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If r, s, and t are positive integers, is r + s + t even?

(1) r + s is even.

(2) s +t is even.

r+s+t even?

1. r+s doesnt say anything we do not know if t is even or odd

2. s+t as well alone doesnt say anything

combined. even +even=even r+s+s+t=even so r+t is even 2s is even.
but r can be odd and t can be odd as well. or all of three integers can be odd
so cannot say yes or no

(1) r + s is even (therefore r & s are either both even or both odd), t could be odd or even, therefore not enough info

(2) same analysis, s + t is even (therefore s & t are either both even or both odd), r could be odd or even, therefore not enough info

Combine (1) & (2): if we start by assuming that r & s are both even (from statement (1)), then we know that s & t will also both be even (from statement (2)), therefore r + s + t would be even.

BUT

if we then assume that r & s are both odd (also from statement (1)), then we know that s & t will also both be odd (from statement (2)), therefore r + s + t would be odd