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23 May 2020, 07:54
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
70% (02:01) correct
30%
(02:01)
wrong
based on 503
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What is the area of circle O ?
(1) The ratio of the area of the square circumscribed about circle O to the square inscribed in it is 2 to 1.
(2) The ratio of the length of a side of the square circumscribed about circle O to the diameter of O is 1 to 1.
DS21214
Are You Up For the Challenge: 700 Level Questions
(1) The ratio of the area of the square circumscribed about circle O to the square inscribed in it is 2 to 1.
(2) The ratio of the length of a side of the square circumscribed about circle O to the diameter of O is 1 to 1.
DS21214
Are You Up For the Challenge: 700 Level Questions
Bunuel
What is the area of circle O ?
(1) The ratio of the area of the square circumscribed about circle O to the square inscribed in it is 2 to 1.
(2) The ratio of the length of a side of the square circumscribed about circle O to the diameter of O is 1 to 1.
DS21214
(1) The ratio of the area of the square circumscribed about circle O to the square inscribed in it is 2 to 1.
(2) The ratio of the length of a side of the square circumscribed about circle O to the diameter of O is 1 to 1.
DS21214
STATEMENT 1: Let the radius of circle = r units
Let the side of the inscribed square be a units.
Let's focus on the inscribed square first.
The diagonal of this square will be the diameter of the circle. Using pythagoras algorithm, we have -
\((2r)^2 = a^2 + a^2 \)
Upon solving, we get : a = \sqrt{2r}
For the circumbscribed square, the diameter of the circle = the side of the square.
Therefore, side of sqaure = 2r
The area of the square circumscribed about circle O ^ The area of the square inscribed in circle O
= 2r^2 ^ sqrt(2)
= 2 : 1
This is already stated in STATEMENT 1. The radius of the circle can be of any measurement.
Insufficient (BCE)
STATEMENT 2:
As discussed in statement 1, the ratio of the length of the square circumscribed = 2r = diameter of the circle.
Thus, their ratio is 1:1.
Again, we already knew this. The value of radius can be anything for this rule to hold true.
Insufficient (CE)
Even upon combiing the two statements, we don't have a fixed value of the radius, thus, (E).
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24 May 2020, 00:27
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Bunuel
What is the area of circle O ?
(1) The ratio of the area of the square circumscribed about circle O to the square inscribed in it is 2 to 1.
(2) The ratio of the length of a side of the square circumscribed about circle O to the diameter of O is 1 to 1.
DS21214
(1) The ratio of the area of the square circumscribed about circle O to the square inscribed in it is 2 to 1.
(2) The ratio of the length of a side of the square circumscribed about circle O to the diameter of O is 1 to 1.
DS21214
Let the radius of the circle be r.
Now the side of circumscribed square = 2r.
=> Area of the circumscribed square = 4r^2.
For the inscribed square, the radius of the circle would be the diagonal of the smaller square.
Thus the side of the inscribed square = \sqrt{r}
=> Area of the inscribed square = r.
Statement 1: The ratio of the area of the square circumscribed about circle O to the square inscribed in it is 2 to 1.
=> 4r^2/r = 2r.
We still dont know the value of r to find the area. Thus Insufficient.
Statement 2: The ratio of the length of a side of the square circumscribed about circle O to the diameter of O is 1 to 1.
2r/2r = 1:1.
This information is of no use to us, as we cannot calculate the value of r, thus the area.
Thus, Insufficient.
Statement 1+ Statement 2 : We have only 2r, but no value of r, thus we cannot calculate the area of the circle.
So Insufficient.
Answer E.
