There are 5 concentric circles that are spaced equally from each other

Question

https://gmatclub.com/forum/download/file.php?id=54366 There are 5 concentric circles that are spaced equally from each other by 1.25 cms as shown above. The innermost circle has a square of side √(32) cm inscribed in it. If the outermost circle is inscribed in a square, what is the area of that square? A. 524 sq. cm. B. 424 sq. cm. C. 324 sq. cm. D. 162 sq. cm. E. 160 sq. cm. Project PS Butler Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS Are You Up For the Challenge: 700 Level Questions mensuration-16.png

yashikaaggarwal · Answer

Using Pythagoras theorem
(Diagonal of square)^2 = (√32)^2 + (√32)^2
D^2=64 =>>>> D=8 now the radius of inner circle is 4
Now 5 concentric circle having space of 1.25 in between them.
So from the centre of inner circle+4*the space of concentric circles =
4+4(1.25)=9
The diameter of outer circle is 18. Which is also the value of the side of the outer square whose sides are tangent to the circle.
18^2=324
Answer should be C

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gopalsdestiny · Answer

Dia of outer circle is 18.
As we need area of square in outer most circle, we need square of the side.
So 18^2 = 2S^2 
324 = 2S^2
Or S^2 = 162.
Option D

GMATWhizTeam · Answer

Solution 
 • Diameter of the inner most circle = Diagonal of the square inscribed in it  = \sqrt{2}*\sqrt{32} = 8cms 
 o Radius of the inner circle  = 4cms  
• Since, each concentric circle is 1.25cms apart from each other and there are 5 concentric circles.
 o So, radius of the outer most circle  = 4 + 1.25*4 = 4 + 5 = 9cms  
• As shown in below diagram, the outer most circle is inscribed in a square.
 https://www.dropbox.com/s/j1itslcjwc0pz7r/Circle_in_square.png?dl=1 
 o So, side of square = diameter of the outermost circle = 2*9 = 18cms 
• Thus, the area of the square  = 18^2 = 324  sq. cm. 
 I guess there is a typo in answer options.

poojakhanduja3017 · Answer

I Feel there's something wrong(typo) with the options. The answer should be 324 cm^2

The side of the inner square is \sqrt{32}. So, Diagonal of Square, also the diameter of inner circle is : \sqrt{ ( ( 32})^2 + (\sqrt{32})^2 )   = 8
Now 8 is the diameter.

We can see four gaps of 1.25 on each of this circle. Adding 1.25*8 = 10 to 8 gives us the diameter of the outermost circle as 18.

This is also the side of the outer square.

Hence the answer is 18^2 = 324.

Bunuel · Answer

Edited the typo in the options. Thank you.

sambitspm · Answer

The question is straight-forward.

The square side is √32
This means the diagonal is 8 units.
and there are total of 4 concentric circles.

We know that center of inscribed and circle passing through vertices of the square coincides with the midpoint of the diagonal. 
Hence the radius of first circle = 4 unit
The radius of outermost circle = 4+ 4*1.25 => 9 units.

Thus the side of square inscribing the outermost circle will be 18 units
Area -> 324 sq.units

There are 5 concentric circles that are spaced equally from each other

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There are 5 concentric circles that are spaced equally from each other

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