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30 Mar 2022, 07:30
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
84% (01:07) correct
16%
(01:00)
wrong
based on 128
sessions
History
Date
Time
Result
Not Attempted Yet
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
(1) r and s are prime numbers
(2) r - s = 2
31 Mar 2022, 07:00
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Bunuel
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
19 Sep 2024, 04:48
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