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Hemavakade
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Is P positive? (1) P^3 = P (2) |P| = P 16 Sep 2015, 12:31
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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45% (medium)

Question Stats:

50% (00:51) correct 50% (00:43) wrong based on 325 sessions

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Is P positive?

(1) P^3 = P
(2) |P| = P
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E
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HieuNguyenVN
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Is P positive? (1) P^3 = P (2) |P| = P 16 Sep 2015, 19:59
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Both (1) and (2) are insufficient because P can be 0 or a positive number.
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Bunuel
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Is P positive? (1) P^3 = P (2) |P| = P 20 Nov 2017, 01:42
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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.

Answer: E.
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Is P positive? (1) P^3 = P (2) |P| = P 20 Nov 2017, 01:44
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Hemavakade
Is P positive?

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

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

S2) |P| = P
=> P ≥ 0
Insufficient.

Quote:
Combining both statements
Show more
This gives us no new information
Insufficient.

E is the answer.
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Is P positive? (1) P^3 = P (2) |P| = P 20 Nov 2017, 01:46
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akshayk
Hemavakade
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.

E is the answer.
Show more

The highlighted part is not correct.

P^3 = P gives 3 values: P = 0, P = 1, or P = -1.
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Is P positive? (1) P^3 = P (2) |P| = P 20 Nov 2017, 01:48
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Bunuel
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Hemavakade
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.

E is the answer.

The highlighted part is not correct.

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

Thanks mate. Yes, I changed it. Posted that solution by mistake.
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Is P positive? (1) P^3 = P (2) |P| = P Updated on: 19 Jul 2025, 08:49
Originally posted by nikhilm14 on 19 Jul 2025, 08:47.
Last edited by nikhilm14 on 19 Jul 2025, 08:49, edited 1 time in total.
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When you combine the statements, how can you say that P can be any positive number? that would contradict the statement 1 where P is either 1,0 or -1. If P can be a positive number (except 1) P ^3 cannot be equal to P. The only value of P that satisfies both is that P=1 right?
Bunuel
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.

Answer: E.
Show more
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Is P positive? (1) P^3 = P (2) |P| = P 19 Jul 2025, 10:46
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nikhilm14
When you combine the statements, how can you say that P can be any positive number? that would contradict the statement 1 where P is either 1,0 or -1. If P can be a positive number (except 1) P ^3 cannot be equal to P. The only value of P that satisfies both is that P=1 right?
Bunuel
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.

Answer: E.
Show more


Where does the solution you quoted claim that P can be any positive number? It clearly says P can be 1 or 0.
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Is P positive? (1) P^3 = P (2) |P| = P 20 Jul 2025, 08:00
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Bunuel
nikhilm14
When you combine the statements, how can you say that P can be any positive number? that would contradict the statement 1 where P is either 1,0 or -1. If P can be a positive number (except 1) P ^3 cannot be equal to P. The only value of P that satisfies both is that P=1 right?
Bunuel
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.

Answer: E.


Where does the solution you quoted claim that P can be any positive number? It clearly says P can be 1 or 0.
Show more
i meant after you combined the statements, you mentioned p still can be positive...as i have highlighted
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Is P positive? (1) P^3 = P (2) |P| = P 20 Jul 2025, 09:03
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nikhilm14


Where does the solution you quoted claim that P can be any positive number? It clearly says P can be 1 or 0.
Show more
i meant after you combined the statements, you mentioned p still can be positive...as i have highlighted[/quote]

P can be positive number, 1.
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Is P positive? (1) P^3 = P (2) |P| = P 23 Jul 2025, 04:34
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Hemavakade
Is P positive?

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


P>0????

1. p^3=P IMPLIES P>=0. ---Insufficient.
2. |P| = P .. p can be positive or negative ---Insufficient.

Combining the two --- p>=0, p can be positive or zero .. Answer is still Maybe. Hence, E will be the answer
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