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

 It is currently 23 Jan 2019, 05:39

### 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 rectangular PQRS above, arcs QT and RT are quarter circles with cen

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52430
In rectangular PQRS above, arcs QT and RT are quarter circles with cen  [#permalink]

### Show Tags

21 Nov 2017, 22:28
00:00

Difficulty:

35% (medium)

Question Stats:

87% (00:56) correct 13% (01:12) wrong based on 27 sessions

### HideShow timer Statistics

In rectangular PQRS above, arcs QT and RT are quarter circles with center P and S respectively. If the radius of each circle is 1, what is the area of the shaded region?

(A) 1 – π/4
(B) 2 – π/2
(C) 2 – π/4
(D) π/4
(E) 2/3

Attachment:

2017-11-22_1022_002.png [ 4.01 KiB | Viewed 636 times ]

_________________
Manager
Joined: 05 Dec 2016
Posts: 243
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: In rectangular PQRS above, arcs QT and RT are quarter circles with cen  [#permalink]

### Show Tags

21 Nov 2017, 23:30
2 quarter circles equal to 1 semi-circle, thus area would be 1/2 * p * r^2=1/2*p*1^2=p/2
area of rectangle = 2*1=2
are of shaded region = 2 - p/2
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: In rectangular PQRS above, arcs QT and RT are quarter circles with cen  [#permalink]

### Show Tags

27 Nov 2017, 11:40
Bunuel wrote:

In rectangular PQRS above, arcs QT and RT are quarter circles with center P and S respectively. If the radius of each circle is 1, what is the area of the shaded region?

(A) 1 – π/4
(B) 2 – π/2
(C) 2 – π/4
(D) π/4
(E) 2/3

Attachment:
2017-11-22_1022_002.png

Since the radius of each circle is 1, the combined area of the two quarter circles is:

1/4 x π x 1^2 + 1/4 x π x 1^2 = (1/4)π + (1/4)π = (1/2)π

We also see that the width of the rectangle is 1 and the length is 2, so the area is 2.

Thus, the area of the shaded region is 2 - (1/2)π.

_________________

Jeffery Miller

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

Re: In rectangular PQRS above, arcs QT and RT are quarter circles with cen &nbs [#permalink] 27 Nov 2017, 11:40
Display posts from previous: Sort by