Is m positive?

Target question: Is m positive?

Statement 1: m³ = m
Subtract m from both sides to get: m³ - m = 0
Factor: m(m² - 1) = 0
Factor more: (m)(m + 1)(m - 1) = 0
This means m = 0, or m + 1 = 0, or m - 1 = 0

So, there are three possible cases:
case a: m = 0, in which case m is NOT positive
case b: m = -1, in which case m is NOT positive
case c: m = 1, in which case m IS positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |m| = m
When solving equations involving ABSOLUTE VALUE, there are 3 steps:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

So, applying the above rule, we have two equations to solve: m = m, and m = -m
If m = m, then m can equal ANY number, as long as m is POSITIVE. So, m can be ANY positive number.
If m = -m, then m = 0, which means m is NOT positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that m can equal 0, -1, or 1
Statement 2 tells us that m can equal any positive number, or m can equal 0
When we combine the statements, we can see that m can equal 0 or 1.
If m = 0, then m is NOT positive
If m = 1, then m IS positive
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent