Geometry Problem

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pm; Thanked: 114 times; Followed by:11 members

Geometry Problem

by knight247 » Sun Jul 03, 2011 9:07 am

Two congruent triangles ABC and DEF are inscribed in two semicircles. What is the area of both the circles?
(1) Perimeter of one of the circles if 10 units
(2) BC=8 units and DF=6 units.

Don't have an OA. But I'm certain the answer is A

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Source: Beat The GMAT — Data Sufficiency | Sun Jul 03, 2011 9:07 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Sun Jul 03, 2011 11:16 pm

knight247 wrote:Two congruent triangles ABC and DEF are inscribed in two semicircles. What is the area of both the circles?
(1) Perimeter of one of the circles if 10 units
(2) BC=8 units and DF=6 units.

Statement 1: We don't have any information about the other circle.

Not Sufficient

Statement 2: BC = 8 and DF = 6 implies EF = 8 and AC = 6 as the triangles are congruent. But we don't have any necessary information to determine the area of the circle.

Not Sufficient

1 & 2 Together: Doesn't yield any new or necessary information.

Not sufficient.

The correct answer is E.

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 am; Location: pune; Thanked: 36 times; Followed by:3 members

by amit2k9 » Mon Jul 04, 2011 1:18 am

a 2r+pi*r = 10 where r = 10/5.414 approx = 1.7

nothing has been mentioned about the other circle. Not sufficient.

b ABC may or may not be right triangle.similar it is true for DEF too.
not sufficient.

a+b not sufficient.

E it is.

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BY: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Jun 21, 2011 1:47 am

by BY » Wed Jul 06, 2011 3:21 am

If statement-1 replaced as : Perimeter of triangle ABC is 10 and the statement-2 is same, then what will be the answer ?

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Wed Jul 06, 2011 3:33 am

BY wrote:If statement-1 replaced as : Perimeter of triangle ABC is 10 and the statement-2 is same, then what will be the answer ?

Then the statements will contradict each other and the question will never appear in actual GMAT or any legitimate material.

That's because from statement 2, BC = 8 and AC = 6.
Hence, perimeter of ABC will be always greater than 10.

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mirantdon: Master | Next Rank: 500 Posts; Posts: 135; Joined: Thu May 05, 2011 9:00 am; Thanked: 4 times; Followed by:1 members; GMAT Score:700

by mirantdon » Fri Jul 08, 2011 12:47 pm

+1 for A.
If the triangles are congruent then the information about the other semicircle is immaterial .
Since both the triangles will share the same base . hence the length of both these will be equal . And also any triangle within a semicircle will subtend 90 degrees . hence if the triangle are congruent we can consider this as a uniform circle

A : Statement A provides us a Circumference ,(Common base for congruent triangles) well thats enough isnt it ? SUFFICIENT

B We are not sure what side is congruent to which one
hENCE a

Kindly provide your inputs

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rishijhawar: Master | Next Rank: 500 Posts; Posts: 138; Joined: Mon Mar 14, 2011 8:24 pm; Thanked: 1 times

by rishijhawar » Sun Jul 10, 2011 2:51 am

mirantdon, the question doesn't mention that both semi-circle are part of the same circle (and thats why probably you assumed the triangles have same base). hope it helps.