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

 It is currently 23 Jan 2019, 06:19

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

Events & Promotions

Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
• Free GMAT Number Properties Webinar

January 27, 2019

January 27, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.

If a square is inscribed in a circle of radius r as shown above, then

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52431
If a square is inscribed in a circle of radius r as shown above, then  [#permalink]

Show Tags

21 Nov 2017, 22:19
00:00

Difficulty:

25% (medium)

Question Stats:

84% (01:20) correct 16% (01:25) wrong based on 52 sessions

HideShow timer Statistics

If a square is inscribed in a circle of radius r as shown above, then the area of the square region is

(A) r^2/2π
(B) πr^2/2
(C) πr^2
(D) r^2
(E) 2r^2

Attachment:

2017-11-21_1033.png [ 4.39 KiB | Viewed 6612 times ]

_________________
Current Student
Joined: 18 Aug 2016
Posts: 623
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: If a square is inscribed in a circle of radius r as shown above, then  [#permalink]

Show Tags

21 Nov 2017, 22:32
Bunuel wrote:

If a square is inscribed in a circle of radius r as shown above, then the area of the square region is

(A) r^2/2π
(B) πr^2/2
(C) πr^2
(D) r^2
(E) 2r^2

Attachment:
2017-11-21_1033.png

Diagonal of Square = 2r = $$x\sqrt{2}$$
Area of square = $$(\sqrt{2}r)^2$$
=2r^2

E
_________________

We must try to achieve the best within us

Thanks
Luckisnoexcuse

Senior SC Moderator
Joined: 22 May 2016
Posts: 2368
If a square is inscribed in a circle of radius r as shown above, then  [#permalink]

Show Tags

26 Nov 2017, 21:43
Bunuel wrote:

If a square is inscribed in a circle of radius r as shown above, then the area of the square region is

(A) r^2/2π
(B) πr^2/2
(C) πr^2
(D) r^2
(E) 2r^2

Attachment:
2017-11-21_1033.png

Derive side length of square from its diagonal.

Diagonal, d, of square = $$2r$$

Side, s, of square*:

$$s\sqrt{2} = d$$

$$s = \frac{d}{\sqrt{2}}$$

$$s=\frac{2r}{\sqrt{2}}$$ *$$\frac{\sqrt{2}}{\sqrt{2}}$$

$$s= \frac{2r\sqrt{2}}{2}=r\sqrt{2}$$

Area of square = $$s^2$$

A= $$(r\sqrt{2})^2 = 2r^2$$

* derived from
$$s^2 + s^2 = d^2$$
$$2s^2 = d^2$$
$$\sqrt{2}*\sqrt{s^2} = \sqrt{d^2}$$
$$s\sqrt{2} = d$$
$$s = \frac{d}{\sqrt{2}}$$

_________________

Life’s like a movie. Write your own ending.

Kermit the Frog

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4612
Location: United States (CA)
Re: If a square is inscribed in a circle of radius r as shown above, then  [#permalink]

Show Tags

29 Nov 2017, 09:57
Bunuel wrote:

If a square is inscribed in a circle of radius r as shown above, then the area of the square region is

(A) r^2/2π
(B) πr^2/2
(C) πr^2
(D) r^2
(E) 2r^2

Attachment:
2017-11-21_1033.png

Since the radius is r, the circle’s diameter = diagonal of square = 2r.

Since diagonal = side√2:

2r = side√2

2r/√2 = side

Thus, area of the square = (2r/√2)^2 = 4r^2/2= 2r^2.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If a square is inscribed in a circle of radius r as shown above, then &nbs [#permalink] 29 Nov 2017, 09:57
Display posts from previous: Sort by