odd, 2 is even, etc.

2) 0 is a "NULL" value. It is neither positive, nor negative.

3) The product of ANY number and 0 is 0.

4) As such, 0 is a MULTIPLE of EVERY number.

GMAT assassins aren't born, they're made,
Rich

Some facts about the magical number zero =>
zero is not a natural number
zero is a whole number
zero is an integer
zero is neither positive nor negative
zero is neither prime nor composite
zero is divisible by every number except zero itself => Hence zero isn't a multiple of every number EMPOWERgmatRichC
zero is an even integer as it is divisible by 2.
if P is a product of many numbers and one out of them is zero => p =zero

Zero is multiple of every number.

x * 0 = 0 for all x

NOT AT ALL Mate.
I still remember i read it in maths textbook at my high school library

See if 0/0 is defined then the concept of limits and infinity will be breached and they aren't on scope with gmat
0/0 =Not defined
anything/0 is not defined.
Maybe Bunuel can shed some light on whether 0/0 is defined or not.
I hope i am not wrong..!!

Regards
Stone Cold

Maybe this will clear :

is-0-zero-to-be-considered-as-a-multiple-of-every-number-104179.html

It does clear everything
Bunuel clearly states zero is divisible by every integer EXCEPT FOR ZERO ITSE:.
I said it

Regards
Stone Cold

Few extra tips:

1. zero is even

2. If a question states X is a number, X can be positive, negative, zero, fraction and anything.

3. If a question states X is a positive integer, then x starts from 1,2,3....

4. If a question states X is a whole number, then "0" is also a part of X

5. If a questions states X is a non-negative integer, then X starts from 0,1,2...

Cheers
Balaji

If 0 is a multiple of every number then what are the reasons 0 is not consider least common multiple of some numbers. For eg why LCM of 4 and 6 is 12 and not 0.

Posted from my mobile device

LCM(a, b), is the smallest positive integer that is divisible by both a and b. (However, some authors define LCM (a,0) as 0 for all a)
Source: https://en.wikipedia.org/wiki/Least_common_multiple

(Moreover, if you remove the positive integer constraint even 0 is not the lowest but there can be infinitely lower negative value integer.)

We can leave the debate safely, as GMAT will not ask question testing this ambiguous topic.

Hi ISBtarget

Thank you for posting this interesting question. This concept plays a key role in many Data Sufficiency questions.

For a number to be even, it has to be divisible by 2 leaving a remainder = 0.

This condition is fulfilled by 0. Therefore, 0 is an even number.

Other interesting facts about 0 that you need to know for GMAT are following:
Zero multiplied to any number gives Zero.

Zero divided by any number other than zero gives zero.

Square root of zero is zero.

Any number divided by zero gives an undefined answer.

Zero raised to a positive power gives zero.

Zero is equal to its opposite.

Zero is multiple of all numbers.

Any number (other than zero) raised to the power zero is 1.

I hope you understand the concept better now. Pls drop in a message for any further query.
I shall be happy to help.
All the best.

Hi !
This is an old question but an interesting one.

What's an even integer?
Any number that is perfectly divisible by 2 is an even integer. They are represented as 2n where n is an integer.
So, numbers like 2,4,6,8,.....OR -2,-4,-6,-8,...are even integers.

Can I represent 0 in the same way?
Sure , I can!
2 * 0=0 ; so if n=0 the definition of even numbers is satisfied by 0.
Hence 0 can be represented as 2n and hence 0 is an even number.

Input- 0 is a real number and 0 is Neither positive NOR negative!

Hope this helps!

Devmitra Sen
GMAT Mentor