abhinav008 wrote:

If m is a positive integer and m = x + y + 2z, is m odd ?

(1) x and y are consecutive positive integers.

(2) 4z is even.

Good question.

The trick here is to recognize that there is no mention that x,y,z have to be integers. Even if you dont recognise this initially, statement 1 should tell you that.

Given, m>0 and is an integer.

Qs: Is m = x+y+2z = odd?

Per statement 1, x, y are positive consecutive integers. We do not have any information about z (it can be an integer or maybe not). z can be either 1,2,3,4 etc or 3/4 , 4/5 etc.

Having x,y as consecutive integers means that x+y = odd (always) as 1 out of x or y will be odd and the other will be even.

Thus m= x+y+2z may or maybe not integer (or let alone even or odd). Thus this statement is not sufficient. To test the cases, we can have , m = 1+2+2*1/4=

no or m = 1+2+2*3 =

yes or m = 1+2+2*4=

noPer statement 2, 4 z is even ----> z = 1/4 or 1/2 or 1 or 2 or 3 etc. We do not know anything about x or y. They can be either integers or fractions. By testing cases, x = 1/4, y =1/5 , z=4 =

No but x=1, y =2, 2z = 12 =

Yes. Thus this statement is not sufficient

Combining, we still do not have enough information to say uniquely what values can z take. Thus the 2 statements are still not sufficient and hence E is the correct answer.