Rules for Adding & Multiplying etc Odd & Even Numbers

Question

Addition / Subtraction:  
even +/- even = even;
even +/- odd = odd;
odd +/- odd = even.

Multiplication:  
even * even = even;
even * odd = even;
odd * odd = odd.

Division of two integers can result into an even/odd integer or a fraction.  
Odd/Odd could be Odd or a Fraction (CANNOT be even). For example: 7/1 = 7 = odd and 7/3 = non-integer.
Odd/even is ALWAYS a Fraction. For example: 7/2 = 3.5 = odd and 7/3 = non-integer.
Even/Odd could be Even or a Fraction (CANNOT be odd). For example: 6/3 = 2 = even and 6/13 = non-integer. 
Even/Even could be Even, Odd or a Fraction. For example: 4/2 = 2 = even, 6/2 = 3 = odd and 6/12 = non-integer.

Exponents:  
(Positive Even Integer)^(Positive Even Integer) = Even
(Positive Even Integer)^(Positive Odd Integer) = Even
(Positive Odd Integer)^(Positive Even Integer) = Odd
(Positive Odd Integer)^(Positive Odd Integer) = Odd

Notice here that if the exponent is not positive then these rules break. For example,  2^{(-2)} = \frac{1}{4} ,  3^{(-1)} = \frac{1}{3} ,  2^0 = 1 , ...

Subanta · Answer

Is there any rule for division?

ENGRTOMBA2018 · Answer

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.

abhinav008 · Answer

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 .

EMPOWERgmatRichC · Answer

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.

GMAT assassins aren't born, they're made,
Rich

idan1 · Answer

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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Rules for Adding & Multiplying etc Odd & Even Numbers

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Rules for Adding & Multiplying etc Odd & Even Numbers

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