sjuniv32 wrote:
Are points \((–p, q)\) and \((–q, p)\) in the same quadrant?
(I) \(pq > 0\)
(II) \(p^2 q^2 > 0\)
let A be (-p, q) and B be (-q, p)
Question: are A and B in same quadrant?
Statement 1: pq>0
implies,
p>0, q>0 or
p<0, q<0
now, take p=2, q=3 for both p,q>0
A = (-2, 3) Second Quadrant
B= (-3, 2) Second Quadrant
again, take p=-2, q=-3 for both p,q<0
A= (2, -3) Fourth Quadrant
B= (3, -2) Fourth Quadrant
therefore, statement 1 is sufficient
Statement 2: \(p^2q^2 >0\)
it implies
(pq)^2 >0
anything be it + or - , if raised to even power will always be positive
therefore, pq>0 or pq<0
if pq>0 , we have sufficient info as shown in statement 1
lets check for pq<0
it implies
p>0, q<0
or
p<0, q>0
lets take p=2, q= -3
A= (-2, -3) Third Quadrant
B= (3, 2) First Quadrant
So, when pq<0 we have A and B in different quadrant or not in same quadrant
and for pq>0 we have A and B in same quadrant
Therefore, (pq)^2 >0 is insufficient
Statement 2 is insufficient
Answer: A