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705-805 (Hard)|   Geometry|      
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Mani2879
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In the figure above, the length of segment xz is 24. What is the circu Updated on: 02 Sep 2018, 02:32
Originally posted by Mani2879 on 01 Sep 2018, 12:36.
Last edited by Bunuel on 02 Sep 2018, 02:32, edited 2 times in total.
Renamed the topic and edited the question.
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95% (hard)

Question Stats:

43% (02:13) correct 57% (02:05) wrong based on 208 sessions

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In the figure above, the length of segment xz is 24. What is the circumference of the circle with diameter wy?

(1) The length of segment wx is 40.

(2) The length of segment xy is 30.


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fskilnik
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In the figure above, the length of segment xz is 24. What is the circu 01 Sep 2018, 16:09
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Hi there!

The technique presented in the solution (image attached) takes into account the Pythagoras theorem and a nice way of calculating the area of a right triangle using "two different formulas" simultaneously!

Please note that in Data Sufficiency problems, to do calculations "till the end" is not (in general) the best approach!

The UNIQUENESS of solutions must be your real FOCUS, according to our method!

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
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sumit411
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In the figure above, the length of segment xz is 24. What is the circu 01 Sep 2018, 12:54
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Mani2879
Hi,
I Could not understand the official explanation !

Could someone explain this to me ?

Thank you!
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This is grometry DS. You don't need to solve the question. Try to visualize if the figure can be restricted by the given information.

Both the statements individually don't restrict the figure in only one possible orientation. So they are insufficient on their own. Combining - - - > they are sufficient

For reference:
https://youtu.be/wetqSGMdY7Y

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In the figure above, the length of segment xz is 24. What is the circu 01 Sep 2018, 21:32
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Hi
Thanks a lot for the superb explanation !!

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In the figure above, the length of segment xz is 24. What is the circu 02 Sep 2018, 07:28
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Hi
Thanks a lot for the superb explanation !!
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Hi, Mani!

Thank you for the "kudos" and for your kind words.

See you in other posts!

Regards,
fskilnik.
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AD1511133
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In the figure above, the length of segment xz is 24. What is the circu 31 Jan 2021, 10:07
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Can you please explain how you got 6/5?

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In the figure above, the length of segment xz is 24. What is the circu 31 Jan 2021, 14:11
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AD1511133
Can you please explain how you got 6/5?

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he has used the area of triangle formula,
First case area of traingle XYW,
= 1/2 * (base) * (altitude)
= 1/2*(WY)*(XZ)
= 1/2*(2r)*(24)
= 24r

Second case area of triangle WXY (same triangle but think W is the apex of the traingle)
= 1/2 * (base) * (altitude)
= 1/2*(XY)*(WX)
= 1/2*(XY)*(40)
= 20XY

Since both are essentially the same traingles, equating these two
24r=20.XY,
or, \(XY=\frac{24}{20}r = \frac{6}{5}r\)

Hope this helps.
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In the figure above, the length of segment xz is 24. What is the circu 31 Jan 2021, 20:25
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We just need to figure out that the triangles XYZ and XWZ are similar triangles. Each statement would give you dimensions of one of the triangles (applying Pythagoras), which would be enough to find the other one.

Hence, D.
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In the figure above, the length of segment xz is 24. What is the circu 01 Feb 2021, 07:11
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Each piece of info is sufficient on its own...

Rule: The altitude of conjoined triangles, inscribed in a semicircle, is the Geometric Mean of the individual legs that forms the circles diameter.

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In the figure above, the length of segment xz is 24. What is the circu 11 Feb 2021, 02:57
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No Need to solve. We need to use the following concepts to see if we can find the circumference: pi * D (D = wy)

- Since wy is the diameter, angle at X is 90 degrees.
- We can use area of triangle to form equations: 1/2 * wx * xy = 1/2 * xz * wy.
- Since we have right angle triangles, we can get can write wy*wy = wx*wx + xy*xy.

Now, we are given xz and in each of the statements, either wx or xy is given. Hence we can form an equation with 1 unknown using the above stated concepts. Hence (D).
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In the figure above, the length of segment xz is 24. What is the circu 27 Mar 2021, 14:11
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aaditya005
No Need to solve. We need to use the following concepts to see if we can find the circumference: pi * D (D = wy)

- Since wy is the diameter, angle at X is 90 degrees.
- We can use area of triangle to form equations: 1/2 * wx * xy = 1/2 * xz * wy.
- Since we have right angle triangles, we can get can write wy*wy = wx*wx + xy*xy.

Now, we are given xz and in each of the statements, either wx or xy is given. Hence we can form an equation with 1 unknown using the above stated concepts. Hence (D).
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I am just trying to satisfy my curiosity here. Wondering what I did wrong.

In the figure above, the length of segment xz is 24. What is the circumference of the circle with diameter wy?

(1) The length of segment wx is 40.
XWZ is a 3,4,5 triangle

XW = 5
WZ = 4
XZ = 3
YZ = unknown

5/4 = YZ + 4 / 5 --> 4YZ + 16 = 1 --> 4YZ = -15???

(2) The length of segment xy is 30.

Similar approach.

5/4 = wz + 3 / 5

What did I do wrong insofar as setting up the ratio?
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In the figure above, the length of segment xz is 24. What is the circu 23 Apr 2023, 09:24
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Can someone solve the answer with numbers? All the answer explanations are confusing with variables as answer choices.
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