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08 Jan 2021, 02:35
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B
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Difficulty:
55%
(hard)
Question Stats:
55% (01:42) correct
45%
(01:37)
wrong
based on 92
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In the figure above, does x = 90?
(1) The length of AC is less than the length of BC.
(2) The length of AB is one-fourth the circumference of the circle.
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08 Jan 2021, 02:59
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I think the answer is B..
(1) The length of AC is less than the length of BC..... we can't calculate the measure of x from this , so, this statement is insufficient
(2) The length of AB is one-fourth the circumference of the circle.
Let us assume the radius of the circle is r
Therefore 2πr = 360 degree
AB = (1/4)*2πr
therefore the central angle x = (360/2πr)*( (1/4)*2πr )= 90 degree, So, statement 2 is sufficient
(1) The length of AC is less than the length of BC..... we can't calculate the measure of x from this , so, this statement is insufficient
(2) The length of AB is one-fourth the circumference of the circle.
Let us assume the radius of the circle is r
Therefore 2πr = 360 degree
AB = (1/4)*2πr
therefore the central angle x = (360/2πr)*( (1/4)*2πr )= 90 degree, So, statement 2 is sufficient
08 Jan 2021, 03:00
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In the figure above, does x = 90?
Basically, we need to check either of the following:
1. Whether AB is diameter or the largest possible side of the triangle ABC
2. AC = BC
(1) The length of AC is less than the length of BC.
Whether AC < BC or BC < AC, x can be 90 when AB is longest(diameter). However, as we don't know anything about AB, it can be possible that AB = BC and AC < BC - in this case x < 90.
INSUFFICIENT.
(2) The length of AB is one-fourth the circumference of the circle.
AB = \(\frac{2 * \pi * r}{4} = \frac{\pi * r}{2} = \pi * d/4\)
Hence AB < diameter of circle.
\(\implies\) x > 90 or x < 90
SUFFICIENT.
Answer B.
