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

 It is currently 24 Sep 2018, 05:11

### 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

# In the figure, vertex Q of square OPQR is on circle with centre O. If

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49385
In the figure, vertex Q of square OPQR is on circle with centre O. If  [#permalink]

### Show Tags

19 Jul 2018, 21:55
00:00

Difficulty:

15% (low)

Question Stats:

84% (00:48) correct 16% (01:21) wrong based on 31 sessions

### HideShow timer Statistics

In the figure, vertex Q of square OPQR is on circle with centre O. If the area of the square is 8, what is the area of the circle?

A. $$8 \pi$$

B. $$8 \sqrt{2} \pi$$

C. $$16 \pi$$

D. $$32 \pi$$

E. $$64 \pi$$

Attachment:

figure 11.jpg [ 14.68 KiB | Viewed 367 times ]

_________________
RC Moderator
Status: Perfecting myself for GMAT
Joined: 22 May 2017
Posts: 640
Concentration: Nonprofit
Schools: Haas '21
GPA: 4
WE: Engineering (Computer Software)
In the figure, vertex Q of square OPQR is on circle with centre O. If  [#permalink]

### Show Tags

19 Jul 2018, 22:08
1
vertex Q of square OPQR is on circle with centre O

=> radius of the circle = diagonal of the square

area of square is $$a^2$$ = 8

=> a = $$2\sqrt{2}$$

diagonal of the square = $$\sqrt{a^2 + a^2}$$

=> diagonal = $$\sqrt{8 + 8}$$

=> diagonal = $$\sqrt{16}$$ = 4

=> radius of the circle = 4

=> Area of the circle = $$4^2 \pi$$ = $$16 \pi$$

Hence option C
_________________

If you like my post press kudos +1

New - RC Butler - 2 RC's everyday

Tag me in RC questions if you need help. Please provide your analysis of the question in the post along with the tag.

Senior Manager
Joined: 22 Feb 2018
Posts: 326
Re: In the figure, vertex Q of square OPQR is on circle with centre O. If  [#permalink]

### Show Tags

19 Jul 2018, 23:28
Bunuel wrote:

In the figure, vertex Q of square OPQR is on circle with centre O. If the area of the square is 8, what is the area of the circle?

A. $$8 \pi$$

B. $$8 \sqrt{2} \pi$$

C. $$16 \pi$$

D. $$32 \pi$$

E. $$64 \pi$$

Attachment:
figure 11.jpg

OA:C
As per figure,Diagonal ($$diagonal_{square}$$) of Square is equal to Radius of circle.
Area of Square = $$\frac{1}{2}*Diagonal_{square}^2=8$$
$$Diagonal_{square}^2=16$$;
As $$Diagonal_{square}$$ = Radius of circle
$${Radius}^2 =16$$
Area of circle= $$\pi *$$ $${Radius}^2=\pi*16$$
_________________

Good, good Let the kudos flow through you

Director
Joined: 31 Oct 2013
Posts: 582
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: In the figure, vertex Q of square OPQR is on circle with centre O. If  [#permalink]

### Show Tags

19 Jul 2018, 23:32
Bunuel wrote:

In the figure, vertex Q of square OPQR is on circle with centre O. If the area of the square is 8, what is the area of the circle?

A. $$8 \pi$$

B. $$8 \sqrt{2} \pi$$

C. $$16 \pi$$

D. $$32 \pi$$

E. $$64 \pi$$

Attachment:
figure 11.jpg

Note :

Area of the square = 1/2 $$(d)^2$$

Given

1/2*$$(d)^2$$ = 8

d = 4.

Now diagonal has become the radius of the of circle.

Area of the circle = pie * $$r^2$$

= 16 pie.

SC Moderator
Joined: 30 Jan 2015
Posts: 596
Location: India
Concentration: Operations, Marketing
GPA: 3.5
Re: In the figure, vertex Q of square OPQR is on circle with centre O. If  [#permalink]

### Show Tags

20 Jul 2018, 02:13
+1 for C.

Area of the Square = L^2 = 8
L = 2 root 2

Diagonal of the Square = D
D^2 = (2root2)^2 + (2root2)^2
D^2 = 16
D = 4 = Radius of the circle

Area of the Circle = (Radius)^2*pi = (4^2)pi = 16 pi

Hence, C.
_________________

The few, the fearless !

Thanks

Re: In the figure, vertex Q of square OPQR is on circle with centre O. If &nbs [#permalink] 20 Jul 2018, 02:13
Display posts from previous: Sort by

# In the figure, vertex Q of square OPQR is on circle with centre O. If

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.