Is p positive?

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

Is p positive?

by Vincen » Fri Sep 29, 2017 6:11 pm

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?

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Source: Beat The GMAT — Data Sufficiency | Fri Sep 29, 2017 6:11 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Thu Oct 05, 2017 9:40 pm

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Dec 12, 2017 4:25 pm

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

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