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19 Dec 2022, 07:00
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
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Question Stats:
27% (01:38) correct
73%
(02:17)
wrong
based on 118
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12 Days of Christmas GMAT Competition with Lots of Fun
In the given figure both the co-ordinate axes are tangent to the drawn circle. If A is a point on the circumference of the circle as shown, then what is the radius of the circle?
(1) The co-ordinate of A is (4, 8).
(2) The radius is greater than 15.
2022-12-12_18-00-51.png [ 12.54 KiB | Viewed 3249 times ]
In the given figure both the co-ordinate axes are tangent to the drawn circle. If A is a point on the circumference of the circle as shown, then what is the radius of the circle?
(1) The co-ordinate of A is (4, 8).
(2) The radius is greater than 15.
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Attachment:
2022-12-12_18-00-51.png [ 12.54 KiB | Viewed 3249 times ]
20 Dec 2022, 05:17
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Bunuel
GMATWhiz Official Explanation:
Step 1: Analyse Question Stem:
- • We are given the figure.
- o The co-ordinate axes are tangent to the drawn circle.
o If A is a point on the circumference of the circle as shown.
- o Let the radius = r.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The co-ordinate of A is (4, 8).
- • The co-ordinate of A is (4,8)
• We can say that OA is the radius and thus it should be = r.
- o Thus, distance between O and A = \(\sqrt{(r-8)^2+(r-4)^2} = r\)
\(\sqrt{(r-8)^2+(r-4)^2} = r\)
Or, \((r-8)^2+(r-4)^2 = r^2\) (Squaring each side)
Or, \(r^2-16r+64+ r^2-8r+16 = r^2\)
Or, \(r^2-24r+80 = 0\)
Or, \((r – 20) (r – 4) = 0\)
Or, r = 20 or 4.
• However, we know the point A has a co-ordinate of (4, 8).
- o And as per the figure r must be greater than both 4 and 8.
o Thus, only possible value is 20.
Statement 2: The radius is greater than 15.
- • We can see that there are infinite possibilities for radius from this info.
The answer is option A.
Attachment:
2022-12-20_16-11-02.png [ 27.04 KiB | Viewed 2508 times ]
General Discussion
19 Dec 2022, 07:20
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In the given figure both the co-ordinate axes are tangent to the drawn circle. If A is a point on the circumference of the circle as shown, then what is the radius of the cube?
Let the radius of the circle is r.
The equation of the circle with centre (r, r) and radius r:
(x-r)^2 + (y-r)^2 = r^2
Quote:
Since A(4,8) is on the circumference of the circle, it should satisfy equation of the circle.
(4-r)^2 + (8-r)^2 = r^2
r^2 - 8r + 16 + 64 - 16r + r^2 = r^2
r^2 - 24r + 80 = 0
(r-20)(r-4) = 0
From the figure it is clear that both 4 & 8 are less than r
r = 20
SUFFICIENT
Quote:
No information is provided to calculate r.
NOT SUFFICIENT
IMO A
