If a, b, and c are integers, is a - b + c greater than a + b

Target question: Is 2a – b + c > a – b – 2c?
This is a great candidate for rephrasing the target question.

Aside: We have a video with tips on rephrasing the target question (below)

Take 2a – b + c > a – b – 2c
Add b to both sides to get: 2a + c > a – 2c
Add 2c to both sides to get: 2a + 3c > a
Subtract a from both sides to get: a + 3c > 0

REPHRASED target question: Is a + 3c > 0?

Statement 1: a is positive.
No information about c, so there's no way to determine whether a + 3c > 0

Alternatively, we can examine some conflicting cases that satisfy statement 1 (a is positive):
Case a: a = 1 and c = 1, in which case a + 3c > 0
Case b: a = 1 and c = -1, in which case a + 3c < 0
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: c is positive.
No information about c, so there's no way to determine whether a + 3c > 0

Alternatively, we can examine some conflicting cases that satisfy statement 2 (c is positive):
Case a: a = 1 and c = 1, in which case a + 3c > 0
Case b: a = -5 and c = 1, in which case a + 3c < 0
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 a is positive
Statement 2 tells us that c is positive
If a and c are both positive, then it MUST BE THE CASE that a + 3c > 0
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer = C


Hi, how is the question rephrase from "If a, b, and c are integers, is a - b + c greater than a + b - c?" to "2a – b + c > a – b – 2c"?
Thank you.