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 a square is inscribed in the outermost circle, 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 Similar questions: https://gmatclub.com/forum/there-are-5- ... 23195.html

nick1816 · Answer

Diagonal of the square = Diameter of the innermost circle = √2*√(32) = 8

Diameter of the outermost circle = 8+2*(4*1.25) = 18

Diagonal of the square inscribed in the outermost circle = 18

Area  = \frac{18^2}{2} = 162

ArunSharma12 · Answer

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 a square is inscribed in the outermost circle, 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.

A. 524 sq. cm.
B. 424 sq. cm.
C. 324 sq. cm.
D. 162 sq. cm.
E. 160 sq. cm.

innermost square diameter =  \sqrt{32}*\sqrt{2}  =  \sqrt{64}=8 
radius of innermost circle = 4
radius of outermost circle =  4 + 1.25 	imes 4  = 9
diameter of bigger square =  \sqrt{2}a  = 18
side of bigger square, a =  \frac{18}{\sqrt{2}} 
area of bigger square =  (\frac{18}{\sqrt{2}})^2  =  (\frac{18*18}{2})  = 162
Ans: D

unraveled · Answer

Image
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 a square is inscribed in the outermost circle, 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.

Side of square shown in image, a =  \sqrt{32} 
Diameter of innermost circle = Diagonal of innermost square =  \sqrt{2}*a  =  \sqrt{2} * \sqrt{32}  = 8 cm

Increment in diameter of outermost circle = 1.25*4*2 = 10 cm
Diameter of outermost circle = 8 + 10 = 18 cm
Again Diameter of outermost circle = Diagonal of outermost square =  \sqrt{2}*a'  = 18 
 a' = 9\sqrt{2}

Area of outermost square =  a'^2  =  (9\sqrt{2})^2  = 162 sq. cm

Answer D.

freedom128 · Answer

The diagonal of the square inscribed in innermost circle = the diameter of the innermost circle:
Side = √32
--> Diagonal = √32 * √2 = 8 cm

The circles are spaced at 1.25 cm, so the distance between innermost and outermost circles = 1.25 * 4 = 5 cm. 
--> The diameter of the outermost circle = 5 cm + diagonal of inscribed square + 5cm = 18 cm

The diagonal of the square that needs to be inscribed in outermost circle = the diameter of the outermost circle:
D √2 = 18 --> D = 9 √2 cm
Area = 9 √2 * 9 √2 = 162 sq. cm

FINAL ANSWER IS (D) 162 sq.cm.

Posted from my mobile device

exc4libur · Answer

diagonal inner sqr is the inner circ's diameter
sqr's diagonal ratio is side√2 = √32√2 = √64 = 8
circ's diameter = 8, radius = 4
radius of outermost circ is 4 + 1.25(4) = 9
diam of outer circ is diagonal of large sqr
18=y√2, y=18√2/2=9√2
area large sqr = 81*2 = 162

ans (D)

ashwink · Answer

The diagonal of the given square (inscribed in inner circle) is the diameter of the innermost circle:

Side=√32, hence Diagonal = √32 * √2 = 8cm

Circles're spaced 1.25cm, hence total distance from inside to outside = 1.25 * 4 = 5cm

Diameter of outmost circle = 5cm + diameter of innermost circle + 5cm = 18 cms

This is same as the diagonal of the square inscribed in outermost circle, thus side of that square = a√2 = 9√2
Area = 9√2 * 9√2 = 162 sq. cm

Thus, D.

AnirudhaS · Answer

diagonal of small square =  side.\sqrt{2} = 8 
radius of smallest circle =  \frac{8}{2} = 4 
radius of largest circle =  4 + (1.25*5) = 9 
diagonal of largest circle =  2*9 = 18 
area of largest square =  \frac{diagonal^2}{2} = \frac{18^2}{2} = 162

Answer:  D

AyushAgrawal1005 · Answer

Is the solution D) 162 sq cm?

chaitralirr · Answer

info given is that the distance between circles is 1.25 four circles then the distance becomes 5 cm on one side if we add 5 from other side too it becomes 10.

The side of square is root 32 then the diagonal will be S root 2 therefore diagonal length is 8

total diagonal length of the circle inscribed in the outer circle will be 10 +8= 18

if diagonal is 8 the side will be 9 root 2 using Pythagoras. square area will be (9 root 2) 2= 162

IMO D

ScottTargetTestPrep · Answer

Recall that the diagonal of a square that is inscribed in a circle is the diameter of the circle. Since the innermost inscribed square has a side length of √32, its diagonal is √32 x √2 = √64 = 8, which is also the diameter of the innermost circle. Therefore, the diameter of the outermost circle is 8 + 1.25 x 8 = 8 + 10 = 18, which is also the diagonal of the outermost inscribed square. Since the diagonal of the outermost inscribed square is 18, its side length is 18/√2 and its area therefore is (18/√2)^2 = 324/2 = 162 sq. cm.

Answer: D

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

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

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

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