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If ab ≠ 0, in what quadrant of the coordinate system below does point

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If ab ≠ 0, in what quadrant of the coordinate system below does point  [#permalink]

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New post 23 Sep 2018, 05:22
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If ab ≠ 0, in what quadrant of the coordinate system below does point (a, b) lie?


(1) (b, a) lies in quadrant IV.

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


Attachment:
Quadrants.GIF
Quadrants.GIF [ 1.2 KiB | Viewed 442 times ]

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Re: If ab ≠ 0, in what quadrant of the coordinate system below does point  [#permalink]

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New post 23 Sep 2018, 06:46
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Bunuel wrote:
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If ab ≠ 0, in what quadrant of the coordinate system below does point (a, b) lie?

(1) (b, a) lies in quadrant IV.

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

Attachment:
Quadrants.GIF


Target question: In what quadrant of the coordinate system below does point (a, b) lie?

Statement 1: (b, a) lies in quadrant IV.
In Quadrant IV, the x-coordinate is POSITIVE, and the y-coordinate is NEGATIVE
So, if (b, a) lies in quadrant IV, then b is POSITIVE, and the a is NEGATIVE

If a (the x-coordinate of (a,b)) is NEGATIVE and b (the y-coordinate of (a,b)) is POSITIVE, then (a, b), must lie in Quadrant II
So, the answer to the target question is (a, b) lies in Quadrant II
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: (a, -b) lies in quadrant III.
In Quadrant III, the x-coordinate is NEGATIVE, and the y-coordinate is NEGATIVE
So, if (a, -b) lies in quadrant III, then a is NEGATIVE, and the -b is NEGATIVE
If -b is NEGATIVE, then b is POSITIVE

If a (the x-coordinate of (a,b)) is NEGATIVE and b (the y-coordinate of (a,b)) is POSITIVE, then (a, b), must lie in Quadrant II
So, the answer to the target question is (a, b) lies in Quadrant II
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
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Re: If ab ≠ 0, in what quadrant of the coordinate system below does point  [#permalink]

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New post 23 Sep 2018, 12:06
This is a pretty simple one. Especially with the quadrant diagram that goes along just in case someone forgets which quadrant is numbered what.
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Re: If ab ≠ 0, in what quadrant of the coordinate system below does point &nbs [#permalink] 23 Sep 2018, 12:06
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