Is Zero Even or Odd?

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sanjib: Master | Next Rank: 500 Posts; Posts: 109; Joined: Sun May 10, 2009 7:53 am

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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Source: Beat The GMAT — Problem Solving | Tue May 26, 2009 1:51 pm

ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

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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gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

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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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

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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ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

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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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

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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mikeCoolBoy: Master | Next Rank: 500 Posts; Posts: 119; Joined: Tue Jan 20, 2009 10:16 pm; Thanked: 9 times; GMAT Score:730

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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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

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.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
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ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

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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VP_Jim: GMAT Instructor; Posts: 1223; Joined: Thu May 01, 2008 3:29 pmFollowed by: 15 members; Location: Los Angeles, CA; Thanked: 185 times

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.

Jim S. | GMAT Instructor | Veritas Prep

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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

:roll:

= wordless

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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