Need help with a math problem

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aniruddhkashyap: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sun Apr 11, 2010 11:25 pm

by aniruddhkashyap » Thu Apr 22, 2010 8:58 pm

The question is as follows

Q8: The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4Pi/3, what is the length of line segment RU?

A. 4/3
B. 8/3
C. 3
D. 4
E. 6

The book gives the answer as D but according to me it should be A

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Thu Apr 22, 2010 10:01 pm

Let the centre of the circle be 0.
Let the arc RTU subtend angle x at O.
So length of arc RTU is (x/360) * 2*pi*radius = (x/360) * 2 * pi * 4 = (4/3)*pi { given in the question}.
So x = 60
Now triangle ROU is isosceles because RO and OU are radius and angle ROU is 60.
So angle OUR = angle ORU =(180 -60)/2 = 60.
So triangle ROU is an equilateral triangle and hence all sides are equal.
Or OR = OU = RU = 4

The correct answer is D..

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akhpad: Legendary Member; Posts: 809; Joined: Wed Mar 24, 2010 10:10 pmFollowed by: 4 members; Thanked: 50 times

by akhpad » Fri Apr 23, 2010 7:33 am

Agree that RU = 4

First find angle subtended by arc at center = 60. Adjacent sides are equal.

So, it should be equilateral triangle.

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poohv005: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Wed Jan 06, 2010 7:06 am; Thanked: 1 times

by poohv005 » Fri Apr 23, 2010 11:26 am

To find the length of RU we need to find the angle of the arc RTU,
X = (360*4pi/3)/2pi(4) = 60

This implies that all the angle of triangle formed in circle is 60

therefore all the sides are equal and so RU is 4
answer is D.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Fri Apr 23, 2010 4:56 pm

aniruddhkashyap wrote:The question is as follows

Q8: The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4Pi/3, what is the length of line segment RU?

A. 4/3
B. 8/3
C. 3
D. 4
E. 6

Hi,

the algebra in the other answers is just fine, so I just want to review the general formula for this type of question, the circle sector formula.

For a sector of a circle with degree measure x and that's formed by minor arc AB, we have:

x/360 = AB/circumference = area of sector/area of circle

Questions involving circle sectors almost always come down to some application of that formula.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
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aniruddhkashyap: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sun Apr 11, 2010 11:25 pm

by aniruddhkashyap » Wed May 05, 2010 9:02 pm

Need help with the following DS questions

Q7:
Is xy > x^2y^2?
(1) 14x^2 = 3
(2) y^2 = 1

Q36:
If n is an integer and 100 < n <200, what is the value of n?
(1) 36n is an odd integer.
(2) 45n is an even integer.

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