If a and b are positive integers

Question

If a and b are positive integers, is a/b an even integer?

1. ab is an even integer
2. b/a is an even integer

Capricorn369 · Answer

1. ab is an even integer - we've 3 options - 
a = even & b = even 
a = odd & b = even
a = even & b = odd 
Can't conclude that a/b is an even integer or not. Insuff.

2. b/a is an even integer - this means that B is greater than a and the value is one among 0, 2, 4, 6 etc.
However, the reverse of these numbers are 1/2,1/4,1/6,1/8 etc, and we know that these numbers are not even.
Sufficient.

My answer is B.
Cheers!

Bunuel · Answer

m19 q31

If a and b are positive integers, is a/b an even integer?

(1) ab is an even integer. If  a=b=2  then the answer is NO but if  a=2  and  b=1  then the answer is YES. Not sufficient.

(2) b/a is an even integer -->  \frac{b}{a}=even  -->  \frac{a}{b}=\frac{1}{even}
eq{integer} , so  \frac{a}{b}
eq{even} . Sufficient.

Answer: B.

Hope it's clear.

bumpbot · Answer

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If a and b are positive integers

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