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If BD = CD, what is the degree measure of x + y?

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If BD = CD, what is the degree measure of x + y? [#permalink]

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If BD = CD, what is the degree measure of x + y?

(1) v = 74 degrees

(2) w = 32 degrees

[Reveal] Spoiler:
Attachment:
touchingtriangles.jpg
touchingtriangles.jpg [ 3.4 KiB | Viewed 1472 times ]
[Reveal] Spoiler: OA

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Re: If BD = CD, what is the degree measure of x + y? [#permalink]

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New post 01 Apr 2016, 04:47
Okay here is my approach
we need to get x+y
as per statement 1 => u = given so as u=v => we have v too
great..
now using angle sum property => we have w too
now using the exterior angle property => z=w+u => we have z too
again using angle sum property we have x+y too
hence sufficient.
similarly we have statement 2 => sufficient
hence D
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Re: If BD = CD, what is the degree measure of x + y? [#permalink]

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New post 03 Apr 2016, 04:21
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If BD = CD, what is the degree measure of x + y?

(1) v = 74 degrees

(2) w = 32 degrees


When you modify the original condition and the question, x+y=v is derived. From, v=u and w+2v=180, if you figure out w, you can figure out v as well.
For 1), v=74 and it is sufficient.
For 2), substitute w=32 to w+2v=180 -> 32+2v=180, 2v=148 and v=74.
Thus, 1)=2) and the answer is D.


 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: If BD = CD, what is the degree measure of x + y? [#permalink]

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New post 18 Sep 2016, 00:03
Bunuel wrote:
Image
If BD = CD, what is the degree measure of x + y?

(1) v = 74 degrees

(2) w = 32 degrees

[Reveal] Spoiler:
Attachment:
touchingtriangles.jpg

For such questions..is it not necessary to have "Ac is straight line "mentioned in stem itself???

Plz reply someone...

Thanks

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Re: If BD = CD, what is the degree measure of x + y? [#permalink]

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New post 18 Sep 2016, 01:10
rohit8865 wrote:
Bunuel wrote:
Image
If BD = CD, what is the degree measure of x + y?

(1) v = 74 degrees

(2) w = 32 degrees

[Reveal] Spoiler:
Attachment:
touchingtriangles.jpg

For such questions..is it not necessary to have "Ac is straight line "mentioned in stem itself???

Plz reply someone...

Thanks


Unless we are explicitly stated that the figure is not drawn to scale, we should take the given figure as it appears.
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Re: If BD = CD, what is the degree measure of x + y? [#permalink]

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New post 29 May 2017, 10:01
Bunuel wrote:
Image
If BD = CD, what is the degree measure of x + y?

(1) v = 74 degrees

(2) w = 32 degrees

[Reveal] Spoiler:
Attachment:
touchingtriangles.jpg


This problem is all about preparation. Once you re-draw the triangle, you will note that x+y = v since an exterior angle of a triangle is equal to the sum of the opposite interior angles. Likewise, u = v since BC = CD. So we really need to determine either the value of v or u or even the value of w.

Statement 1) v = 74. Sufficient.

Statement 2) w = 32.

w = 32
v+u + 32 = 180
2v + 32 = 180 since v=u
2v = 148
v = 74

Sufficient.

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Re: If BD = CD, what is the degree measure of x + y? [#permalink]

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New post 06 Sep 2017, 19:15
Bunuel wrote:
Image
If BD = CD, what is the degree measure of x + y?

(1) v = 74 degrees

(2) w = 32 degrees

[Reveal] Spoiler:
Attachment:
touchingtriangles.jpg


An interesting thing about this question is that if know how similar triangles work, then we can basically see that statement 1 and statement 2 have the exact same usefulness as each other- from statement 1 we can derive the exact same amount of information as statement 2 and vice-versa.

D

Kudos [?]: 36 [0], given: 164

Re: If BD = CD, what is the degree measure of x + y?   [#permalink] 06 Sep 2017, 19:15
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