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E because even though you can tell that the point is within a line, there is no way of telling where the point is exactly; ant he line itself is not on either side of the points, it is directly in the middle and equidistant from both points. therefore it is impossible to tell how far it would be to either other point.

Act maybe A, because if A is on y=x then A must be equidistant from both points, which does answer the question in an outside the box way, someone else please put in your input.

I say C because if x=y and -x=y, only possible point is the origin. Therefore, they're both equal distance from the origin and sufficient to answer the question.

stm1. point A lies on the line y=x Solution is 0,0/1,1 / 2,2 / 3,3 / ....................... -1,-1/ -2,-2 either both X&Y are positive with same value / X&Y are negative with same value. distance between A(X,Y) and point (1,2) = A(X,Y)and point (2,1). Sufficient stm1. point A lies on the line y=-x Solution is 0,0 / 1,-1 / 2,-2 .................... -1,1 / -2,2

Taking A(0,0) distance between A and both the given points is \sqrt{5} - equidistant taking A(-1,1) distance between A & (1,2) = \sqrt{5} Distance between A & (2,1)= 3 Not equidistant. Insufficient.

For (2): point A is on the red line. Now, if point A is in the II quadrant then it will be closer to point (1, 2) than to point (2, 1), so answer wold be YES BUT if point A is in the IV quadrant (or at the origin) then it won't be closer to point (1, 2) than to point (2, 1), so answer wold be NO. Two different answers. Not sufficient.
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You can see that no matter where on blue line point A is, it will always be equidistant from the given points. So statement (1) is sufficient.

But if A is on the red line we can not say whether it's closer to point (1, 2) than to point (2, 1). Not sufficient.

Answer: A.

Nice Explanantion...I got my approach right by drawing the diagram..Since y=x was equidistant from the given points, therefore got down to ans options A & D...though i missed drawing the y=-x line in the 2nd Quadrant, thus thought the ans to be D....that opened my eyes!! :D

A line is a collection of points joined together.So how can you guys be so sure about the exact location of point A.It can be anywhere on the line x=y and x=-y.In both cases,the distance will vary accordingly.

But if we combine the two fact statements,we can only get one value A(0,0) and thus we can have a unique solution that point (1,2) is closer than point (2,1).

A line is a collection of points joined together.So how can you guys be so sure about the exact location of point A.It can be anywhere on the line x=y and x=-y.In both cases,the distance will vary accordingly.

But if we combine the two fact statements,we can only get one value A(0,0) and thus we can have a unique solution that point (1,2) is closer than point (2,1).

Hence the correct answer should be C.

OA for this question is A, not C.

We are not told to determine the exact location of point A. The question asks: is point A closer to point (1,2) than to point (2,1)? This is YES/NO data sufficiency question: In a Yes/No Data Sufficiency question, each statement is sufficient if the answer is “always yes” or “always no” while a statement is insufficient if the answer is "sometimes yes" and "sometimes no".

For (1): no matter where exactly on \(y=x\) (blue line) point A is, it will always be equidistant from the given points. So the answer to the question "is point A closer to point (1,2) than to point (2,1)?" is always NO. So statement (1) is sufficient.

For (2): if point A is in the II quadrant on line \(y=-z\) then it will be closer to point (1, 2) than to point (2, 1), so answer would be YES BUT if point A is in the IV quadrant on line [m]y=-z[/m (or at the origin) then it won't be closer to point (1, 2) than to point (2, 1), so answer would be NO. Two different answers. Not sufficient.

I thought it was that in DS the statements will never contradict each other...and in this case the only time that does not happen is if the point is at the origin..am i not understanding this problem correctly?

I thought it was that in DS the statements will never contradict each other...and in this case the only time that does not happen is if the point is at the origin..am i not understanding this problem correctly?

Yes, on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

Now, if we consider 2 statements together we'll get that as point A lies on both blue and red lines then it must be at the origin (intersection point of these 2 lines).
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