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O is the center of the circle
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01 Feb 2019, 10:59
01 Feb 2019, 10:59
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Question Stats:
52% (02:01) correct
47% (02:10) wrong based on 153 sessions
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#GREpracticequestion O is the center of the circle.jpg [ 14.04 KiB | Viewed 9939 times ]
O is the center of the circle
PQ=6
OR=12
Quantity A |
Quantity B |
x |
45 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: O is the center of the circle
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06 Feb 2019, 08:31
06 Feb 2019, 08:31
1
Expert Reply
Carcass wrote:
Attachment:
#GREpracticequestion O is the center of the circle.jpg
O is the center of the circle
PQ=6
OR=12
Quantity A |
Quantity B |
x |
45 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Let us take triangle PQR..
PQ=6 and OP=OR=12..
so in triangle PQR, a right angled triangle, hypotenuse is 12 and one side is 6 so the other side = \(\sqrt{12^2-6^2}=\sqrt{108}\), between 10 and 11..
In this triangle, PQ is least of all sides, so the angle opposite it will be less than the one opposite OQ and Sum of two is 90, so x<90/2 or x<45
Hence B
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O is the center of the circle
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06 Feb 2019, 11:42
06 Feb 2019, 11:42
3
Carcass wrote:
Attachment:
#GREpracticequestion O is the center of the circle.jpg
O is the center of the circle
PQ=6
OR=12
Quantity A |
Quantity B |
x |
45 |
Since O is the center of the circle, we know that side OR is the RADIUS of the circle.
So, the radius of the circle = 12
Since OP is also a radius of the circle, we know that side OP also has length 12
So, let's add these lengths to our diagram:
At this point, we should notice that the length of side PQ (length 6) is HALF the length of the hypotenuse OP PQ (length 12)
This should remind us of the base SPECIAL 30-60-90 right triangle shown in purple below:
IMPORTANT: Geometric diagrams on the GRE are NOT necessarily drawn to scale [for more on this, watch the video below]
So, while it's tempting to conclude that angle x = 60° (because it LOOKS like 60°), we can't be so bold.
Instead, take a look at at the base SPECIAL 30-60-90 right triangle (in purple).
Notice that the side opposite the 30° angle is HALF the length of the hypotenuse.
Since the length of side PQ is HALF the length of the hypotenuse OP, we know that side PQ must be opposite the 30° angle
In other words, x = 30°
We get:
QUANTITY A: 30
QUANTITY B: 45
Answer: B
Cheers,
Brent
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