Vincen wrote:Is p positive?

(1) |p - 4| = 6
(2) 10 - p > 0

The OA is C.

I know that each statement alone is not sufficient but how can I use them together?

From Statement 1, we get p = 10 or -6. Can't decide.

From Statement 2, we get 10 > p. We find that p can be positive, 0, or even negative. Can't decide.

From Statement 1 & 2, we get p = -6 (the only qualifying value). Thus, the answer is NO. Sufficient.

The correct answer: C

Hope this helps!

-Jay

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Vincen wrote:Is p positive?

(1) |p - 4| = 6
(2) 10 - p > 0

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