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# If ab≠0 and points (-a,b) and (-b,a) are in the same

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If ab≠0 and points (-a,b) and (-b,a) are in the same [#permalink]

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28 Aug 2005, 09:46
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If ab≠0 and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane, is point (-x,y) in the same quadrant?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-ab-0-and-a-b-and-b-a-are-in-the-same-quadrant-is-126039.html
[Reveal] Spoiler: OA
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28 Aug 2005, 10:06
yaron wrote:
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

Could you explain you result?
Thanks, Yaron

IMO C

From stem it can be concluded, a, b are both + or both -, so they are in either II or IV quad

Condition 1, x,y are both + or - , but still inconclusive,
Condition 2, also inconclusive

COmbining both x and a are both positiv or both negative so the signs of b and y should follow...
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29 Aug 2005, 14:06
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C it is

Stem says, both points are in 2nd or 4th quad

1) xy > 0 meaning both are +ve or -ve.
so consider point (-x, y).

lets say x = 2 and y = 2 then (-2,2) is in 2nd quad
says x= -2 and y = -2 then (2, -2) is in 4th,

SO 1 is Not suff..

2) no values of y is given. but it says that either a and x are both -ve or both +ve

combine 1 and 2.

a = 2 and x = 2 and y = 2 and b = 2, then all the points are in 2nd quad
if a = -2, x = -2, y = -2 and b = -2, all are in 4th quad

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29 Aug 2005, 20:14

in statement one X and Y can be anything -> insuff
in statement two there is no relation with Y -> insuff

both together it is suff - it gives a relation between a,x,y and b
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31 Aug 2005, 00:09
first from the stem it seems that points are either in II or in IV quadrant cause (-a;b) and (-b;a) are in the same quadrant, or they should have similar signs.
From stmnt 1) X and Y are either both + or both - so the point is in II or IV quadrant so 1 is suff.
From stmnt 2- gives nothing abt Y-insuff.
So A) IMO
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10 Nov 2005, 08:02
If ab is not equal to 0 and points (-a,b) and (-b, a) are in the same quadrant of the xy plane, is point (-x, y) in the same quadrant?

1) xy>0
2) ax>0

C
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10 Nov 2005, 08:19
C)...for the statement to be true...a and b must be both +ve or both -ve...

1) says x and y are both -ve or both +ve...insuff

2) a and x have the same sign...insuff

1)+2) a and x and y have the same sign...suff
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10 Nov 2005, 08:49
christoph wrote:
C)...for the statement to be true...a and b must be both +ve or both -ve...

1) says x and y are both -ve or both +ve...insuff

2) a and x have the same sign...insuff

1)+2) a and x and y have the same sign...suff

shouldnt A be sufficient.. Since x and y can be both positive or they can be both negative.

since xy >0
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10 Nov 2005, 08:57
bewakoof wrote:
christoph wrote:
C)...for the statement to be true...a and b must be both +ve or both -ve...

1) says x and y are both -ve or both +ve...insuff

2) a and x have the same sign...insuff

1)+2) a and x and y have the same sign...suff

shouldnt A be sufficient.. Since x and y can be both positive or they can be both negative.

since xy >0

x and y and a and b must have the same sign to be in the same quadrant...1) says x and y are the same sign but what are a and b...
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10 Nov 2005, 11:25
got C as well

a,-b and b,-a are in the same quard and ab != o that means

a and b both has same sign. they can be both positive or they can be both negative.

statement 1) says xy >0 that mean x and y both have the same sign. but in order for -x,y to be in the same quard as a,-b x,y needs to have the same sign as a and b. but from this statement we don't know whether x and y are both positive or negative, at the same time we don't know whether a, b are both positive or negative

statement 2) ax > 0 that nells a and x has the same sign. statement 2 alone is not sufficient because x and y need to have the same sign as well in order to be in the quard.

but if we take both the statement, we can solve the problem

So, C it is!
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10 Nov 2005, 11:27
nakib77 wrote:
got C as well

a,-b and b,-a are in the same quard and ab != o that means

a and b both has same sign. they can be both positive or they can be both negative.

statement 1) says xy >0 that mean x and y both have the same sign. but in order for -x,y to be in the same quard as a,-b x,y needs to have the same sign as a and b. but from this statement we don't know whether x and y are both positive or negative, at the same time we don't know whether a, b are both positive or negative

statement 2) ax > 0 that nells a and x has the same sign. statement 2 alone is not sufficient because x and y need to have the same sign as well in order to be in the quard.

but if we take both the statement, we can solve the problem

So, C it is!

