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In the rectangular quadrant system shown above, which quadrant, if any

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In the rectangular quadrant system shown above, which quadrant, if any [#permalink]

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New post 28 Aug 2016, 09:43
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In the rectangular quadrant system shown above, which quadrant, if any, contains no point (x, y) that satisfies the equation x^2 − 2y = 3?

A. none
B. I
C. II
D. III
E. IV

[Reveal] Spoiler:
Attachment:
2016-08-28_2141.png
2016-08-28_2141.png [ 1.33 KiB | Viewed 1057 times ]
[Reveal] Spoiler: OA

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Re: In the rectangular quadrant system shown above, which quadrant, if any [#permalink]

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New post 28 Aug 2016, 10:20
Bunuel wrote:
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In the rectangular quadrant system shown above, which quadrant, if any, contains no point (x, y) that satisfies the equation x^2 − 2y = 3?

A. none
B. I
C. II
D. III
E. IV

[Reveal] Spoiler:
Attachment:
2016-08-28_2141.png


Answer is A.

If we draw the x and y intercepts of this equation, we will get a V Shaped curve passing from (0,-3/2) to (1.732,0) and (0,-3/2) to (-1.732,0). Hence, it will pass through all the quadrants.
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Re: In the rectangular quadrant system shown above, which quadrant, if any [#permalink]

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New post 25 Feb 2017, 07:02
Bunuel wrote:
Image
In the rectangular quadrant system shown above, which quadrant, if any, contains no point (x, y) that satisfies the equation x^2 − 2y = 3?

A. none
B. I
C. II
D. III
E. IV

[Reveal] Spoiler:
Attachment:
2016-08-28_2141.png


Hi Bunuel,
Is there an algebraic approach to solve such qsns ? I'm looking for the fastest alternative to tackle such problems and for me, graphs take too long. :cry:
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In the rectangular quadrant system shown above, which quadrant, if any [#permalink]

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New post 25 Feb 2017, 11:34
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Expert's post
Bunuel wrote:
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In the rectangular quadrant system shown above, which quadrant, if any, contains no point (x, y) that satisfies the equation x^2 − 2y = 3?

A. none
B. I
C. II
D. III
E. IV


I'd be inclined to just pick numbers on this one. I don't remember off the top of my head how to plot a parabola on a graph (without testing my work by using numbers anyways), so I might as well just try it with arithmetic.

We'll need to try both positive and negative values for x, in order to maximize our chances of hitting all of the quadrants.

If x = 3, then 9 - 2y = 3. So, y = -3. The point (3,-3) works (quadrant IV).

If x = -3, then 9 - 2y = 3. So, y = -3. The point (-3, -3) works (quadrant III).

Let's try some large values for x:

x = 10. 100 - 2y = 3. y = 97/2. (10,97/2) works (quadrant II).

x = -10. 100 - 2y = 3. y = 97/2. (-10, 97/2) works (quadrant I).

We have points in all four quadrants, so we can pick A.

It's interesting to note that the quadrant system in this problem is different from the usual quadrant system (where I and II would be swapped). I don't think I've seen the GMAT do this. It doesn't matter in this problem, because there are points in all four quadrants that work, but it might matter if the missing points were in quadrant I or II.
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In the rectangular quadrant system shown above, which quadrant, if any   [#permalink] 25 Feb 2017, 11:34
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