GEOMETRY

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CSASHISHPANDAY: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Sat Jun 18, 2011 9:50 pmFollowed by: 3 members; Location: New Delhi; Thanked: 35 times; GMAT Score:800

by CSASHISHPANDAY » Wed Sep 19, 2012 10:32 pm

In the figure attached, 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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Source: Beat The GMAT — Problem Solving | Wed Sep 19, 2012 10:32 pm

KapilKapoor: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Sat Aug 25, 2012 11:50 pm; Thanked: 2 times

by KapilKapoor » Wed Sep 19, 2012 10:50 pm

Hi,

As wy is diameter (d), triangle wxy is right angled triangle. so

1/2* wy * xz = 1/2 * wx * xy
1/2* d * 24 = 1/2 * wx * xy ----1

Moreover d = wz + zy ----2

Stmt 1: wx = 40
=> wz = 32 (sqrt(40^2-24^2))
Assume xy = p
Putting values in equ(2)
32 + sqrt(p^2-24^2) = d ----3
Putting values in equ(1)
d/2*24 = 1/2*40*p ----4

By solving 3,4 we can get p,d.
d=50
Hence Stmt 1 is sufficient.

In the similar way Stmt 2 is also sufficient.

Hence the answer is D

Thanks & Regards,
Kapil

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anjalimanas: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Fri Apr 27, 2012 1:49 am

by anjalimanas » Wed Nov 21, 2012 1:21 am

Is there an easier / faster way to solve this problem. as i think it is a DS problem. thanks

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Bill@VeritasPrep: GMAT Instructor; Posts: 1248; Joined: Thu Mar 29, 2012 2:57 pmFollowed by: 192 members; Location: Everywhere; Thanked: 503 times; GMAT Score:780

by Bill@VeritasPrep » Wed Nov 21, 2012 9:43 am

anjalimanas wrote:Is there an easier / faster way to solve this problem. as i think it is a DS problem. thanks

If you recognize that you can set up the Pythagorean theorem 3 times (once for each of the smaller triangles and once for the big triangle), then you should see that you're left with two unknowns: WZ and ZY. Since each statement fills in one of your unknowns, you can then solve for the other and find the diameter. You don't actually have to do the math.

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