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Math Expert V
Joined: 02 Sep 2009
Posts: 59229
What is the value of p ? (1) |p – |p|| = 3 (2) 2|p| = 3  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 56% (01:28) correct 44% (01:35) wrong based on 210 sessions

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What is the value of p ?

(1) |p – |p|| = 3
(2) 2|p| = 3

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NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1018
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: What is the value of p ? (1) |p – |p|| = 3 (2) 2|p| = 3  [#permalink]

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1
1
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.

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examPAL Representative P
Joined: 07 Dec 2017
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What is the value of p ? (1) |p – |p|| = 3 (2) 2|p| = 3  [#permalink]

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3
1
Bunuel wrote:
What is the value of p ?

(1) |p – |p|| = 3
(2) 2|p| = 3

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.

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Re: What is the value of p ? (1) |p – |p|| = 3 (2) 2|p| = 3  [#permalink]

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2
Bunuel wrote:
What is the value of p?

(1) |p – |p|| = 3
(2) 2|p| = 3

(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.

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Re: What is the value of p ? (1) |p – |p|| = 3 (2) 2|p| = 3  [#permalink]

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1
Afc0892 wrote:
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.

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.
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Re: What is the value of p ? (1) |p – |p|| = 3 (2) 2|p| = 3  [#permalink]

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kylebecker9 wrote:
Afc0892 wrote:
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.

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.

Agree . Made a silly mistake
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Math Expert V
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Re: What is the value of p ? (1) |p – |p|| = 3 (2) 2|p| = 3  [#permalink]

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Bunuel wrote:
What is the value of p ?

(1) |p – |p|| = 3
(2) 2|p| = 3

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What is the value of p ? (1) |p – |p|| = 3 (2) 2|p| = 3  [#permalink]

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Bunuel wrote:
What is the value of p ?

(1) |p – |p|| = 3
(2) 2|p| = 3

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
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Originally posted by Kinshook on 08 Oct 2019, 05:23.
Last edited by Kinshook on 08 Oct 2019, 06:28, edited 1 time in total.
Intern  B
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Re: What is the value of p ? (1) |p – |p|| = 3 (2) 2|p| = 3  [#permalink]

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thinkvision - any better way to solve this puzzle?
Director  P
Joined: 24 Nov 2016
Posts: 824
Location: United States
Re: What is the value of p ? (1) |p – |p|| = 3 (2) 2|p| = 3  [#permalink]

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Bunuel wrote:
What is the value of p ?

(1) |p – |p|| = 3
(2) 2|p| = 3

(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;

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Re: What is the value of p ? (1) |p – |p|| = 3 (2) 2|p| = 3  [#permalink]

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Chethan92 wrote:
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.

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 Re: What is the value of p ? (1) |p – |p|| = 3 (2) 2|p| = 3   [#permalink] 08 Nov 2019, 09:14
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