integers

[naaga]

. If x and y are integers and xy2 is a positive odd integer, which of the following must be true?
Ⅰ. xy is positive.
Ⅱ. xy is odd.
Ⅲ. x + y is even.
folks please explain how many statements of the above are sufficient to answer the question..

[sureshbala]

I will take it as (xy)^2 is positive and odd.

(xy)^2 is always positive either xy is positive or negative.

So I need not be true.

(xy)^2 will be odd provided xy is odd, which means both x and y are odd.

So II must be true.

Also if x and y both are odd, x+y must be even. So III also must be true.

[Etoiles]

. If x and y are integers and xy2 is a positive odd integer, which of the following must be true?
Ⅰ. xy is positive.
Ⅱ. xy is odd.
Ⅲ. x + y is even.
folks please explain how many statements of the above are sufficient to answer the question..

let 's start
xy2 is a positive odd
xy must be odd
so x+y are odd why ? Because what ever time even is even so no even here
both are odd adding 2 odd give even
but we can't say that both are positive since -X- = + so we know they have the same sign

so the sum is even xy odd
that 's all

[Bidisha800]

II & III

[earth@work]

II & III
(XY)^2 is odd means both x & y are odd
now 4 possibilities:
1) x (positive) & y (negative)
2) x (positive) & y (positive)
3) x (negative) & y (negative)
4) x (negative) & y (positive)
this means I is not always true

II - odd x odd = odd ..true
III - odd + odd = even ....true