Coordinate Geometry question

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Spartacus2000: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Sun May 01, 2011 2:31 pm

by Spartacus2000 » Fri Jun 17, 2011 4:36 am

If ab != 0 and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane, is point (-x,y) in this same quadrant?

(1) xy > 0
(2) ax > 0

What is the best way to tackle this?

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Source: Beat The GMAT — Data Sufficiency | Fri Jun 17, 2011 4:36 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Fri Jun 17, 2011 5:23 am

Hi,
(-a,b) and(-b,a) are in the same quadrant. So, a and b must be of the same sign. So, these points can both be in Q2 in a,b > 0
or Q4 if a,b < 0
From(1): xy>0
So, x and y are of same sign.
So,(-x,y) will be in Q2 in x,y > 0
or Q4 if x,y < 0
Not sufficient
From(2): ax>0
So, either both a,x >0 or both a,x <0
No info. about y
Not sufficient

Both (1)&(2):
a,b,x,y should be of the same sign.
Then (-x,y) will be in the same quadrant as (-a,b) (-b,a) are.
Sufficient

Hence, C

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by Anurag@Gurome » Fri Jun 17, 2011 5:32 am

Rahul has provided a very elaborate discussion on this one here : https://www.beatthegmat.com/quadrant-pro ... tml#310294

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Fri Jun 17, 2011 6:41 am

for (x,y) positive quadrant is 2nd
for (x,y) negative quadrant is 4th

x,y cannot be one positive and one negative. hence 3rd and 1st quadrant not considered.

1 x,y both positive then same quadrant.
x,y where x>0 and y<0 quadrant changes. Not sufficient.

2. same as above. not sufficient.

1+2 a,b and x,y are of same signs. thus they will be either in quadrant 2nd or 4th.

sufficient.
hence C.

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