In the figure above, the length of segment xz is 24. What is the circu

Question

https://gmatclub.com/forum/download/file.php?id=43179 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. circles3.PNG Untitled.png

sumit411 · Answer

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 Thank you = Kudos

fskilnik · Answer

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.

Mani2879 · Answer

Hi
Thanks a lot for the superb explanation !!

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fskilnik · Answer

Hi, Mani!

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

See you in other posts!

Regards,
fskilnik.

AD1511133 · Answer

Can you please explain how you got 6/5?

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AnirudhaS · Answer

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.

MBAB123 · Answer

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.

Hence, D.

princewilson · Answer

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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aaditya005 · Answer

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).

CEdward · Answer

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?

gmat190010 · Answer

Can someone solve the answer with numbers? All the answer explanations are confusing with variables as answer choices.

In the figure above, the length of segment xz is 24. What is the circu

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