Very good explanation. Thanks.
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11 Nov 2005, 22:10
From the question stem, (-a, b) and (-b, a) can either be in quadrant 2 and quadrant 4 with b, a > 0 and b, a < 0 respectively.

(1) Insufficient.

We have two cases: x, y > 0 and x, y < 0. This means that (-x, y) can be in either quadrand 2 and quadrand 4. However, nothing is said about a and b.

(2) Insufficient

No condition is given about y.

(1/2)
We have two cases: a, x, y > 0 and a, x, y < 0

If a, x, y > 0 then (-a, b), (-b, a) and (-x, y) are in quadrant 2

If a, x, y < 0 then (-a, b), (-b, a) and (-x, y) are in quadrant 4

Therefore, I pick C.
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20 Apr 2006, 16:35
If ab does not equal 0 and points (-a,b) and (-b,a) are in the same quadrant of the xy plane, is point (-x,y) in the same quadrant?

1) xy>0

2) ax>0
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20 Apr 2006, 16:42
IMO C.

From question - (-a,b) and (-b,a) are in the same quadrilateral.
=> a and b have the same sign.

2) tells that a and x have the same sign.

1) tell that x and y have the same sign.

2 & 1 => x, y and a have the same sign.

Hence all, a,b,x, and y have the same sign.

- Vipin
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28 May 2006, 19:18
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
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28 May 2006, 19:52
This is an question.. May be there is a simpler solution..

Pick some values and it can be seen that (-a,b) and (-b,a) can be in the same quadrant only if a & b are of the same sign..
Eg. a = 1, b =2 => (-1,2) & (-2,1) .. lie in 2nd quadrant..
a = -1, b = -2 => (1,-2) & (2,-1) ... lie in 4th quadrant.
a = -1, b = 2 => (1,2) & (-2, -1) --- don't lie in the same quadrant.
Similarly for a +ve and b -ve ... not possible.

So both a & b are both +ve or both -ve. For (-x,y) to be in the same quadrant as that of (-a,b) we need:
a). x & y need to be both +ve or both -ve.
b). x or y should have the same sign as a or b

From (1) => x*y > 0 => x & y have same sign. Still we don't know if (-a,b) and (-b,a) lie in 2nd or 4th quadrant.. INSUFF

From (2) ax > 0 => a and x have same sign. we don't know the sign of y .. INSUFF.

1) & 2)
x, y, and a are of same sign. SUFF to say that (-x,y) and (-a,b) are in same quadrant.
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15 Jun 2006, 07:32
In one of the test questions for data sufficiency the prerequisits were:

- points (a;-b) and (-a;b) are in the same quadrant of the XY-plane;
- a*b is not equal to zero

Now, can anyone explain to the stupid me, how can such a thing be possible???
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15 Jun 2006, 10:58
Is it this one?!

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
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15 Jun 2006, 11:04
helg wrote:
In one of the test questions for data sufficiency the prerequisits were:

- points (a;-b) and (-a;b) are in the same quadrant of the XY-plane;
- a*b is not equal to zero

Now, can anyone explain to the stupid me, how can such a thing be possible???

hmmmmm......

i donot think it is possible. there should be more information. are you sure that the question is complete?
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15 Jun 2006, 11:09
The question is not complete. This is one question from GMATprep. The original one is posted in my above post

Prof: Thank you for your "goodlucks", I'll try my best
15 Jun 2006, 11:09

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