What is the value of p ? (1) |p |p|| = 3 (2) 2|p| = 3

Question

What is the value of p ?

(1) |p – |p|| = 3 
(2) 2|p| = 3

M36-96

Chethan92 · Answer

From statement 1:

|p-|p|| = 3
or p-|p| = +3 or -3
p-3 = |p| or p+3 = |p|
Solving gives p = 3/2 or -3/2
Insufficient.

From statement 2:

2|p| = 3
|p| = 3/2
or p = 3/2 or -3/2
Insufficient.

Combining both also gives the same result.

E is the answer.

DavidTutorexamPAL · Answer

We'll use a basic property of absolute value to help us solve.
This is a Precise approach.

Recall that |a| = x implies a = x or a = -x.
Then:

(1) |p - |p|| = 3 implies p - |p| = 3 so |p| = p - 3 or p - |p| = -3 in which case |p| = p+3.
We'll simplify again: p = p-3 is impossible and p = -p + 3 give p = 1.5. But - if p = 1.5 then p - 3 = -1.5 so |p| is negative, which is also impossible!
Looking at the other equation, p=p+3 is impossilbe and p = -p-3 gives p = -1.5. This time |p| = p+3=1.5, which is positive, as required. Then p = -1.5
Sufficient.

(2) |p| = 1.5 simplifies directly to p = 1.5 or p = -1.5
Insufficient.

(A) is our answer.

Ypsychotic · Answer

(1)Another way to look at it is that |X-Y| means the distance between point (X,0) and point (Y,0) on the x-axis. So, |p-|P||=3 means distance between point p and point |p| is 3, which is only possible if p is negative, for example, the distance between -2 and |-2| is 4 but the distance between 2 and |2| is zero. So, as the distance between p & |p| is 3. p=-3/2 or -1.5 for the distance between p and origin will be half of that between p & |p| and p is established as negative. so, p=-1.5.

Hence, 1 is sufficient.

(2) 2|p|=3 or |p|=3/2, implies p=+3/2 or -3/2.

2 is Insufficient.

Answer A, 1 is sufficient.

kylebecker9 · Answer

From statement 1 p must be negative. You can try plugging back in your answers to see that if p = 3/2 then the left-hand side will be 0 and not 3. -3/2 is the only solution and thus statement 1 is sufficient.

Chethan92 · Answer

Agree

. Made a silly mistake

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

Kinshook · Answer

What is the value of p ?

(1) |p – |p|| = 3 
If p>0; p-|p| =0
If p<0; p-|p| = 2p
p = - 3/2
SUFFICIENT

(2) 2|p| = 3
p = 3/2 or -3/2
NOT SUFFICIENT

IMO A

nehasomani33 · Answer

thinkvision  - any better way to solve this puzzle?

exc4libur · Answer

(2) 2|p| = 3: |p|=1.5… p=(1.5,-1.5); insufic.

(1) |p – |p|| = 3: sufic.

p≥0: |p-|p||=3…|p-(p)|=3…|0|=3=invalid;
p<0: |p-|p||=3…|p-(-p)|=3…|p+p|=3…|2p|=3…(p<0)…(-2p)=3…p=-1.5;

Answer (A)

Peddi · Answer

Bro , in st1 for p-|p| to be +3 , p>|p| that is never possible, so the only case possible acc to given st is p<|p| ,so st1 is sufficient

Posted from my mobile device

Bunuel · Answer

Official Solution:

What is the value of  p  ? 
 
(1)  |p – |p|| = 3 :
 
When  p \geq 0 , then  |p|=p , so in this case we'd have  |p – p| = 3 , which gives  0=3 . This is obviously incorrect. So,  p  cannot be 0 or positive. 
 
So,  p < 0 . In this case,  |p|=-p , so in this case we'd have  |p + p| = 3 , which gives  |2p|=3 . This gives  p=-\frac{3}{2}  ( p=\frac{3}{2}  is not possible because we know that  p  is negative). Sufficient.. 
 
(2)  2|p| = 3 :
 
 |p|=\frac{3}{2} ;
 
 p=\frac{3}{2}  or  p=-\frac{3}{2} . Not sufficient.

Answer: A

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What is the value of p ? (1) |p |p|| = 3 (2) 2|p| = 3

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