What is the value of x^3 + y^3?

Target question: What is the value of x³ + y³?

Statement 1: x + y = 12
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 12 and y = 0. In this case x³ + y³ = 12³ + 0³ = 12³
Case b: x = 10 and y = 2. In this case x³ + y³ = 10³ + 2³ = 1008
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: x − y = 8
This information is very similar to the information in statement 1, so let's test some values again
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 8 and y = 0. In this case x³ + y³ = 8³ + 0³ = 8³
Case b: x = 10 and y = 2. In this case x³ + y³ = 10³ + 2³ = 1008
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x + y = 12
Statement 2 tells us that x − y = 8
Here, we have 2 different linear equations with 2 variables.
Since we COULD solve this system for x and y, we COULD answer the target question with certainty.
As such, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent