Does 3^(r+s) = 27^6 ?

[ktrout2020]

Does 3^(r+s) = 27^6 ?

(1) r - s = 8
(2) 5r = 13s

Source: Princeton Review

[Brent@GMATPrepNow]

Does 3^(r+s) = 27^6 ?

(1) r - s = 8
(2) 5r = 13s

Source: Princeton Review

Target question: Does 3^(r + s) = 27^6 ?
This is a good candidate for rephrasing the target question.
To get the same base on both sides, rewrite 27 as 3^3.
We get: 3^(r + s) = (3^3)^6
Apply power of power rule to get: 3^(r + s) = 3^18
Now that the bases are the same, we can conclude that: r + s = 18
So, we can REPHRASE the target question....

REPHRASED target question: Does r + s = 18?
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: r - s = 8
Does this provide enough information to answer the REPHRASED target question? No.
There are several values of r and s that satisfy statement 1. Here are two:
Case a: r = 8 and s = 0, in which case r + s = 8 + 0 = 8
Case b: r = 13 and s = 5, in which case r + s = 13 + 5 = 18
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 5r = 13s
There are several values of r and s that satisfy statement 2. Here are two:
Case a: r = 0 and s = 0, in which case r + s = 0 + 0 = 0
Case b: r = 13 and s = 5, in which case r + s = 13 + 5 = 18
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that r - s = 8
Statement 2 tells us that 5r = 13s
So, we have a system of two different linear equations with 2 different variables.
Since we COULD solve this system for r and s, we could determine whether or not r + s = 18, which means we COULD answer the REPHRASED target question with certainty.
So,the combined statements are SUFFICIENT

Answer: C