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.
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which quadrant of the coordinate system does point(a, b)lie
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sidmaru123
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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
(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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lunarpower
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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...
sufficient.
sufficient.
that's it -- it's (d). no need to slog through all the work on this one.
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...
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".himu wrote:If ab ≠0, in which quadrant of the coordinate system does point (a, b) lie?
this is a single quadrant, implying that the signs of both x and y are known.(1) (-b, a) lies in quadrant I.
sufficient.
this is a single quadrant, implying that the signs of both x and y are known.(2) (-a, b) lies in quadrant III.
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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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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Learn more about ron
