operations for odd and even numbers- HELPFUL

Question

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!)

mrblack · Answer

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

firasath · Answer

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)

mrblack · Answer

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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

operations for odd and even numbers- HELPFUL

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards