Number Properties

vishugogo wrote:If a and b are integers and the sum of ab and b is odd, which of the following could be true?

I. a and b are both odd

II. a is even and b is odd

III. a is odd and b is even

Addition of an Odd and Even will result in ODD

So either of ab or b has to be ODD or EVEN

I. a and b are odd

so ab=odd and b=odd so odd + odd = even Wrong

II a is even and b is odd

so a*b= even and b is odd so even + odd = odd Yes

III a is odd and b is even

so ab is even and b is even so even + even = even wron

Only II

vishugogo wrote:If a and b are integers and the sum of ab and b is odd, which of the following could be true?

I. a and b are both odd

II. a is even and b is odd

III. a is odd and b is even

Out of three you can rule out 3. Because B has to be odd otherwise ab=even and B is even and even+even=even
you can also rule out 1 as well. Because if A and B both are odd them ab=odd and B is odd and odd+odd=even.


In the addition of two integer one has to be odd sothat the sum can be odd. Here AB is considered as one part and B is considered as another. So the correct answer is 2

vishugogo wrote:If a and b are integers and the sum of ab and b is odd, which of the following could be true?

I. a and b are both odd

II. a is even and b is odd

III. a is odd and b is even

I only
II only
III only
I and II
I and IIII

Since a and b must be positive integers, the only issue here is EVEN VS. ODD.
We can test values.
If a statement holds true for the tested values, it will hold true for ANY even/odd combination.
If a statement does NOT hold true for the tested values, it will NOT hold true for ANY even/odd combination.

Statement I:
If a=1 and b=1, then ab + b = 1*1 + 1 = 2.
The condition that ab+b = ODD is not satisfied.
Thus, statement I is not possible.
Eliminate A, D and E.

Statement 2:
If a=2 and b=1, then ab + b = 2*1 + 1 = 3.
This works.
Eliminate C, which does not include statement II.

The correct answer id B.