It is currently 17 Dec 2017, 15:16

Close

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
Your Progress

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

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

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the figure above, the circles touch each other and touch the sides

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42652

Kudos [?]: 135981 [0], given: 12719

In the figure above, the circles touch each other and touch the sides [#permalink]

Show Tags

New post 16 Nov 2017, 21:50
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

82% (00:46) correct 18% (01:03) wrong based on 32 sessions

HideShow timer Statistics

Image
In the figure above, the circles touch each other and touch the sides of the rectangle at the lettered points shown. The radius of each circle is 1. Of the following, which is the best approximation to the area of the shaded region?

(A) 6
(B) 4
(C) 3
(D) 2
(E) 1

[Reveal] Spoiler:
Attachment:
2017-11-17_0946.png
2017-11-17_0946.png [ 7.88 KiB | Viewed 651 times ]
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135981 [0], given: 12719

Director
Director
User avatar
P
Joined: 18 Aug 2016
Posts: 598

Kudos [?]: 181 [0], given: 139

GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: In the figure above, the circles touch each other and touch the sides [#permalink]

Show Tags

New post 16 Nov 2017, 23:00
Bunuel wrote:
Image
In the figure above, the circles touch each other and touch the sides of the rectangle at the lettered points shown. The radius of each circle is 1. Of the following, which is the best approximation to the area of the shaded region?

(A) 6
(B) 4
(C) 3
(D) 2
(E) 1

[Reveal] Spoiler:
Attachment:
2017-11-17_0946.png


Length of BC = BF = 2

Area of square BCFE = 4

Area of Circle (unshaded part which overlaps Square) = 2 * 1/2 * pie * r^2 = pie

Shaded region area = 4- pie = ~1

E
_________________

We must try to achieve the best within us


Thanks
Luckisnoexcuse

Kudos [?]: 181 [0], given: 139

VP
VP
avatar
P
Joined: 22 May 2016
Posts: 1140

Kudos [?]: 408 [0], given: 648

Re: In the figure above, the circles touch each other and touch the sides [#permalink]

Show Tags

New post 17 Nov 2017, 13:39
Bunuel wrote:
Image
In the figure above, the circles touch each other and touch the sides of the rectangle at the lettered points shown. The radius of each circle is 1. Of the following, which is the best approximation to the area of the shaded region?

(A) 6
(B) 4
(C) 3
(D) 2
(E) 1

Attachment:
mmmm.png
mmmm.png [ 17.04 KiB | Viewed 305 times ]

The area of the shaded region equals
(Rectangle area) - (circles' area)/2

Rectangle area: L * W
The circles' radii completely span the length and width of the rectangle
Radius of one circle = 1

LENGTH = 4 radii = 4
WIDTH = 2 radii = 2
Rectangle's area = 4 * 2 = 8

Area of both circles, where r = 1: \(2(πr^2) = 2π\)

Area of shaded region
The "extra" area between the rectangle's edges and the circles' edges consists of 8 equal regions. See diagram.
Four of 8 are shaded = 1/2 of extra is shaded.

To get total extra area, subtract circles' area from rectangle's area.
To get half the total extra area (shaded region), subtract circles' area from rectangle's area and divide by 2.

Half of extra area = area of shaded region:

(rectangle area, R) - (circles' area, C) divided by 2:

\(\frac{(R - C)}{2}\)

\(\frac{(8 - 2π)}{2}\)

\(π\approx{3.14}\)

\(\frac{(8 - 6.28)}{2}= \frac{1.72}{2} = .86\)

\(0.86\approx{1}\)

Answer E

Kudos [?]: 408 [0], given: 648

Manager
Manager
User avatar
S
Joined: 14 Sep 2016
Posts: 57

Kudos [?]: 14 [0], given: 119

Concentration: Finance, Economics
Re: In the figure above, the circles touch each other and touch the sides [#permalink]

Show Tags

New post 17 Nov 2017, 15:09
Bunuel wrote:
Image
In the figure above, the circles touch each other and touch the sides of the rectangle at the lettered points shown. The radius of each circle is 1. Of the following, which is the best approximation to the area of the shaded region?

(A) 6
(B) 4
(C) 3
(D) 2
(E) 1

[Reveal] Spoiler:
Attachment:
The attachment 2017-11-17_0946.png is no longer available


Inside square has a an area of 4.
Subtract 2 half pokeballs from 4, so subtract one full pokeball.
Square Area 4 - Pokeball area of 3.1 = .9 shaded or E.
Attachments

poke.png
poke.png [ 17.4 KiB | Viewed 274 times ]

Kudos [?]: 14 [0], given: 119

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1945

Kudos [?]: 1024 [0], given: 3

Location: United States (CA)
Re: In the figure above, the circles touch each other and touch the sides [#permalink]

Show Tags

New post 20 Nov 2017, 11:30
Bunuel wrote:
Image
In the figure above, the circles touch each other and touch the sides of the rectangle at the lettered points shown. The radius of each circle is 1. Of the following, which is the best approximation to the area of the shaded region?

(A) 6
(B) 4
(C) 3
(D) 2
(E) 1

[Reveal] Spoiler:
Attachment:
2017-11-17_0946.png


We can see that the area of the shaded region is half the area of the region inside of the rectangle but outside of the two circles. Thus, the area of the shaded region is half the difference between the area of the rectangle and the total area of the two circles.

Area of the rectangle = 2 x 4 = 8

Area of a circle = π x 1^2 = π

Area of shaded region = ½ x (8 - 2π) = 4 - π

Since π is approximately 3.14, the area of the shaded region ≈ 4 - 3.14 = 0.86 ≈ 1.

Answer: E
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Kudos [?]: 1024 [0], given: 3

Re: In the figure above, the circles touch each other and touch the sides   [#permalink] 20 Nov 2017, 11:30
Display posts from previous: Sort by

In the figure above, the circles touch each other and touch the sides

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.