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M18-34

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M18-34  [#permalink]

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New post 16 Sep 2014, 01:04
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A
B
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D
E

Difficulty:

  95% (hard)

Question Stats:

33% (01:16) correct 67% (01:32) wrong based on 216 sessions

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\(A\) and \(B\) are points on a circle of radius \(\frac{2}{\pi}\) and \(O\) is the center of the circle. If the length of arc \(AB\) is 0.8, what is the value of angle \(OAB\)?

A. 30 degrees
B. 36 degrees
C. 48 degrees
D. 54 degrees
E. 72 degrees

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Re: M18-34  [#permalink]

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New post 16 Sep 2014, 01:04
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1
Official Solution:

\(A\) and \(B\) are points on a circle of radius \(\frac{2}{\pi}\) and \(O\) is the center of the circle. If the length of arc \(AB\) is 0.8, what is the value of angle \(OAB\)?

A. 30 degrees
B. 36 degrees
C. 48 degrees
D. 54 degrees
E. 72 degrees


Look at the diagram below:

Image

The circumference of the circle is \(2\pi{r}=2\pi{*\frac{2}{\pi}}=4\). Now, since arc \(AB\) is \(\frac{0.8}{4}=\frac{1}{5}\) of the circumference (360 degrees) then angle \(AOB\) is \(\frac{1}{5}*360=72\) degrees.

Next, since triangle \(ABO\) is isosceles \((OA=OB=r)\) then \(\angle{OAB}=\frac{180-72}{2}=54\) degrees.


Answer: D
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Collection of Questions:
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M18-34  [#permalink]

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New post Updated on: 25 Jun 2015, 18:13
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Dear Bunuel,
That is 180-72/2=54
Not same as you write 360−72/2= 144 Not 54.
Please repair it.

Originally posted by Mrtinhnv on 24 Jun 2015, 22:51.
Last edited by Mrtinhnv on 25 Jun 2015, 18:13, edited 1 time in total.
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Re: M18-34  [#permalink]

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New post 25 Jun 2015, 02:19
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Re: M18-34  [#permalink]

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New post 18 Jun 2016, 09:44
I think,in this question triangle formation OAB need to be captured in the problem definition. When you say angle OAB it can be also arc's angle [ I know this is not in the GMAT scope].
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Re M18-34  [#permalink]

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New post 30 Aug 2016, 05:06
I think this is a high-quality question and I agree with explanation.
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Re: M18-34  [#permalink]

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New post 20 Sep 2016, 11:00
As of now 78% chose E hence answered incorrectly. The question in a tricky way asks to find an angle.
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Re: M18-34  [#permalink]

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New post 15 Jun 2018, 00:17
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Actually not that difficult. You just need to read precisely.
I got it wrong though :sad:
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Re: M18-34  [#permalink]

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New post 22 Sep 2018, 02:31
HIGH QUALITY QUESTION!
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Re: M18-34 &nbs [#permalink] 22 Sep 2018, 02:31
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