If a and b are integers, is a + b odd? (1) a/b is odd (2) ab is even

Question

If a and b are integers, is a + b odd?

(1) a/b is odd. 
(2) ab is even.

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firas92 · Answer

(1) a/b is odd.

a=b*odd

If b is odd, a is odd
If b is even, a is even

So a and b are either both odd or both even which means a+b must be even

1 is sufficient
 
(2) ab is even.

Case 1: a is odd and b is even - a+b is odd
Case 2: a is even and b is odd - a+b is odd
Case 3: a is even and b is even - a+b is even

So a+b may be odd or even

2 is not sufficient

Answer is  (A)

yashikaaggarwal · Answer

Statement 1: A/B is odd

Case 1: A = 6 and B = 2 
Therefore, A/B = 6/2 = 3 (odd)
A + B = even + even = even

Case 2: A = 9 and B = 3
Therefore, A/B = 9/3 = 3 (odd)
Odd+odd = even

Therefore A+B can never be odd if A/B is Odd. (Sufficient)

Statement 2: AB = even

Case 1: A = 6 and B = 2 
Therefore, A*B = 6*2 = 12 (even)
A+B = even + even = even

Case 2: A = 6 and B = 3
Therefore, A*B = 6*3 = 18 (even)
A+B = even + odd = odd

(Insufficient)

IMO A

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sambitspm · Answer

Kindly see the attachment. Try to find relation between a and b and you will get the answer.
IMO A

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