Data Sufficiency

If r, s, and t are positive integers, is r + s + t even?
(1) r + s is even.
(2) s +t is even.

If r, s, and t are positive integers, is r + s + t even?
(1) r + s is even.
(2) s +t is even.

Statement 1
r +s is even...
when t is even then r+s+t is also even
but when t is odd... r+s+t is odd...
insuficient

Statement 1
s +t
similar reasoning as statement one...
insufficient...

From 1 and 2

r, s, and t can be both odd or even
when all are even the sum is also even...
when all are odd the sum is also odd...
insufficient
Ans E

Let r = 3, s = 3, t = 3

statement 1 - r + s = even
statement 2 - s + t = even

r + s + t = odd

Let r = 2, s = 2, t = 2

statement 1 - r + s = even
statement 2 - s + t = even

r + s + t = even

therefore we cannot conclude that r + s + t is even. answer E