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# What is the ratio of OA to AC? (1) OD is half the length of DC

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Math Expert
Joined: 02 Sep 2009
Posts: 50004
What is the ratio of OA to AC? (1) OD is half the length of DC  [#permalink]

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18 Sep 2018, 22:02
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Difficulty:

45% (medium)

Question Stats:

67% (01:48) correct 33% (02:14) wrong based on 57 sessions

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What is the ratio of OA to AC? (Assume O is the center of the circle)

(1) OD is half the length of DC
(2) The area of ADC is 20.

Attachment:

image008.jpg [ 3.19 KiB | Viewed 627 times ]

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Re: What is the ratio of OA to AC? (1) OD is half the length of DC  [#permalink]

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21 Sep 2018, 04:47
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Bunuel wrote:

What is the ratio of OA to AC?

(1) OD is half the length of DC
(2) The area of ADC is 20.

Attachment:
The attachment image008.jpg is no longer available

Question stem:- OA:AC=?

St1:- OD is half the length of DC

Applying Pythagoras theorem in the triangle OAD, $$AD=2\sqrt{2}x$$
Again, Applying Pythagoras theorem in the triangle ADC, $$AC=2\sqrt{3}x$$

Now ratio of OA to AC can be determined.

Sufficient.

St2:- The area of ADC is 20.

No information is provided on the measure of AD and DC.

Insufficient.

Ans. (A)
Attachments

Circle ratio.PNG [ 74.38 KiB | Viewed 477 times ]

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PKN

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Joined: 27 Oct 2017
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Re: What is the ratio of OA to AC? (1) OD is half the length of DC  [#permalink]

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23 Sep 2018, 01:01
Bunuel, Do we have to consider that O is Center?
if O is not the center, it seems E

Bunuel wrote:

What is the ratio of OA to AC?

(1) OD is half the length of DC
(2) The area of ADC is 20.

Attachment:
image008.jpg

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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 892
WE: Supply Chain Management (Energy and Utilities)
Re: What is the ratio of OA to AC? (1) OD is half the length of DC  [#permalink]

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23 Sep 2018, 01:05
I think we must consider point 'O' centre of the circle in the same way we do consider Angle ADC 90 degree.

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PKN

Rise above the storm, you will find the sunshine

Senior DS Moderator
Joined: 27 Oct 2017
Posts: 878
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: What is the ratio of OA to AC? (1) OD is half the length of DC  [#permalink]

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23 Sep 2018, 01:08
I couldn't get you, We can still have angle ADC= 90, without O as Center.

PKN wrote:
I think we must consider point 'O' centre of the circle in the want we do consider Angle ADC 90 degree.

Posted from my mobile device

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Re: What is the ratio of OA to AC? (1) OD is half the length of DC  [#permalink]

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23 Sep 2018, 01:32
gmatbusters wrote:
I couldn't get you, We can still have angle ADC= 90, without O as Center.

PKN wrote:
I think we must consider point 'O' centre of the circle in the want we do consider Angle ADC 90 degree.

Posted from my mobile device

We can't assume that OC is radius because it is not mentioned anywhere in the statement. The trap in DS problem is that if it is not given we can't assume.

If it's mentioned that OC is radius then the answer will be A .

Therefore it is E.
Director
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WE: Supply Chain Management (Energy and Utilities)
Re: What is the ratio of OA to AC? (1) OD is half the length of DC  [#permalink]

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23 Sep 2018, 02:10
gmatbusters wrote:
I couldn't get you, We can still have angle ADC= 90, without O as Center.

PKN wrote:
I think we must consider point 'O' centre of the circle in the want we do consider Angle ADC 90 degree.

Posted from my mobile device

My reasoning:-
1) Notice a square symbol at point D. And we say angle ADC or Angle ADO is 90 degree

In the same way,

2) Notice "a BOLD DOT mark" at point O. We can say point 'O' the centre of the circle.
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PKN

Rise above the storm, you will find the sunshine

Math Expert
Joined: 02 Sep 2009
Posts: 50004
Re: What is the ratio of OA to AC? (1) OD is half the length of DC  [#permalink]

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23 Sep 2018, 03:22
gmatbusters wrote:
Bunuel, Do we have to consider that O is Center?
if O is not the center, it seems E

Bunuel wrote:

What is the ratio of OA to AC?

(1) OD is half the length of DC
(2) The area of ADC is 20.

Attachment:
image008.jpg

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Fixed. Thank you.
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Re: What is the ratio of OA to AC? (1) OD is half the length of DC &nbs [#permalink] 23 Sep 2018, 03:22
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