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Is Zero Even or Odd?

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Is Zero Even or Odd?

by sanjib » Tue May 26, 2009 1:51 pm
Lynda recently purchased a new combination lock for her gym locker but can’t remember the combination. What she does remember is that of the four digits, all between 0 and 9, the first is a prime number and the last is an even digit. How many different four-digit number combinations must Lynda try to be certain of opening her lock?

A 200
B1296
C1600
D1620
E2000

OA is E

I do have a huge doubt on this .
Because if wte consider 0 as even digit then the ans. is E

If not consider 0 as even then it is D
Pls help .What the official GMAC Strategy regarding O
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by ssmiles08 » Tue May 26, 2009 2:01 pm
0 is even.

_ _ _ _

first digit has 4 possibilities : 2,3,5,7
last digit has 5 possibilities : 0,2,4,6,8
the middle two have 10 possibilities

4*10*10*5 = 2000
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by gmat740 » Tue May 26, 2009 7:29 pm
0 is even.
0 is neither even nor odd

This is a very basic concept and it will not change even if we give GMAT or GRE.
first digit has 4 possibilities : 2,3,5,7

First digit is a prime number : why are we not considering 1 as prime. To my best knowledge one is also prime and hence for first digit we have = 5 possibilities
last digit has 5 possibilities : 0,2,4,6,8


we need not to consider 0,so last digit has only 4 possibilities

rest middle digits as said,10 possibilities


so we have

5*10*10*4

ans = 2000


Please note we may arrive on a correct answer but the method may be wrong.

It is very important to learn the method of approach.

Hope this helps
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by cramya » Tue May 26, 2009 7:49 pm
0 is neither even nor odd

This is a very basic concept and it will not change even if we give GMAT or GRE.
Karan,
0 IS EVEN


Regards,
CR
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by ssmiles08 » Tue May 26, 2009 7:49 pm
0 is neither even nor odd

https://en.wikipedia.org/wiki/Evenness_of_zero

https://mathforum.org/library/drmath/view/57104.html

Proof That Zero is Even

Zero is neither positive nor negative.

An integer n is called even if there exists
an integer m such that n = 2m, and odd if n+1 is even. From this,
it is clear that 0 = (2)(0) is even.

You are right in the sense that I mistook the first number to be the "even digit" and the last number to be the "prime digit."
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by cramya » Tue May 26, 2009 7:52 pm
NOTE:

When a problem reads NON POSITIVE INTEGERS then it will be

0 and all negative ints

When a problem reads NON NEGATIVE INTEGERS then it will be

0 and all positive ints

In some DS question the consideartion of 0 as part of such a list will end up being the key to the problem


Like Smiles said 0 is non positive and non negative

Regards,
CR
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by mikeCoolBoy » Tue May 26, 2009 7:53 pm
I think ssmiles08 is right. 0 is even and 1 is not prime.
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by Stuart@KaplanGMAT » Tue May 26, 2009 8:14 pm
mikeCoolBoy wrote:I think ssmiles08 is right. 0 is even and 1 is not prime.
Correct.

0 is uncharged (neither positive nor negative), but is even.

2 is the smallest prime number and the only even prime number.
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by ssmiles08 » Tue May 26, 2009 8:15 pm
gmat740 wrote:

First digit is a prime number : why are we not considering 1 as prime. To my best knowledge one is also prime and hence for first digit we have = 5 possibilities
A prime number (n) is defined as an integer which has 2 factors: 1 and n itself.

1 is NOT a Prime number because it only has 1 factor which is 1.
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by VP_Jim » Wed May 27, 2009 8:42 am
It's amazing how little bits of trivia can really affect a score. I've had GMAT students who are engineers and quant finance people, and when I asked them if zero is even, odd, or neither, I got blank stares! So, the lesson is - no matter how confident you are in your math skills, make sure you look over the basics so that little things like this don't throw you off. Many questions hinge on knowing that zero is even, or that non-negative does not mean positive, or that two is the only even prime, etc.
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by sanju09 » Fri May 29, 2009 2:02 am
gmat740 wrote:
0 is even.
0 is neither even nor odd

This is a very basic concept and it will not change even if we give GMAT or GRE.
first digit has 4 possibilities : 2,3,5,7

First digit is a prime number : why are we not considering 1 as prime. To my best knowledge one is also prime and hence for first digit we have = 5 possibilities
last digit has 5 possibilities : 0,2,4,6,8


we need not to consider 0,so last digit has only 4 possibilities

rest middle digits as said,10 possibilities


so we have

5*10*10*4

ans = 2000


Please note we may arrive on a correct answer but the method may be wrong.

It is very important to learn the method of approach.

Hope this helps
:shock: :roll: :wink: B-) :) = wordless
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