GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 24 May 2020, 20:42

### 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

# In the diagram above, all the points are on a line, and the number of

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64068
In the diagram above, all the points are on a line, and the number of  [#permalink]

### Show Tags

11 Mar 2015, 03:52
1
5
00:00

Difficulty:

15% (low)

Question Stats:

85% (02:38) correct 15% (02:34) wrong based on 149 sessions

### HideShow timer Statistics

Attachment:

cpotg_img6.png [ 39.45 KiB | Viewed 2775 times ]
In the diagram above, all the points are on a line, and the number of each point indicates how many units that point is from zero. The points #1 – #6 are the centers of the six circles, and all circles pass through point zero. What is the total area of the shaded region?

A. $$12\pi$$
B. $$21\pi$$
C. $$24\pi$$
D. $$46\pi$$
E. $$48\pi$$

Kudos for a correct solution.

_________________
Manager
Status: A mind once opened never loses..!
Joined: 05 Mar 2015
Posts: 186
Location: India
MISSION : 800
WE: Design (Manufacturing)
Re: In the diagram above, all the points are on a line, and the number of  [#permalink]

### Show Tags

11 Mar 2015, 05:47
Hi

Interesting and fun question

Moreover geometry is always fun
Plz find the attachment for the answer
Attachments

circle.png [ 57.56 KiB | Viewed 2629 times ]

Manager
Joined: 27 Jun 2014
Posts: 65
Location: New Zealand
Concentration: Strategy, General Management
GMAT 1: 710 Q43 V45
GRE 1: Q161 V163

GRE 2: Q159 V166
GPA: 3.6
WE: Editorial and Writing (Computer Software)
Re: In the diagram above, all the points are on a line, and the number of  [#permalink]

### Show Tags

12 Mar 2015, 16:08
1
1
Bunuel wrote:
Attachment:
cpotg_img6.png
In the diagram above, all the points are on a line, and the number of each point indicates how many units that point is from zero. The points #1 – #6 are the centers of the six circles, and all circles pass through point zero. What is the total area of the shaded region?

A. $$12\pi$$
B. $$21\pi$$
C. $$24\pi$$
D. $$46\pi$$
E. $$48\pi$$

Kudos for a correct solution.

Shaded region 2: 16pi-9pi = 7pi

Total = 21 pi which is answer B.
_________________
"Hardwork is the easiest way to success." - Aviram

One more shot at the GMAT...aiming for a more balanced score.
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1709
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: In the diagram above, all the points are on a line, and the number of  [#permalink]

### Show Tags

12 Mar 2015, 19:47
2
Answer = B. $$21\pi$$

Radii of all green shaded circles is even i.e 2, 4, 6

Radii of all white circles is odd i.e 1, 3, 5

Area of required shaded region $$= \pi(2^2 + 4^2 + 6^2) - \pi(1^2 + 3^2 + 5^2)$$

$$= \pi(4+16+36 - 1 - 9 - 25) = 21\pi$$
Math Expert
Joined: 02 Sep 2009
Posts: 64068
Re: In the diagram above, all the points are on a line, and the number of  [#permalink]

### Show Tags

15 Mar 2015, 20:36
Bunuel wrote:

In the diagram above, all the points are on a line, and the number of each point indicates how many units that point is from zero. The points #1 – #6 are the centers of the six circles, and all circles pass through point zero. What is the total area of the shaded region?

A. $$12\pi$$
B. $$21\pi$$
C. $$24\pi$$
D. $$46\pi$$
E. $$48\pi$$

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

First, let’s look at the outer “lobe,” the one between 10 and 12. The circle through point 12 has a center a 6 and radius of 6, so its area is 36pi. The circle through point 10 has a center a 5 and radius of 5, so its area is 25pi. If we subtract the latter from the former, we an area of 11pi for this lobe.

Now, let’s look the middle lobe, the one between 6 and 8. The circle through point 6 has a center a 3 and radius of 3, so its area is 9pi. The circle through point 8 has a center a 4 and radius of 4, so its area is 16pi. If we subtract the latter from the former, we an area of 7pi for this lobe.

Now, let’s look the smallest lobe, the one between 2 and 4. The circle through point 2 has a center a 1 and radius of 1, so its area is pi. The circle through point 4 has a center a 2 and radius of 2, so its area is 4pi. If we subtract the latter from the former, we an area of 3pi for this lobe.

Add the areas of the three separate lobes: 3pi +7pi + 11pi = 21pi.

_________________
Manager
Joined: 25 May 2016
Posts: 84
Location: Singapore
Concentration: Finance, General Management
GMAT 1: 620 Q46 V30
Re: In the diagram above, all the points are on a line, and the number of  [#permalink]

### Show Tags

08 Jul 2016, 00:54
We divide the it into 3 parts with 2 circles each then add the 3 parts to get the total area as follows:
[pi(2)^2-pi(1)^2] + [pi(4)^2-pi(3)^2]+[pi(6)^2-pi(5)^2]
=3pi + 7pi + 11pi
=21 pi
Current Student
Joined: 18 Oct 2014
Posts: 774
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: In the diagram above, all the points are on a line, and the number of  [#permalink]

### Show Tags

08 Jul 2016, 04:30
Bunuel wrote:
Attachment:
cpotg_img6.png
In the diagram above, all the points are on a line, and the number of each point indicates how many units that point is from zero. The points #1 – #6 are the centers of the six circles, and all circles pass through point zero. What is the total area of the shaded region?

A. $$12\pi$$
B. $$21\pi$$
C. $$24\pi$$
D. $$46\pi$$
E. $$48\pi$$

Kudos for a correct solution.

36pi-25pi+16pi-9pi+4pi-pi

we are subtracting (25+9+1) i.e. an odd number from even number. Answer will be odd and there is only only odd option in the answer choices.

_________________
I welcome critical analysis of my post!! That will help me reach 700+
Non-Human User
Joined: 09 Sep 2013
Posts: 14969
Re: In the diagram above, all the points are on a line, and the number of  [#permalink]

### Show Tags

15 Dec 2018, 14:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: In the diagram above, all the points are on a line, and the number of   [#permalink] 15 Dec 2018, 14:47