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# In the figure above, what is the value of x + y ?

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In the figure above, what is the value of x + y ? [#permalink]

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28 Dec 2011, 07:48
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OG-DS-140.png [ 9.11 KiB | Viewed 7114 times ]
In the figure above, what is the value of x + y ?

(1) x = 70
(2) ΔABC and ΔADC are both isosceles triangles.

I thought the answer is A

here is my reasoning

From 1.From the Figure As per triangles property when x=70 then Y=140, i.e Inscribed angle = twice the central angle...But In the Answer it says Y can vary.....

From 2. as we don't have any sides or angles we can't get anything from here

So I thought the answer is A..But surprisingly the answer is E.......

Can anyone please explain,How is it so.....

[Reveal] Spoiler: OA

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Re: Geometry(Official Guide 12th Edition #Q140 DS) [#permalink]

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28 Dec 2011, 08:53
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Expert's post

Here's a rough version of the image.

Statement 1 is insufficient.
We know angle x is 70, but we know nothing about the placement of point D. The lower the placement of point D the greater the angle y, so y could really be any number of values. Remember we can't assume anything about the placement of a point, unless we are explicitly told about the placement in the question.

Statement 2 is insufficient.
x and y could be any number of values. For instance x could be 50 degrees or 70 degrees. All we know is that the triangles are isosceles, but we know nothing about the angles.

Statements 1 and 2 together are insufficient.
From statement 1 we know x is 70 and that angles BAC and BCA are both 55. But again we know nothing about the placement of point D. Point D could be very close to B in which case y would be close to 70 degrees or point D could be close to the segment AC in which case y would be close to 180 degrees.

I hope that helps!
Bhavin
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Re: Geometry(Official Guide 12th Edition #Q140 DS) [#permalink]

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21 Apr 2012, 09:16
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The OG explanation assumes that given that the triangles are isosceles, then the pairs of sides that are equal are (AB, BC) and (AD, DC). Why OG does that!? I think we cannot assume anything regarding which side is the base of each triangle.
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Re: Geometry(Official Guide 12th Edition #Q140 DS) [#permalink]

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21 Jun 2012, 17:44
fcomorales wrote:
The OG explanation assumes that given that the triangles are isosceles, then the pairs of sides that are equal are (AB, BC) and (AD, DC). Why OG does that!? I think we cannot assume anything regarding which side is the base of each triangle.

You are correct. Unless there is some information about which side is base, it shouldn't assume that AB, BC and AD, DC are equal.

My take,

1 - Even if x=70, there is no information given about the placement of point D / the relation between the triangles - INSUFFICIENT
2 - Two triangles are isosceles. We cannot determine which two sides are equal and cannot determine the values of x & y. - INSUFFICIENT

1 & 2 combined together are also not sufficient.

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Re: In the figure above, what is the value of x + y ? [#permalink]

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22 Jun 2012, 01:31
Hi Kotela,

I have a question for you. Lets say x = 70, y = 140, will D be the center of the center of circle passing through A, B & C? Think!

Regards,

kotela wrote:
Attachment:
OG-DS-140.png
In the figure above, what is the value of x + y ?

(1) x = 70
(2) ΔABC and ΔADC are both isosceles triangles.

I thought the answer is A

here is my reasoning

From 1.From the Figure As per triangles property when x=70 then Y=140, i.e Inscribed angle = twice the central angle...But In the Answer it says Y can vary.....

From 2. as we don't have any sides or angles we can't get anything from here

So I thought the answer is A..But surprisingly the answer is E.......

Can anyone please explain,How is it so.....

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Re: In the figure above, what is the value of x + y ? [#permalink]

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06 Feb 2017, 23:26
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Re: In the figure above, what is the value of x + y ?   [#permalink] 06 Feb 2017, 23:26
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