Is P positive? (1) P^3 = P (2) |P| = P

Question

Is P positive?

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

HieuNguyenVN · Answer

Both (1) and (2) are insufficient because P can be 0 or a positive number.

Bunuel · Answer

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.

akshayk · Answer

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

S2) |P| = P
=> P ≥ 0
Insufficient.

This gives us no new information
Insufficient.

E is the answer.

Bunuel · Answer

The highlighted part is not correct.

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

akshayk · Answer

Thanks mate. Yes, I changed it. Posted that solution by mistake.

nikhilm14 · Answer

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 · Answer

Where does the solution you quoted claim that P can be any positive number? It clearly says P can be 1 or 0.

nikhilm14 · Answer

i meant after you combined the statements, you mentioned p still can be positive...as i have highlighted

Bunuel · Answer

i meant after you combined the statements, you mentioned p still can be positive...as i have highlighted

P can be positive number, 1.

Rahilgaur · Answer

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

Is P positive? (1) P^3 = P (2) |P| = P

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