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# Is P positive?

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Intern
Joined: 19 Dec 2014
Posts: 35

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16 Sep 2015, 12:31
1
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Difficulty:

55% (hard)

Question Stats:

51% (00:50) correct 49% (00:44) wrong based on 192 sessions

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Is P positive?

(1) P^3 = P
(2) |P| = P
Intern
Joined: 21 Nov 2014
Posts: 31
Location: Viet Nam
GMAT 1: 760 Q50 V44

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16 Sep 2015, 19:59
2
Both (1) and (2) are insufficient because P can be 0 or a positive number.
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Math Expert
Joined: 02 Sep 2009
Posts: 50009

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20 Nov 2017, 01:42
Is P positive?

(1) P^3 = P
P^3 - P = 0
P(P^2 - 1) =0
P(P - 1)(P + 1) = 0
P = 0, P = 1, or P = -1. Not sufficient.

(2) |P| = P. This implies that P is 0 or any positive number. Not sufficient.

(1)+(2) P still can be positive, 1, or 0. Not sufficient.

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Joined: 06 Jul 2016
Posts: 382
Location: Singapore
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20 Nov 2017, 01:44
Is P positive?

(1) P^3 = P
(2) |P| = P

S1) $$P^3$$ = P
=> P($$P^2$$ - 1) = 0
=> P = -1,0,1
Insufficient.

S2) |P| = P
=> P ≥ 0
Insufficient.

Quote:
Combining both statements

This gives us no new information
Insufficient.

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Math Expert
Joined: 02 Sep 2009
Posts: 50009

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20 Nov 2017, 01:46
akshayk wrote:
Is P positive?

(1) P^3 = P
(2) |P| = P

S1) $$P^3$$ = P
=>P ≥ 0
Insufficient.

S2) |P| = P
=> P ≥ 0
Insufficient.

Quote:
Combining both statements

This gives us no new information
Insufficient.

The highlighted part is not correct.

P^3 = P gives 3 values: P = 0, P = 1, or P = -1.
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Joined: 06 Jul 2016
Posts: 382
Location: Singapore
Concentration: Strategy, Finance

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20 Nov 2017, 01:48
Bunuel wrote:
akshayk wrote:
Is P positive?

(1) P^3 = P
(2) |P| = P

S1) $$P^3$$ = P
=>P ≥ 0
Insufficient.

S2) |P| = P
=> P ≥ 0
Insufficient.

Quote:
Combining both statements

This gives us no new information
Insufficient.

The highlighted part is not correct.

P^3 = P gives 3 values: P = 0, P = 1, or P = -1.

Thanks mate. Yes, I changed it. Posted that solution by mistake.
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Re: Is P positive? &nbs [#permalink] 20 Nov 2017, 01:48
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