Is p positive?

Target question: Is p positive?

Statement 1: |p – 4| = 6
There are 3 steps to solving equations involving ABSOLUTE VALUE:
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 step 1, EITHER p – 4 = 6 OR p – 4 = -6, which means p = 10 or p = -2. When we test each solution, they both work.
case a: If p = 10, then p IS positive
case b: If p = -2, then p is NOT positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 10 – p > 0
Add p to both sides to get: 10 > p
There are MANY possible values of p.
For example, p COULD equal 5, in which case p IS positive
Or, p could equal -5, in which case p 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 EITHER p = 10 OR p = -2
Statement 2 tells us that p is less than 10, which rules out the possibility that p = 10, which means p must equal -2
If p = -2, then p is definitely NOT positive
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent