If P & Q are integers such that |P|Q=4|P|Q=4 , is P negative? (1) |P|+

Question

If P & Q are integers such that  |P|^Q=4 , is P negative?

(1)  |P|+|Q|=|P+Q| 
(2)  P^2−5|P|+4=0

Bunuel · Answer

If P & Q are integers such that  |P|^Q=4 , is P negative?

|P|^Q=4 :

a. p = 4 and q = 1
b.  p = -4  and q = 1
c. p = 2 and q = 2
d.  p = -2  and q = 2

(1)  |P|+|Q|=|P+Q| . This is true only for cases a and c, where p is positive. Not sufficient.

(2)  P^2−5|P|+4=0 . All for possible values of p satisfy this equation. Not sufficient.

Answer: A.

rt9 · Answer

from 1) P, Q have same sign. so P must be positive
from 2) P can be positive or negative, since no restriction on sign of Q exists.

Answer is A

amanvermagmat · Answer

Considering that both P & Q are integers, lets see how can 4 be written as (base)^exponent
4 = 2^2 Or (-2)^2 Or 4^1 Or (-4)^1

So we have cases:
P = 2, Q = 2
P = -2, Q = 2 (in both these cases, |P|=2)
P = 4, Q = 1
P = -4, Q = 1 (in both these cases, |P|=4)

as we can see, P can be both positive and negative, but Q can only be positive

Statement 1. |P| + |Q| = |P+Q|
If P is negative and Q is positive, then above statement  cannot be true 
But if P and Q are both positive, then above statement  is definitely true 
 
So we get that P is positive, thus it answers NO to the question asked.  Sufficient

Statement 2. P^2 - 5|P| + 4 = 0
Note that P^2 can also be written as |P|^2

So we have |P|^2 - 5|P| + 4 = 0
Factorise this quadratic equation to get
(|P| - 1)(|P| - 4) = 0
So |P| = 1 OR |P| = 4

Now |P| = 1 is not possible if |P|^Q = 4
But for |P| = 4, we have |P| =4, Q = 1 so that 4^1 = 4

But still here we can have P = 4 or P = -4
Cant say whether P is positive or negative.  Insufficient

Hence answer is  A

matt882 · Answer

In DS the question is the third condition - read it carefully.
Since P and Q are integer, Q, in the equation |P|^Q=4, must be always positive.

1 - True only if either P+ and Q+ or P- and Q-. As per question stem Q always positive. A is sufficient. 
2 - (|P|-4)(|P|-1)=0 - clearly not suff

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If P & Q are integers such that |P|Q=4|P|Q=4 , is P negative? (1) |P|+

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If P & Q are integers such that |P|Q=4|P|Q=4 , is P negative? (1) |P|+

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards