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Are points (–p, q) and (–q, p) in the same quadrant? (I) pq > 0 (II) p

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Are points (–p, q) and (–q, p) in the same quadrant? (I) pq > 0 (II) p  [#permalink]

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New post 31 May 2020, 10:42
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Are points \((–p, q)\) and \((–q, p)\) in the same quadrant?

(I) \(pq > 0\)

(II) \(p^2 q^2 > 0\)
Kellogg School Moderator
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Re: Are points (–p, q) and (–q, p) in the same quadrant? (I) pq > 0 (II) p  [#permalink]

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New post 31 May 2020, 15:28
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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
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Re: Are points (–p, q) and (–q, p) in the same quadrant? (I) pq > 0 (II) p  [#permalink]

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New post 31 May 2020, 20:50
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Top Contributor
sjuniv32 wrote:
Are points \((–p, q)\) and \((–q, p)\) in the same quadrant?

(I) \(pq > 0\)

(II) \(p^2 q^2 > 0\)


we need signs of numbers to determine coordinates

I (i)both p & q are positive

both coordinates indicates negative x axis and positive y axis which is quad II

(ii)both p & q are negative

both coordinates indicates positive x axis and negative y axis which is quad IV

in both cases yes both are in same quadrant

A is sufficient

II square of any integer is always positive so that gives no additional information

not sufficient
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Re: Are points (–p, q) and (–q, p) in the same quadrant? (I) pq > 0 (II) p  [#permalink]

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New post 31 May 2020, 23:01
3
sjuniv32 wrote:
Are points \((–p, q)\) and \((–q, p)\) in the same quadrant?

(I) \(pq > 0\)

(II) \(p^2 q^2 > 0\)


Being in same quadrant means that the x coordinates of both points and y-coordinates of both points have same sign.

So -p and -q should have same sign. (x-coordinates)
Also q and p should have same sign. (y-coordinates)

Both the above basically says that both p and q should have same sign.

(I) \(pq > 0\)
This means p and q have same sign.
Suff

(II) \(p^2 q^2 > 0\)
\((pq)^2>0\)...So both pq<0 and pq>0 are possible.
Insuff

A
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Re: Are points (–p, q) and (–q, p) in the same quadrant? (I) pq > 0 (II) p   [#permalink] 31 May 2020, 23:01

Are points (–p, q) and (–q, p) in the same quadrant? (I) pq > 0 (II) p

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