A circle is circumscribed around a square and inscribed in a

Question

A circle is circumscribed around a square and inscribed in a larger square. A point inside the larger square is chosen at random. Which of the following best approximates the probability that this point is inside the circle but outside the square inscribed in the circle?

(A) 28% (B) 31% (C) 35% (D) 39% (E) 43%

sgrover · Answer

Let,
radius of circle -- r
diagonal of inside square - 2r, side = sqrt(2)*r
side of larger square - 2r

Prob = (pi*r^2 - 2^r^2)/4r^2 = 28% (A)

ps_dahiya · Answer

Let radius of circle = r
Area of circle = PI*r^2
Total Area (Area of outer square) = (2r)*(2r)
Area of inner circle = (SQRT(2)*r)^2 = 2r^2

Prob = (PI*r^2 - 2r^2)/4r^2 = (PI-2)/4 = 28% approx.

alimad · Answer

A circle is circumscribed around a square and inscribed in a larger square. A point inside the larger square is chosen at random. Which of the following best approximates the probability that this point is inside the circle but outside the square inscribed in the circle? 

(A) 28% (B) 31% (C) 35% (D) 39% (E) 43%

If you look at the answers you'd notice that only (A) when subtracted from 100 would result in an amount equally divided by 4 ( 4 quadrants of a square) = 100 - 28 = 72 /4 = 18. I used this as a short cut to estimate my answer. 

That's the shortest way I could find the answer. What do you guys think??

ghantark · Answer

I'll Go with A.
Just curious, where did you get this question from. I took GMAT in 2000 and remember seeing something very similar.
-Regards

kevincan · Answer

I make them up. I took the GMAT 17 years ago. It's nice to know that sometimes I am on the same wavelength as the exam writers. The main thing, though, is to hone your skills!

kevincan · Answer

A circle is circumscribed around a square and inscribed in a larger square. A point inside the larger square is chosen at random. Which of the following best approximates the probability that this point is inside the circle but outside the square inscribed in the circle?

 (A) 28% (B) 31% (C) 35% (D) 39% (E) 43%

haas_mba07 · Answer

A. 28%

Let side of inner square = a
Area of inner square = a^2

Diameter of circle = a x sqrt(2)
Radius = a x sqrt(2) /2

Area of circle = pi x a^2/2 = 22a^2/7x2 = 11a^2/7

Area of circle not part of inner square = 11a^2/7 - a^2 = 4a^2/7

Side of outer Square = diameter of circle = a x sqrt(2) = 2a^2

Prob(Success) = Area of inner circle not part of Square/Area of outer square 
= (4a^2/7)/(2a^2) = 2/7 = 28.5%

Answer: A.

cicerone · Answer

Answer is A.
Infact the exact answer will be 28.56...%

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A circle is circumscribed around a square and inscribed in a

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards