# If a is an even integer, which of the following is definitely not an odd integer?

Q) If a is an even integer, which of the following is definitely not an odd integer?

a) a*b, where b is odd
b) a/b, where b is an even number greater than 0
c) ab-1 where b is an even number greater than 3
d) 3(ab-2) where b is an even number
e) 5(a+b)where b is an odd number

Before we go into the question, remember the properties of odd and even number arithmetic operations:

Odd x Even = Even
Odd x Odd = Odd
Even x Even = Even
Odd + Even = Odd
Even – Odd = Odd
Odd + Odd = Even

Now let us look at the question: which of the following is definitely not an odd integer.
The key phrase is definitely. You have to be 100% sure, than the number is not an Odd Integer.

Let us look at the answer choices:

a) (a*b)^3 - 1, where b is greater than or equal to 1

This is a direct properties question. The product of even and odd integer will be even and the cube again will be even. But if you deduct 1, the result will be odd.

b) a/b, where b is an even number greater than 0

This condition would have given a non-odd integer but for condition when a=b, the result will be odd.

c) ab-1 where b is an even number greater than 3

Another operation to subtract 1 from the product of Even and Even number

Even X Even = Even

But Even – 1 = Odd

d) 3(ab-2) where b is an even number

Even X Even = Even

But Even  - 2 = Even

3 X (Even – 2) = Odd X (Even) = Even

e) 5(a+b) where b is an odd number

Odd + Even = Odd
Odd x Odd = Odd

a+b = Odd

5 x Odd = Odd

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