Last visit was: 13 Nov 2024, 22:33 It is currently 13 Nov 2024, 22:33

Close

GRE Prep 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
Your Progress

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

Practice
Pays

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12188 [0]
Given Kudos: 136
Send PM
Retired Moderator
Joined: 07 Jan 2018
Posts: 739
Own Kudos [?]: 1442 [0]
Given Kudos: 93
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 29955
Own Kudos [?]: 36213 [0]
Given Kudos: 25903
Send PM
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12188 [0]
Given Kudos: 136
Send PM
Re: If each of the 4 circles above has radius 1, [#permalink]
GreenlightTestPrep wrote:
Image

If each of the 4 circles above has radius 1, what is the area of the shaded region?
A) 1 – π/4
B) 2 – π/4
C) 2 – π/2
D) 4 – π
E) 4 – 2π


Here's a different approach:

Let's place a square around just one of the circles
Image


Notice that the shaded area IN the square represents 1/4 of the TOTAL shaded area in the diagram.
Image


This means that the shaded area in THIS diagram will be the same as the TOTAL shaded area in the ORIGINAL diagram.
Image


So, let's determine the area of the shaded area in the diagram below.
Image

Each side of the square has length 2, so the area of the SQUARE = (2)(2) = 4

The circle has radius 1.
So, the area of the CIRCLE = π(radius)² = π(1)² = π

So, the area of the SHADED region = 4 - π

Answer: D

Cheers,
Brent
Retired Moderator
Joined: 07 Jan 2018
Posts: 739
Own Kudos [?]: 1442 [0]
Given Kudos: 93
Send PM
Re: If each of the 4 circles above has radius 1, [#permalink]
1
GreenlightTestPrep wrote:
GreenlightTestPrep wrote:
Image

If each of the 4 circles above has radius 1, what is the area of the shaded region?
A) 1 – π/4
B) 2 – π/4
C) 2 – π/2
D) 4 – π
E) 4 – 2π


Here's a different approach:

Let's place a square around just one of the circles
Image


Notice that the shaded area IN the square represents 1/4 of the TOTAL shaded area in the diagram.
Image


This means that the shaded area in THIS diagram will be the same as the TOTAL shaded area in the ORIGINAL diagram.
Image


So, let's determine the area of the shaded area in the diagram below.
Image

Each side of the square has length 2, so the area of the SQUARE = (2)(2) = 4

The circle has radius 1.
So, the area of the CIRCLE = π(radius)² = π(1)² = π

So, the area of the SHADED region = 4 - π

Answer: D

Cheers,
Brent

This approach would save some time

Posted from my mobile device Image
Prep Club for GRE Bot
Re: If each of the 4 circles above has radius 1, [#permalink]
Moderators:
GRE Instructor
78 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne