Is pq 0? (1) (2q)^p = 1 (2) p

Question

Is  pq > 0 ?

(1)  (2q)^p = 1

(2)  p < 0

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IanStewart · Answer

If p = -2, say, then q can be either 1/2 or -1/2, and pq can be positive or negative, so the answer is E.

exc4libur · Answer

(1)  (2q)^p = 1   insufic

2q^p=1…2q=1,q=1/2…p=any
ie. q=0.5…p=0…pq=0…ans=no
ie. q=0.5…p=1…pq=0.5…ans=yes

(2)  p < 0   insufic

(1&2)    insufic

p<0≠0: q=0.5…p=-2…2(0.5)^(-2)=1…pq=-1
p<0≠0: q=-0.5…p=-2…2(-0.5)^(-2)=(-1)^2=1/(-1)^2=1…pq=1

Ans (E)

LeoN88 · Answer

Let's start with easy- #2. p is <0 but q can be anything /= zero. Insufficient #1. p can be 0 and at the same time p can be 1 so Insufficient. 1+2. p has to be a -ve value say -1,-2,-1.5 etc. Inside the braces q can be +ve as well as -ve. Put q= 1/2 and (-1/2) to check. So overall #1+2 is also Insufficient. E

HoneyLemon · Answer

1) (2q)^p=1
 P could be 0 ---- pq =0 OR q could be 0.5 and p can be anything . so Insufficient..

(2) p<0 ... q can be 0.5 or -0.5 .. accordingly value can change .. So insufficient

Combining (1&2)

p<0≠0: q=0.5…p=-2…2(0.5)^(-2)=1…pq=-1
p<0≠0: q=-0.5…p=-2…2(-0.5)^(-2)=(-1)^2=1/(-1)^2=1…pq=1

still insufficient
Hence 
Ans  (E)

chetan2u · Answer

pq>0 basically means both p and q have same sign.

(1)  (2q)^p = 1 
If p=0, q could be anything...so pq=0,  that is answer is NO 
If  p=1 , and  q=\frac{1}{2} ..... pq=2*\frac{1}{2}=1>0 ,  that is answer is YES 
Insuff

(2)  p < 0 
Nothing about q
Insuff

Combined
If  p=-1,  and  q=\frac{1}{2}....(2*\frac{1}{2})^{-1}=1 and p*q=-1*\frac{1}{2}=-\frac{1}{2} ....... answer is NO 
If  p=-2 , and  q=-\frac{1}{2}....(2*-\frac{1}{2})^{-2}=(-1)^{-2}=\frac{1}{(-1)^2}=1  and  pq=-2*-\frac{1}{2}=1>0 ... answer is Yes 
Insuff

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Is pq > 0? (1) (2q)^p = 1 (2) p < 0

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