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A circle with center (1, 0) and radius 2 lies in the coordinate plane

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Math Expert
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Joined: 02 Sep 2009
Posts: 62285
A circle with center (1, 0) and radius 2 lies in the coordinate plane  [#permalink]

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New post 17 Sep 2018, 20:52
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

49% (02:25) correct 51% (02:28) wrong based on 57 sessions

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IESE School Moderator
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Joined: 11 Nov 2017
Posts: 138
Location: Belgium
Concentration: Technology, Operations
GMAT 1: 670 Q47 V34
GMAT 2: 750 Q50 V41
GMAT 3: 750 Q50 V41
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WE: Engineering (Aerospace and Defense)
Re: A circle with center (1, 0) and radius 2 lies in the coordinate plane  [#permalink]

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New post 18 Sep 2018, 14:18
3
1
i recommend sketching the circle with radius 2 and center (1,0)

1: either
y >1 --> it could be in quadrant 1 or 2 already NS, no need to look further
but lets do it anyway
or
y < -1 -> it could be in quadrant 3 or 4 (still see y>1, so NS)

2)
x is > 1 --> it could be in quadrant 1 or 4 --> sufficient so far
x is < -1 --> point has to be on the circle, since the circle has radius 2 and center 1,0
point -1,0 is the lefternmost point on the circle however this lies on the X axis, and does not belong to a quadrant, so it does not lie in Q2

Sufficient

B

kudos if this helped.
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Re: A circle with center (1, 0) and radius 2 lies in the coordinate plane  [#permalink]

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New post 16 Feb 2020, 23:31
Bunuel wrote:
Image
A circle with center (1, 0) and radius 2 lies in the coordinate plane shown above. If point (x, y) lies on the circle is (x, y) in quadrant 2?

(1) |y| > 1
(2) |x| > 1


Attachment:
image017.jpg


Solution:


    • Centre of the circle = \((1, 0)\)
    • The radius of the circle = \(2\) Units
    Image
    • \((x, y)\) lies on the circle.
We need to find the whether \((x, y)\) is in second quadrant or not.
• Whether x < 0 and y > 0 or not
Statement 1: \(|y| > 1\)
    • \(y < -1\) or \(y > 1\)
    • If \(y < -1\), then \((x, y)\) lies in either in \(III\) or \(IV\) quadrant.
    • If \(y > 1\), then \((x, y)\) lies in either \(I\) or \(II\) quadrant.
Hence, statement 1 is not sufficient, we can eliminate the answer option A and D.
Statement 2: \(|x| > 1\)
    • \(x < -1\) or \(x > 1\)
    • If \(x > 1\), then \((x, y)\) lies in either \(I\) or \(IV\) quadrant.
    • If \(x < -1\), then \((x, y)\) does not lies on the circle. it means \(x\) cannot be less than \(-1\), we can discard this case.
      o We can surely say that \((x, y)\) does not lies in \(II\) or \(III\) quadrant.
Hence, the correct answer is Option B.
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Re: A circle with center (1, 0) and radius 2 lies in the coordinate plane   [#permalink] 16 Feb 2020, 23:31
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