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Rules for Odd and even number operations

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Rules for Odd and even number operations  [#permalink]

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New post 14 Dec 2009, 12:35
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Hi all,

I was just reviewing the rules for odd and even number operations:

Odd + Odd = Even
Even + Even = Even
Odd +Even = Odd

Odd x Odd = Odd
Even x Even = even
Odd x even = even

(Essentially the only things that result in odd numbers are: odd + even = Odd and Odd x Odd = Odd)

And was wondering if anyone could confirm - do these rules also apply to subtraction and division?

Ie) odd - even = odd or even - odd = odd
and Odd divided by odd = odd

Off the top of my head, they seem to work for division and subtraction as well.
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Re: Rules for Odd and even number operations  [#permalink]

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New post 15 Dec 2009, 22:34
Yes, it works for subtraction, but not division.

Division can result in non-integer answers so beware of division!
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New post 16 Jun 2015, 23:42
Is there any rule for division?
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Re: Rules for Odd and even number operations  [#permalink]

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New post 17 Jun 2015, 01:04
Subanta wrote:
Is there any rule for division?


As mentioned in the post above yours, division is tricky.

For example, 9/3 = integer but 5/3= 1.67, not an integer.

2/4= not an integer but 6/2 or 4/2= an integer.

Thus, odd/odd may or may be not an integer.

Similarly, even/even may or may not be an integer.

The best way out is to test a couple of simple cases as shown above to tackle DS problems that deal with such equations.
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Re: Rules for Odd and even number operations  [#permalink]

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New post 15 Jul 2015, 10:16
Engr2012 wrote:
Subanta wrote:
Is there any rule for division?


As mentioned in the post above yours, division is tricky.

For example, 9/3 = integer but 5/3= 1.67, not an integer.

2/4= not an integer but 6/2 or 4/2= an integer.

Thus, odd/odd may or may be not an integer.

Similarly, even/even may or may not be an integer.

The best way out is to test a couple of simple cases as shown above to tackle DS problems that deal with such equations.


Thank You Engr2012
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Rules for Odd and even number operations  [#permalink]

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New post 15 Jul 2015, 10:38
ael719 wrote:
Yes, it works for subtraction, but not division.

Division can result in non-integer answers so beware of division!


since even number can be written as even * odd or even * even
so even / even can be even * even / even which is even
even * odd / even can be odd.
So even / even can be both odd and even.

Similarly even / odd can be even .
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Re: Rules for Odd and even number operations  [#permalink]

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New post 15 Jul 2015, 19:44
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Hi abhinav008,

You have to be careful about your Number Property rules; from what you've posted, you don't appear to account for NON-INTEGER possibilities.

For example...Even/Even COULD be even OR odd OR non-integer...

eg.

8/2 = 4
8/8 = 1
8/6 = Non-integer

Number Property knowledge can be quite useful on Test Day, but if you're going to take a 'theory'-based approach, then you have to make sure that you haven't missed any of the possibilities.

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Re: Rules for Odd and even number operations  [#permalink]

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New post 18 Jul 2015, 23:06
Hi,

another 2 (obvious) rules that derive from your own, but still need to be written (for the quick answer):

1. powers don't change the Odd-Even.
what works for me is just "covering" the powers and continue as usual.

2. when i see then term "ax" (while a is a random integer),
if a=> even, then i cover the "x" (ax is even)
if a=> odd, then i cover the "a" (the even -odd property of "ax" is determent solely by "x")


one more point to notice while dividing is that its a derivative of multiplication.

assuming the the multiplication is integer, the only rule is :

ODD X odd = odd(r) => odd(R)/odd = ODD or odd(r)/ODD = odd

because multiply even by any number result an even, the division of even by any number is not clear for its odd-even property.
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