Is p positive?

Question

Is p positive?

(1) |p – 4| = 6 
(2) 10 – p > 0

giobas · Answer

from 1) p = 10 or p = -2 insufficient
statement 2 is insufficient. as p can be both positive or negative
 
if we combine we will have that p = -2 as, p cannot be 10 as 10-10 is not more than 0

answer is C

BrentGMATPrepNow · Answer

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

enantiodromia · Answer

Hi Brent why have you reversed the inequality sign after adding p to both sides in statement 2?

Sent from my iPhone

BrentGMATPrepNow · Answer

I reversed the inequality sign because I'm typing too fast :-)

I've edited my response. Cheers and thanks, Brent

ScottTargetTestPrep · Answer

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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Is p positive?

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Is p positive?

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