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I. says that m/2 can be an odd integer or even a fraction .. Insufficient II. sufficient.

a fraction? but (1) say not AN EVEN INTEGER... so we can't assume that it is ODD Integer?

so 1 to me says m is integer AND m is NOT even integer... so M could be 2 or 6 or 10... it can't be 20 because it would contradict st (1) that says outcome isn't even... which makes M even still confused...

(1) m/2 is not an even integer (2) m-3 is an even integer

is (1) saying that m isn't an integer, or it isn't an even integer, or it isn't integer at all

u2 baby, it is clearly said in the question that m is an integer. but we donot know whether it is even or odd. if it is even, m/2 is an odd integer. if it is odd, m/2 is a fraction. so m is a multiple of odd integers. but be sure that m cannot be 0 or multiples of 4.

IMO we make these stupid errors because of overconfidence and tryign to solve something fast.

Of course reading (1) its easy to assume that m/2 is an odd integer. But the fact remains that m/2 is not even integer. It can be a fraction hence cannot say anything about m