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

 It is currently 23 Jan 2019, 10:40

### 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.

# In the figure above, a circle with center O touches three sides of a

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52431
In the figure above, a circle with center O touches three sides of a  [#permalink]

### Show Tags

21 Nov 2017, 22:09
00:00

Difficulty:

15% (low)

Question Stats:

83% (00:55) correct 17% (01:22) wrong based on 51 sessions

### HideShow timer Statistics

In the figure above, a circle with center O touches three sides of a rectangle of length m and width n. Which of the following gives the area of the shaded region?

(A) πn^2/4
(B) mn – 2πn
(C) mn – πn^2
(D) mn – πn^2/2
(E) mn – πn^2/4

Attachment:

2017-11-21_1031.png [ 3.95 KiB | Viewed 648 times ]

_________________
Senior Manager
Joined: 08 Aug 2017
Posts: 302
Re: In the figure above, a circle with center O touches three sides of a  [#permalink]

### Show Tags

21 Nov 2017, 22:22
[(m*n)-{(3.14*(n^2)/4}]
Senior SC Moderator
Joined: 22 May 2016
Posts: 2372
In the figure above, a circle with center O touches three sides of a  [#permalink]

### Show Tags

26 Nov 2017, 20:02
Bunuel wrote:

In the figure above, a circle with center O touches three sides of a rectangle of length m and width n. Which of the following gives the area of the shaded region?

(A) πn^2/4
(B) mn – 2πn
(C) mn – πn^2
(D) mn – πn^2/2
(E) mn – πn^2/4

Attachment:
2017-11-21_1031.png

Rectangle area = mn

The radius of the circle is $$\frac{1}{2}n$$

The area of the circle is
$$\pi r^2 = \pi* (\frac{1}{2}n)^2=\frac{n^2}{4}\pi$$

(Rectangle area) - (circle area) = Shaded area

Shaded area = $$mn - \frac{n^2}{4}\pi$$

_________________

Sometimes at night I would sleep open-eyed underneath a sky dripping with stars.
I was alive then.

—Albert Camus

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4612
Location: United States (CA)
Re: In the figure above, a circle with center O touches three sides of a  [#permalink]

### Show Tags

29 Nov 2017, 09:57
Bunuel wrote:

In the figure above, a circle with center O touches three sides of a rectangle of length m and width n. Which of the following gives the area of the shaded region?

(A) πn^2/4
(B) mn – 2πn
(C) mn – πn^2
(D) mn – πn^2/2
(E) mn – πn^2/4

Attachment:
2017-11-21_1031.png

We see that the area of the shaded region is the difference between the area of the rectangle and the area of the circle. Since the width of the rectangle is n, we see that n is also the diameter of the circle. Thus, the radius of the circle is n/2.

Area of the rectangle = m x n = mn

Area of the circle = π x (n/2)^2 = π x (n^2/4) = πn^2/4

Thus, the area of the shaded region = mn - πn^2/4.

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Re: In the figure above, a circle with center O touches three sides of a &nbs [#permalink] 29 Nov 2017, 09:57
Display posts from previous: Sort by