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# M18-34

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Math Expert
Joined: 02 Sep 2009
Posts: 52294

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16 Sep 2014, 00:04
1
3
00:00

Difficulty:

95% (hard)

Question Stats:

32% (01:15) correct 68% (01:28) wrong based on 234 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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Math Expert
Joined: 02 Sep 2009
Posts: 52294

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16 Sep 2014, 00:04
1
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:

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.

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Joined: 09 Feb 2015
Posts: 20

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Updated on: 25 Jun 2015, 17:13
1
Dear Bunuel,
That is 180-72/2=54
Not same as you write 360−72/2= 144 Not 54.

Originally posted by Mrtinhnv on 24 Jun 2015, 21:51.
Last edited by Mrtinhnv on 25 Jun 2015, 17:13, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 52294

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25 Jun 2015, 01:19
Mrtinhnv wrote:
Dear Bunnel,
That is 180-72/2=54
Not same as you write 360−72/2= 144 Not 54.

Edited the typo. Thank you.
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Intern
Joined: 07 Mar 2011
Posts: 24

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18 Jun 2016, 08:44
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].
Senior Manager
Joined: 31 Mar 2016
Posts: 384
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

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30 Aug 2016, 04:06
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 06 Feb 2016
Posts: 48
Location: Poland
Concentration: Finance, Accounting
GMAT 1: 730 Q49 V41
GPA: 3.5

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20 Sep 2016, 10:00
As of now 78% chose E hence answered incorrectly. The question in a tricky way asks to find an angle.
Manager
Joined: 17 Jan 2017
Posts: 61

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14 Jun 2018, 23:17
1
Actually not that difficult. You just need to read precisely.
I got it wrong though
Intern
Joined: 20 May 2018
Posts: 17

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22 Sep 2018, 01:31
HIGH QUALITY QUESTION!
Manager
Joined: 28 Jun 2018
Posts: 96
GMAT 1: 490 Q39 V18
GMAT 2: 640 Q47 V30
GMAT 3: 670 Q50 V31
GMAT 4: 700 Q49 V36
GPA: 4

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05 Dec 2018, 05:47
Fell for E because i read it as Angle of AOB !!!!!!
Not a hard question though.
Damn Bunuel! Thanks for setting such amazing questions!
Re: M18-34 &nbs [#permalink] 05 Dec 2018, 05:47
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# M18-34

Moderators: chetan2u, Bunuel

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