But b can be either a positive number or a negative number. which leaves us with -a.b and (-b,a) can be in the first or the second quadrant. If x and y are positive, then (-x,y) will be in the 2nd quadrant. If x and y are negative, coordinates would be in the 4th quadrant. So to me, with both statements we can say for sure that the three coordinates are in the same quadrant.

Please let me know if I am missing something.

if b is negative then first point would lie in IIIrd quadrant and second point would lie in Ist quadrant (ofcourse assuming that a is positive). This would not satisfy stmt. I

Hi Rahul

if ab does not equal 0, and (-a.b) and (-b,a) are in the same quadrant, is (-x,y) in this quadrant?

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


Your earlier response:

"Combining (1) and (2), we get to know that x, y and a are all positive or all negative that x, y and a have the same sign"

I have QQ the above statement doesnt give any infernece abour B . To determin ( - x and y) lie in same co-ordinate, wht is there no dependency on "b" . How can we conclude with out considering b variable .?

Please throw some light on this one. Thanks!!

HI:
This is the thought process I followed to reach my conclusion:

1. (-a,b) and (-b, a) are in same qudrant as well as ab >0. taking a=2 and b=3 and placing different signs (4 combinations), I got to conclusion that either both are positive or both are negative (meaning that the point -a,b / -b,a is either in quadrant 2 or 4 (repalcing above no's ==> (-2, 3) /(-3, 2) _or_ (-(-2), -3) / (-(-3), -2)

2. STATEMENT #1 - xy >0
means that both are positive or negative (non-zero) - lets take (5,6) and (-5, -6). However this doesn't tell me much becasue (-x,y) = (-5, 6) or (5, -6) may be in opposite quadrant than where a and b are depending on their sign

3. STATEMENT #2 - ax >0
means that both a and x are same sign. given that a and b are also same sign - this means that -x,y may or may not fall in the same quardrant depending on y's sign which we don;t know from this statement alone

4. STATEMENT #1 and #2
means that y is also same sign as a, so all are of same sign and hence -a, b is in same quardrant as -b, a whcih is in same quardrant as -x,y

Rahul@gurome wrote:(1) xy > 0 implies that either both x and y should be positive or both should be negative. So, this is NOT SUFFICIENT to determine whether (-x,y) is in the same quadrant.

(2) ax > 0 implies that either a and x should be positive or both should be negative. But there is no info on y. So, (2) is NOT SUFFICIENT.

Combining (1) and (2), we get to know that x, y and a are all positive or all negative that x, y and a have the same sign.

[spoiler]The correct answer is (C).[/spoiler]

I liked Rahul's explanation but I also tried it a little differently.

Know: (-a, b) and (-b,a) are in the same quadrant

Want: is xy in this quadrant?

Visually setting up a coordinate plane here was helpful as I thought through this.

(1) xy > 0 - this means that x and y either have to be both positive or negative. If we assume that both (-a,b) and (-b,a) are in the upper right quadrant of the coordinate plane (however they could in any one), then those two coordinates are in a place where x>0 and y>0. So if x and y are both positive numbers then xy would be in this quadrant, but if x and y are both negative they would not be, since there are two possibilities (1) is INSUFF,.

(2) ax>0 - thing as statement (1), and we are not given any info about y. Clearly INSUFF

(1) + (2) - Since both -a and a are in the same quadrant (from stem), when you multiply it by either -x or x in accordance with statement (2) it will be in the same quadrant. since ax>0, they have the same signs, since xy>0 that means that they have the same signs, this by extention means that ay>0 and since a and -a are in the same quadrant this means that y or -y will work. Therefore both combinations of x and y should work too, SUFF.

The correct answer is C

Rahul could you comment on my logic here if it is possible to follow it?

Hi Jerks87:

Re your post "Want: is xy in this quadrant? "

Isn't actual want "Want: is -x,y in this quadrant? "

Also given that ab > 0, a,b would never be in upper right quadrant and hence testing x,y against that location is incorrect - do you agree?

C winner here.

According to the problem statement:
and b must be of same sign(as the points have to be in the same quadrant.(Try with actual nos)

(-x,y)

Statement 1:
xy >0 implies x and y are of same signs but no clear info about the quadrants. It can Quadrant 2 or Quadrant 4(test with values. So INSUFFICIENT

Statement 2:
ax > 0 implies and x are of same signs but no info about y. So INSUFFICIENT

Combining (1) and (2)
a,x, y have same signs. So SUFFICIENT

1. Given (-a,b) and (-b,a) are in the same quadrant. This means "a" and "b" have the same signs.(+,-)

1) xy > 0
Means x and y have the same signs. Good. But this does not tell us if the values are in the same quadrant as (-a,b) and (-b,a). Insufficient.

So we need something that links x and y to a and b.Come,Stmt 2
2) ax > 0
Means "a" and "x" have the same signs. The link we are looking for is found, but the statement in itself is insufficient.

Statements 1) + 2) says, a,x and y have the same signs.
Hence C.

Rahul@gurome wrote:(1) xy > 0 implies that either both x and y should be positive or both should be negative. So, this is NOT SUFFICIENT to determine whether (-x,y) is in the same quadrant.

(2) ax > 0 implies that either a and x should be positive or both should be negative. But there is no info on y. So, (2) is NOT SUFFICIENT.

Combining (1) and (2), we get to know that x, y and a are all positive or all negative that x, y and a have the same sign.

[spoiler]The correct answer is (C).[/spoiler]

Yes but, knowing that a and x are of same sign guarantees that they are in the same quadrant, only which quadrant is not clear. If thought from this perspective (B) should be the answer.

Sorry i just ignored y.

S1 x and y are of same sign. Not Sufficient
S2 a and x are of same sign, y sign not clear
Comb: a,x and y are of same sign. Sufficient.
(C)

C !