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

 It is currently 13 Oct 2019, 18:19

### 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

# The diagram shows circular sections of a cone. If x is 20 percent of R

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58335
The diagram shows circular sections of a cone. If x is 20 percent of R  [#permalink]

### Show Tags

05 Oct 2017, 06:07
00:00

Difficulty:

35% (medium)

Question Stats:

61% (01:49) correct 39% (01:50) wrong based on 70 sessions

### HideShow timer Statistics

The diagram shows circular sections of a cone. If x is 20 percent of R, by what percentage is the area of circle C greater than the area of circle B? (Note: Figure not drawn to scale)

A. 250%
B. 400%
C. 500%
D. 2400%
E. 2500%

Attachment:

Cone.png [ 20.91 KiB | Viewed 920 times ]

_________________
Retired Moderator
Joined: 22 Aug 2013
Posts: 1431
Location: India
Re: The diagram shows circular sections of a cone. If x is 20 percent of R  [#permalink]

### Show Tags

05 Oct 2017, 06:42
So basically we have two circles, radius of smaller circle is 20% of radius of larger circle. Let radius of bigger circle = 10, then radius of smaller circle = 2.

Ratio of their areas = pi (10)^2 / pi (2)^2 = 25:1

Since area of bigger circle is 25 times that of smaller circle, it is 2400% more than smaller area. Hence D answer
Manager
Joined: 20 Jan 2016
Posts: 175
Re: The diagram shows circular sections of a cone. If x is 20 percent of R  [#permalink]

### Show Tags

06 Oct 2017, 08:12
I will go with E

x=0.2R
Say R=10
therefore, x=2

Area of R= 314
Area of B= 12.56

Increased percentage = (301/12.56). 100
This is approximately equal to 2500%

E
Senior SC Moderator
Joined: 22 May 2016
Posts: 3536
The diagram shows circular sections of a cone. If x is 20 percent of R  [#permalink]

### Show Tags

06 Oct 2017, 11:54
Bunuel wrote:

The diagram shows circular sections of a cone. If x is 20 percent of R, by what percentage is the area of circle C greater than the area of circle B? (Note: Figure not drawn to scale)

A. 250%
B. 400%
C. 500%
D. 2400%
E. 2500%

Attachment:
Cone.png

The cone does not matter; all we need are areas of two circles.

Choose values

Let R = 5
Let x = 1 (20 percent of 5)

Area of Circle C = $$25\pi$$
Area of Circle B = $$1\pi$$

By what percentage is the area of circle C greater than the area of circle B?

Percent increase = $$\frac{(New - Old)}{Old} * 100$$

$$\frac{(25\pi - 1\pi)}{1\pi} * 100$$

$$\frac{24}{1} * 100$$ = 2400 percent

Circle C's area is 2400 percent greater than Circle B's area

Use multiplier / scale factor
x = .20R

Area of Circle C = $$\pi*R^2$$

Let area of C, $$\pi*R^2 = X$$

Area of Circle B =
(scale factor)$$^2$$ * (Area of C)

$$(.2)^2(X) =.04X =$$Area of B

Percent increase =

$$\frac{(X) - (.04X)}{(.04X)} * 100$$

$$\frac{.96X}{.04X} = (24 * 100)$$ = 2400 percent

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Choose life.
Non-Human User
Joined: 09 Sep 2013
Posts: 13077
Re: The diagram shows circular sections of a cone. If x is 20 percent of R  [#permalink]

### Show Tags

06 Oct 2018, 13:11
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: The diagram shows circular sections of a cone. If x is 20 percent of R   [#permalink] 06 Oct 2018, 13:11
Display posts from previous: Sort by