Author 
Message 
TAGS:

Hide Tags

Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1288
Location: Malaysia

In the diagram above, points A, B, C, D, and E all lie on the same lin [#permalink]
Show Tags
13 Feb 2017, 08:01
3
This post was BOOKMARKED
Question Stats:
64% (01:26) correct 36% (01:48) wrong based on 84 sessions
HideShow timer Statistics
In the diagram above, points A, B, C, D, and E all lie on the same line. Point B is the center of a smaller circle, on which points A and D lie. Point C is the center of a larger circle, on which points A and E lie. If the straightline distance from point C to point D is two meters and the straightline distance from point D to point E is 8 meters, what percentage of the larger circle is filled by the smaller circle? A. 16% B. 25% C. 36% D. 50% E. 64% Attachment:
Untitled.jpg [ 11.82 KiB  Viewed 878 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
"Be challenged at EVERY MOMENT."
“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”
"Each stage of the journey is crucial to attaining new heights of knowledge."
Rules for posting in verbal forum  Please DO NOT post short answer in your post!



SC Moderator
Joined: 13 Apr 2015
Posts: 1616
Location: India
Concentration: Strategy, General Management
WE: Analyst (Retail)

Re: In the diagram above, points A, B, C, D, and E all lie on the same lin [#permalink]
Show Tags
13 Feb 2017, 20:04
1
This post was BOOKMARKED
CD = 2; DE = 8
CE = AC = 10
Area of smaller circle = pi*(AD/2)^2 = 36pi
Area of larger circle = pi*(AC)^2 = 100pi
Smaller circle occupies (36pi/100pi)*100 = 36% of larger circle.
Answer: C



Manager
Joined: 24 Oct 2013
Posts: 152
Location: India
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)

Re: In the diagram above, points A, B, C, D, and E all lie on the same lin [#permalink]
Show Tags
14 Feb 2017, 06:22
larger circle radius = 8 + 2 = 10
inner circle diameter = 10 + 2 = 12 => radius = 6
larger circle area = 100 pi
smaller circle area = 36 pi
there for 36 %
option C



Math Expert
Joined: 02 Sep 2009
Posts: 44588

Re: In the diagram above, points A, B, C, D, and E all lie on the same lin [#permalink]
Show Tags
30 Dec 2017, 02:01
hazelnut wrote: In the diagram above, points A, B, C, D, and E all lie on the same line. Point B is the center of a smaller circle, on which points A and D lie. Point C is the center of a larger circle, on which points A and E lie. If the straightline distance from point C to point D is two meters and the straightline distance from point D to point E is 8 meters, what percentage of the larger circle is filled by the smaller circle? A. 16% B. 25% C. 36% D. 50% E. 64% VERITAS PREP OFFICIAL SOLUTION:The key here is labeling everything that you know. If you know that: DE = 8 CD = 2 and C is the center of the large circle Then you can identify that the radius of the large circle is the distance from C to E which is 10, making the area of that circle equal to 100pi. Then look at the smaller circle. You know that the distance from C to A is the radius of the larger circle, and you've already established that that distance is 10. And if CD is 2, that means that the diameter of the smaller circle is AC + CD (the total distance from A to D) for a total of 12. Since area is based on radius, cut that in half to a radius of 6, meaning that the area is 36pi. Then, since you want to know what percentage the small circle takes up of the large circle, that's 36 pi out of 100 pi, for a total of 36%.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Re: In the diagram above, points A, B, C, D, and E all lie on the same lin
[#permalink]
30 Dec 2017, 02:01






