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# What is the measure of arc XYZ, if points X, Y and Z are points that l

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
What is the measure of arc XYZ, if points X, Y and Z are points that l  [#permalink]

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02 Sep 2018, 22:13
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Difficulty:

35% (medium)

Question Stats:

75% (01:35) correct 25% (01:47) wrong based on 24 sessions

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What is the measure of arc XYZ, if points X, Y and Z are points that lie, in that order, on a circle O?

(1) Sector XYZO has an area of $$\frac{3\pi}{2}$$ and is 1/6 the area of the circle.

(2) The measure of chord XZ is 3.

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Re: What is the measure of arc XYZ, if points X, Y and Z are points that l  [#permalink]

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03 Sep 2018, 03:08
1
Bunuel wrote:
What is the measure of arc XYZ, if points X, Y and Z are points that lie, in that order, on a circle O?

(1) Sector XYZO has an area of $$\frac{3\pi}{2}$$ and is 1/6 the area of the circle.

(2) The measure of chord XZ is 3.

Measure of Any arc = (Angle/360)*2πr

Question : What is the measure of arc XYZ?

i.e. We need
1) Angle drawn by are XYZ at the centre of the circle

Statement 1: Sector XYZO has an area of $$\frac{3\pi}{2}$$ and is 1/6 the area of the circle

i.e. (1/6)πr*2 = $$\frac{3\pi}{2}$$
as well as (1/6) = (Angle)/360
i.e. Angle at centre by XYZ = 60º hence

SUFFICIENT

Statement 2: The measure of chord XZ is 3.

NOT SUFFICIENT

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What is the measure of arc XYZ, if points X, Y and Z are points that l  [#permalink]

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03 Sep 2018, 03:18
Bunuel wrote:
What is the measure of arc XYZ, if points X, Y and Z are points that lie, in that order, on a circle O?

(1) Sector XYZO has an area of $$\frac{3\pi}{2}$$ and is 1/6 the area of the circle.

(2) The measure of chord XZ is 3.

(1) Sector XYZO has an area of $$\frac{3\pi}{2}$$ and is 1/6 the area of the circle.

the angle is 360/6 = 60
$$\pi r^2$$$$\frac{60}{360}$$ = $$3\pi$$
this should give us radius followed by measure of arc , which is 2$$\pi$$r

sufficient

(2) The measure of chord XZ is 3.
clearly insufficient

A
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Re: What is the measure of arc XYZ, if points X, Y and Z are points that l  [#permalink]

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03 Sep 2018, 03:56
The second statement is useless without another parameter like radius or circumference or length of the arc... But without the help of Second statement we could the answer with just statement 1 based on 1/6 th area, hence radius and measure of arc

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Re: What is the measure of arc XYZ, if points X, Y and Z are points that l  [#permalink]

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03 Sep 2018, 04:56
Has to be A.based on the info available in statement 1 , we can easily identify the angle the chord makes at the center and also the radius of the circle.
These 2 parameters can be used to get the length of the arc based on the standard formula

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Re: What is the measure of arc XYZ, if points X, Y and Z are points that l   [#permalink] 03 Sep 2018, 04:56
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