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# operations for odd and even numbers- HELPFUL

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operations for odd and even numbers- HELPFUL [#permalink]  10 Jan 2010, 16:49
I’ve been asking around, doing a bit of research and have compiled this extra list of generalizations for odd/even number operations that will be helpful come test day, especially for data sufficiency.

Could people confirm my thoughts? It would be awesomely appreciated.

1) Odd subtract Even = always Odd
2) Even subtract Odd = always Odd
3) Odd subtract Odd = always Even
4) Odd divided by Odd never equals even (will only result in either Odd numbers or fractions)

(This may have been discussed before, sorry if it’s redundant, but I think these are really helpful and important to get right!)
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Re: operations for odd and even numbers- HELPFUL [#permalink]  10 Jan 2010, 16:58
a), b), and c) are right. Subtracting a number is just like adding a negative number, so the odd/even rules still apply.

For d), consider this:

odd number = 2n+1 (for any n)

Let the bigger odd number be 2n+3 and smaller odd number be 2n+1.

So if we have \frac{2n+3}{2n+1}

=\frac{(2n+1)+2}{2n+1}

=(\frac{2n+1}{2n+1})+(\frac{2}{2n+1})

=1 + 2* \frac{1}{2n+1}

1 is always odd. The second part is always even because it is a multiple of 2. So we have

= odd + even

= always odd
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Re: operations for odd and even numbers- HELPFUL [#permalink]  10 Jan 2010, 17:22
glender wrote:
I’ve been asking around, doing a bit of research and have compiled this extra list of generalizations for odd/even number operations that will be helpful come test day, especially for data sufficiency.

Could people confirm my thoughts? It would be awesomely appreciated.

1) Odd subtract Even = always Odd
2) Even subtract Odd = always Odd
3) Odd subtract Odd = always Even
4) Odd divided by Odd never equals even (will only result in either Odd numbers or fractions)

(This may have been discussed before, sorry if it’s redundant, but I think these are really helpful and important to get right!)

You don't really need to memorize this, just try simple numbers and they will hold for all similar numbers.

1) 3-2 = 1 (odd) --> odd-even = odd for all numbers
2) 6-3 = 3 (odd) --> even - odd = odd for all number
3) 5-3 = 2 (even) --> odd-odd = even for all numbers
4) 9/3 = 3 (odd) --> odd/odd = odd for all numbers (an odd number will not have an even factor)
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Re: operations for odd and even numbers- HELPFUL [#permalink]  18 Jan 2010, 10:39
If the question is x - y, just remember that the only way to get an even number is if BOTH x and y are ODD or EVEN.
Re: operations for odd and even numbers- HELPFUL   [#permalink] 18 Jan 2010, 10:39
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