GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Oct 2019, 21:45

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A circle is inscribed in a square, then a square is inscribed in this

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58453
A circle is inscribed in a square, then a square is inscribed in this  [#permalink]

### Show Tags

24 Mar 2019, 22:48
00:00

Difficulty:

55% (hard)

Question Stats:

52% (02:37) correct 48% (02:12) wrong based on 23 sessions

### HideShow timer Statistics

A circle is inscribed in a square, then a square is inscribed in this circle, and finally, a circle is inscribed in this square. What is the ratio of the area of the smaller circle to the area of the larger square?

(A) $$\frac{\pi}{16}$$

(B) $$\frac{\pi}{8}$$

(C) $$\frac{\pi}{316}$$

(D) $$\frac{\pi}{4}$$

(E) $$\frac{\pi}{2}$$

_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5020
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A circle is inscribed in a square, then a square is inscribed in this  [#permalink]

### Show Tags

25 Mar 2019, 00:46
1
Bunuel wrote:
A circle is inscribed in a square, then a square is inscribed in this circle, and finally, a circle is inscribed in this square. What is the ratio of the area of the smaller circle to the area of the larger square?

(A) $$\frac{\pi}{16}$$

(B) $$\frac{\pi}{8}$$

(C) $$\frac{\pi}{316}$$

(D) $$\frac{\pi}{4}$$

(E) $$\frac{\pi}{2}$$

draw figure a per given description
let side of large square = 8
8 will be equal to diameter of large circle = radius = 4
and diameter of circle = diagonal of small square = 8 = s√2 ; s= 4√2
4√2 = diameter of small circle so ; radis = 2√2
area of small circle (2√2)^2 *pi = 8pi
and large square area = 8^2 = 64 so ratio
8pi/64 = pi/8 IMO B
Senior Manager
Joined: 18 Jan 2018
Posts: 307
Location: India
Concentration: General Management, Healthcare
Schools: Booth '22, ISB '21, IIMB
GPA: 3.87
WE: Design (Manufacturing)
A circle is inscribed in a square, then a square is inscribed in this  [#permalink]

### Show Tags

25 Mar 2019, 23:23
1
let x be the side of the big square S1 => diagonal of S1 = diameter of inscribed circle C1 = $$\frac{x}{(\sqrt{2})}$$
side of inscribed square in CircleC1,S2 => diameter of Circle C1 =$$\frac{x}{(\sqrt{2})}$$
radius of CircleC2 inscribed in S2 ,C2 => Side of S2 =$$\frac{x}{2(\sqrt{2})}$$

Area of Small circle C2 = $$\pi(\frac{x}{2(\sqrt{2})})^2$$
Area of Square S1 = $$x^2$$

Ratio = Area of C2/ Area of S1
= $$\frac{\frac{\Pi x^2}{8}}{ x^2}$$
= $$\frac{\Pi}{8}$$ =option B
A circle is inscribed in a square, then a square is inscribed in this   [#permalink] 25 Mar 2019, 23:23
Display posts from previous: Sort by