Data Sufficiency

BTGmoderatorDC wrote: ↑

Sun Dec 25, 2022 5:40 pm

If r and s are positive integers greater than 10, is r + s even?

(1) r and s are prime numbers
(2) r - s = 2


OA D

Source: Manhattan Prep

Given: r and s are positive integers greater than 10

Target question: Is r + s even?

Statement 1: r and s are prime numbers
Key property: All prime numbers greater than 2 are ODD
Since we're told r and s are integers greater than 10, we now know that r and s are both odd.
Since ODD + ODD = EVEN, we can be certain that r + s is even
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: r - s = 2
Add s to both sides of the equation to get: r = s + 2
Since our goal is to determine whether r + s is even, let's take r + s, and replace r with s + 2.
When we do so we get: r + s = (s + 2) + s = 2s + 2 = 2(s + 1)
At this point, it's clear that r + s is a multiple of 2, which means r + s is even
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D