hideyoshi wrote:

Is \(m\) positive?

1) \(m^3 = m\)

2) \(|m| = m\)

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 positivecase b: m = -1, in which case

m is NOT positivecase c: m = 1, in which case

m IS positiveSince we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |m| = mWhen solving equations involving ABSOLUTE VALUE, there are 3 steps:

1. Apply the rule that says:

If |x| = k, then x = k and/or x = -k2. 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 positiveSince 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 positiveIf m = 1, then

m IS positiveSince we cannot answer the

target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,

Brent

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