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

I reversed the inequality sign because I'm typing too fast

I've edited my response.

Cheers and thanks,
Brent

Statement One Alone:

|p – 4| = 6

We first can solve for p when (p - 4) is positive and then when it is negative.

When (p - 4) is positive:

p - 4 = 6

p = 10

When p - 4 is negative:

-(p - 4) = 6

-p + 4 = 6

-p = 2

p = -2

Since p = 10 or -2, we cannot determine whether p is positive. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

10 – p > 0

We see that 10 > p, or equivalently, p < 10. Since p is less than 10, p could be positive or negative. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using the information in statements one and two, we know that p must equal -2, since p is less than 10. Thus, p is NOT positive.

Answer: C

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