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

Question

If  a  and  b  are nonzero integers, is  \frac{a}{b}  an even number?

(1)  ab  is an odd number.
 
(2)  a + b  is an even number.

Rock750 · Answer

Hi,

The OA is marked  A 
My question is : what if a = 11 and b = 5 (both are integers) then the product is 55, which is odd but as a result , a/b is not an integer and the question did not precise that a should be a multiple of b or the reverse. So picking this two numbers will lead to a not sufficient answer considering (1) ALONE.

Thanks

Chiranjeevee · Answer

Rock750 Please read the question carefully. u can figure it out

is a/b an even integer?

from 1, ab = odd integer, so both a and b are odd.
in any case a/b will not be an even integer

for eg: say a = 9 and b = 3

a/b = 3 odd, not an even integer

or take the same case that u have taken, a = 11 and b = 5

a/b = 2.2 not an even integer

so sufficient

KarishmaB · Answer

Statement 1 is sufficient no matter which numbers you pick. 
The question is: Is a/b an even integer?

For a/b to be an even integer, 'a' must be even (since a and b are given to be integers) and 'b' must be a factor of 'a' such that the quotient is still even.

Statement 1: If 'a' and 'b' are odd, 'a' is not even and hence we can say that a/b is not an even integer. Now whether it is not an integer itself or whether it is not even, doesn't matter to us. What we know is that it is not an 'even integer'.

Bunuel · Answer

Official Solution:

If  a  and  b  are nonzero integers, is  \frac{a}{b}  an even number? 
 
(1)  ab  is an odd number.
 
This statement implies that both  a  and  b  must be odd. Therefore,  \frac{a}{b}  is an odd number divided by an odd number, which cannot be even. Thus, the answer to the question is NO. Sufficient. 
 
(2)  a + b  is an even number.
 
This statement implies that either both  a  and  b  are odd or both of them are even. If both  a  and  b  are odd, then  \frac{a}{b}  is not even. However, if both  a  and  b  are even, then  \frac{a}{b}   can  be even, for example consider  a=4  and  b=2 . It is important to note that if both  a  and  b  are even, then  \frac{a}{b}  can also be odd (consider  a=b=2 ) as well as non-integer (consider  a=2  and  b=4 ). This statement is not sufficient to answer the question.

Answer: A

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

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

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