Data Sufficiency Question in OG 12th Edition

[cmmancin]

Can someone please confirm that my rationale for the question below is correct.

If m is an integer, is m odd?

(1) m/2 is not an even integer.

(2) m-3 is an even integer.

For the first part, I was initially struggling because I assumed that the quotient from m/2 had to be an integer when really the question only states that m is an integer. Is part (1) not sufficient because the quotient does not have to be an integer, therefore, the integer being divided by 2 can either be odd or even? Is it safe to assume that even though it says it is not an even integer, the quotient does not have to be an integer at all?

Thanks in advance for any help!

[melguy]

If m is an integer, is m odd?

(1) m/2 is not an even integer (means m/2 is an odd integer or a fraction!)

if m is even

4/2 = 2,
6/2 = 3 (m is an even integer & m/2 = odd)
8/2 = 4
10/2 = 5

if m is not even

5/2 = 2.5
7/2= 3.5
9/2 = 4.5
11/2 = 5.5

m is an odd integer i.e. m/2 = fraction

IMO - Not Sufficient