geometry tough questn

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sukh: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Tue Nov 09, 2010 11:33 pm

by sukh » Tue Aug 23, 2011 8:10 am

ABCDEFGH is a cube. If the length of the diagonals DF, AG & CE are equal to sides of a triangle , then the circumradius of that triangle would be
a)equal to sides of the cube
b)under-root 3 times the sides of the cube
c) 1/ under-root 3 times the side of the cube
d) Indeterminate

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Source: Beat The GMAT — Quantitative Reasoning | Tue Aug 23, 2011 8:10 am

amit.phatak: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Fri Apr 22, 2011 10:51 pm

by amit.phatak » Tue Aug 23, 2011 12:20 pm

I think it is equal to side of the cube
Ans : A

Explanation :
lets say Side of the cube = a
diagonal = sqrt(3) * a
for equilateral triangle (with sides = DF, AG & CE) each side = sqrt(3) * a
circumradius of equilateral triangle = 2/3 * sqrt(3)/2 * side = 2/3 * sqrt(3)/2 * sqrt(3) * a

Therefore, circumradius = a = side of the cube.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Aug 24, 2011 9:51 am

sukh wrote:ABCDEFGH is a cube. If the length of the diagonals DF, AG & CE are equal to sides of a triangle , then the circumradius of that triangle would be
a)equal to sides of the cube
b)under-root 3 times the sides of the cube
c) 1/ under-root 3 times the side of the cube
d) Indeterminate

Amit is correct - the answer is A.

Aside: I should point out that, on the GMAT, you are not required to know the definition of "circumradius."

The question is also somewhat confusing to follow, and the 4 answer choices indicate that it is not a true GMAT question.

I mention all of this so that students do not become overly concerned if they didn't get the correct answer.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Sun Aug 28, 2011 9:56 am

sukh wrote:ABCDEFGH is a cube. If the length of the diagonals DF, AG & CE are equal to sides of a triangle , then the circumradius of that triangle would be
a)equal to sides of the cube
b)under-root 3 times the sides of the cube
c) 1/ under-root 3 times the side of the cube
d) Indeterminate

Length of the diagonals of a cube is : âˆš3 * a

Sides of the triangle are equal ( Derived from the following statement - diagonals DF, AG & CE are equal to sides of a triangle )

Now Sides of a triangle is âˆš3 * a

We know circumradius of an equilateral triangle is : (âˆš3/3)* sides of an equilateral triangle.

So circumradius of the triangle is :

(âˆš3/3) * âˆš3 * a => a

So option a follows !!

Abhishek

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