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which quadrant of the coordinate system does point(a, b)lie

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Source: — Data Sufficiency |
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by sidmaru123 » Wed Jan 23, 2013 10:05 pm
If ab ≠ 0, in which quadrant of the coordinate system does point (a, b) lie?

(1) (-b, a) lies in quadrant I.

(2) (-a, b) lies in quadrant III.


Ans: ab ≠ 0 says that neither a or b =0 so the point (a,b) will not lie on the X or Y axis.


Statement 1: (-b, a) lies in quad I so we can infer that -b and a both are positive numbers, because in quadrant I both co-ordinates take a positive value.This implies that a is positive but b is negative (because -b is +ve so b is -ve). Thus point (a,b) will lie in quadrant where X co-ordinate is +ve and Y is -ve i.e. quadrant IV. STATEMENT 1 --> Sufficient

Statement 2: (-a, b) lies in quad III so we can infer that -a and b both are negative numbers, because in quadrant III both co-ordinates take a negative value.This implies that a is positive but b is negative (because (-a) is -ve so a is +ve). Thus point (a,b) will lie in quadrant where X co-ordinate is +ve and Y is -ve i.e. quadrant IV. STATEMENT 2 --> Sufficient

Answer D
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by lunarpower » Thu Jan 24, 2013 2:21 am
the solution above works, of course, but it's way too much work.

don't forget that this is data sufficiency! the point here is just to ascertain whether you can solve the problem uniquely -- not actually to solve the problem, if you don't have to.

so...
himu wrote:If ab ≠ 0, in which quadrant of the coordinate system does point (a, b) lie?
each quadrant corresponds to a particular pair of signs for the x- and y-coordinates. therefore, if the signs of x and y are uniquely determined, that's "sufficient"; if more than one sign is possible for either coordinate, that's "not sufficient".
(1) (-b, a) lies in quadrant I.
this is a single quadrant, implying that the signs of both x and y are known.
sufficient.
(2) (-a, b) lies in quadrant III.
this is a single quadrant, implying that the signs of both x and y are known.
sufficient.

that's it -- it's (d). no need to slog through all the work on this one.
Ron has been teaching various standardized tests for 20 years.

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