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# M09-37

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Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139553 [0], given: 12794

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15 Sep 2014, 23:41
Expert's post
8
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Difficulty:

25% (medium)

Question Stats:

76% (01:01) correct 24% (02:04) wrong based on 117 sessions

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If in the picture below, the arc is a quarter of a circle and $$OABC$$ is a rectangle, what is $$AC$$?

A. $$5\sqrt{2}$$
B. $$7\sqrt{2}$$
C. 10
D. 12
E. $$9\sqrt{2}$$
[Reveal] Spoiler: OA

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Kudos [?]: 139553 [0], given: 12794

Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139553 [1], given: 12794

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15 Sep 2014, 23:41
1
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Official Solution:

If in the picture below, the arc is a quarter of a circle and $$OABC$$ is a rectangle, what is $$AC$$?

A. $$5\sqrt{2}$$
B. $$7\sqrt{2}$$
C. 10
D. 12
E. $$9\sqrt{2}$$

$$AC = OB$$ is the radius of the circle, $$5 + 5 = 10$$

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Joined: 19 Sep 2014
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27 Aug 2015, 07:23
Hi,
Could not understand that if AC=OB then why is 5 being added to 5 to get 10.The answer should be 5 only.Please explain where I am going wrong.

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Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139553 [2], given: 12794

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27 Aug 2015, 11:24
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schak2rhyme wrote:
Hi,
Could not understand that if AC=OB then why is 5 being added to 5 to get 10.The answer should be 5 only.Please explain where I am going wrong.

AC is diagonal of the rectangle. The two diagonals of a rectangle are equal, thus AC = OB. But OB is also radius of the circle and radius of the circle according to the figure is 5 + 5 = 10.
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Kudos [?]: 139553 [2], given: 12794

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Joined: 23 Sep 2015
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Location: France
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)

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25 Nov 2015, 06:16
I answerd the question by saying that it was a 30;60;90 triangle. Would this thinking be incorrect for this figure?
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Kudos [?]: 99 [0], given: 72

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15 Feb 2016, 05:34
Icecream87 wrote:
I answerd the question by saying that it was a 30;60;90 triangle. Would this thinking be incorrect for this figure?

Hi Icecream,

I did exactly the same!
In my opinion it is also a valid / possible way of solution.

Thanks!!

Kudos [?]: [0], given: 5

Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139553 [0], given: 12794

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15 Feb 2016, 05:44
AnikaJu wrote:
Icecream87 wrote:
I answerd the question by saying that it was a 30;60;90 triangle. Would this thinking be incorrect for this figure?

Hi Icecream,

I did exactly the same!
In my opinion it is also a valid / possible way of solution.

Thanks!!

On what ground do you assume that the triangle is 30-60-90 triangle?
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15 Feb 2016, 06:20
Bunuel wrote:
AnikaJu wrote:
Icecream87 wrote:
I answerd the question by saying that it was a 30;60;90 triangle. Would this thinking be incorrect for this figure?

Hi Icecream,

I did exactly the same!
In my opinion it is also a valid / possible way of solution.

Thanks!!

On what ground do you assume that the triangle is 30-60-90 triangle?

I know that the angle at point O is 90 degrees and the opposite of the angle of 90 degreed is 2x. x = 5.
However I must admit that I just assumed that the other two angles are 30 and 60, I cannot provide you a proof... mhmmmm

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15 Apr 2016, 06:27
AnikaJu wrote:
Bunuel wrote:
AnikaJu wrote:

Hi Icecream,

I did exactly the same!
In my opinion it is also a valid / possible way of solution.

Thanks!!

On what ground do you assume that the triangle is 30-60-90 triangle?

I know that the angle at point O is 90 degrees and the opposite of the angle of 90 degreed is 2x. x = 5.
However I must admit that I just assumed that the other two angles are 30 and 60, I cannot provide you a proof... mhmmmm

So I did the same way, and while it's not the best way to solve, there's actually a way to prove that the triangle is a 30-60-90 triangle:

Since the object is a rectangle, angle OCA = angle COB. Because the rectangle is inscribed in the circle, we can also say that sin(angle COB) = 5/10 = .5. sin(30) = .5 so we know angle COB = OCA = 30 degrees.

Like I said, this was not at all the best way to answer this question, and I was getting way too analytical about it, but there you go.

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18 Apr 2016, 14:11
diagonals of rectangle are equal in length.
from the figure the radius of circle is 10 units
OB = 10 units
therefore AC = 10 units
correct answer option C

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Intern
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23 Oct 2016, 06:51
Pretty easy question, but for me it was not obvious that the two fives in the figure are measures of total length. I would have expected two points on the x-axis in order to dertermine the radius.

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04 Sep 2017, 13:45
I think this is a poor-quality question and I don't agree with the explanation. This question's drawing is messed up. If you look at the chart it is very clear that what is explained later in the explanation as the "radius" (5+5), the 5 to the right of the 5 on the rectangle is on a line that goes through the edge of the Arc. The image makes it look like line AB is bisecting some line that starts at point O and goes through point A and through the edge of the Arc.

I would think on the gmat this wouldn't be the case, so I won't get up in arms about it. My original interpretation of the problem was "the radius (which will be equal to diagonal AC" will be less than 10 as (5+5) is represented in the image as a length greater than the radius.

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Re M09-37   [#permalink] 04 Sep 2017, 13:45
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# M09-37

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