points (-a,b) and (-b,a) are in the same quadrant of the xy-plane a and b are of same sign
if (-x,y) is also in the same quadrant with (-a,b) and (-b,a),x and y has to be of same sign as a and b

From 1
xy>0..so x and y are of same sign.but no information whether x,y are of same sign as a and b...not sufficient

From2
ax>0..a and x are of same sign..no information about sign of y...not sufficient

combining
all of a,x,y and b are of same sign....sufficient
Ans option C

Let us assume (a,b) = (1,2) where a>0, b>0

so as per the stem : (-a,b) = (-1,2) & (-b,a) = (-2,1). Both these points are in second quadrant.

St1 : xy > 0

case 1: x<0, y<0

Third quadrant

case 2:

x>0, y>0

First quadrant

Inconsistent/. So Insufficient

St 2: ax > 0

we have a>0 , so x>0. But we dont have any idea about y. Insufficient.

Combining we will have, from st2 that x>0,

Recall case 2 of St 1:

when X>0 , then Y has to be >0

so xy>0 where X>0 & Y>0

.Having said that, (-X,Y) will also reside in secon quadrant as that of (-a,b) or (-b,a).

Pick C

This question is a bit challenging because it disguises itself as a geometry question when it's really a number properties question.

Two points can be in the same quadrant only if the x coordinates have the same sign and the y coordinates have the same sign. So this question is asking: Is (-x) of the same sign as (-a) and (-b)? Also is y of the same sign as a and b?

For (-x) to have the same sign as (-a) and (-b), x, a and b must have the same sign. Essentially we're asked whether all variables have the same sign.

The correct answer is C.

To better understand, have a look at the video solution. This is GMATPrep question 1043

-Patrick

Thank you all. The OA indeed is C.

I'm new to this forum and having trouble using the spoiler feature while posting. Could you help?

Step 1: I start composing a post
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yankee.musk,

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