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

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

by Vincen » Wed Feb 23, 2022 4:00 am

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Global Stats

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

(1) $$r$$ is even.
(2) $$s$$ is even.

Source: Official Guide

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Re: If $$r$$ and $$s$$ are positive integers, is $$r + s$$ even?

by [email protected] » Thu Feb 24, 2022 8:06 am

00:00

A

B

C

D

E

Global Stats

Vincen wrote:
Wed Feb 23, 2022 4:00 am
If $$r$$ and $$s$$ are positive integers, is $$r + s$$ even?

(1) $$r$$ is even.
(2) $$s$$ is even.

Source: Official Guide
Given: r and s are positive integers

Target question: Is r + s even?

Statement 1: r is even.
Since we have no information about s, we cannot determine whether r + s is even
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: s is even
Since we have no information about r, we cannot determine whether r + s is even
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that r is EVEN
Statement 2 tells us that s is EVEN
Since EVEN + EVEN = EVEN, we know that r + s is EVEN
Since we can answer the target question with certainty, the combined statements are SUFFICIENT