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

 It is currently 03 Aug 2020, 04:56

### 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 figure above, an unshaded circle with diameter x is surrounded

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 65761
In the figure above, an unshaded circle with diameter x is surrounded  [#permalink]

### Show Tags

23 Jun 2020, 05:25
00:00

Difficulty:

75% (hard)

Question Stats:

33% (02:53) correct 67% (02:36) wrong based on 18 sessions

### HideShow timer Statistics

In the figure above, an unshaded circle with diameter x is surrounded by a shaded region with uniform width of 2. For which of the following values of x is the area of the unshaded circle greater than the area of the shaded region?

I. 9
II. 10
III. 11

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Attachment:

1.jpg [ 14.39 KiB | Viewed 222 times ]

_________________
PS Forum Moderator
Joined: 18 Jan 2020
Posts: 1500
Location: India
GPA: 4
In the figure above, an unshaded circle with diameter x is surrounded  [#permalink]

### Show Tags

23 Jun 2020, 05:47
Given: An unshaded circle with diameter x is surrounded by a shaded region with uniform width of 2.

To find: For which of the following values of x is the area of the unshaded circle greater than the area of the shaded region?

Solution. : x/2 = r
Area of unshaded region = πr^2
Area of shaded region = π(r+2)^2 - πr^2

Au > As
πr^2 > π(r+2)^2 - πr^2
2πr^2 > π(r+2)^2
2r^2 > (r+2)^2

1. 9 => radius = 4.5
2r^2 > (r+2)^2
2(4.5)^2 > (4.5+2)^2
2*20.25 > 6.5^2
40.5 < 42.25 (not satisfying)

2. 10 => radius = 5
2r^2 > (r+2)^2
2(5)^2 > (5+2)^2
2*25 > 7^2
50 > 49 (satisfying)

3. 11 => radius = 5.5
2r^2 > (r+2)^2
2(5.5)^2 > (5.5+2)^2
2*30.25 > 7.5^2
60.5 > 56.25 (satisfying)

Therefore only 2&3 values are statisfying.

Posted from my mobile device
In the figure above, an unshaded circle with diameter x is surrounded   [#permalink] 23 Jun 2020, 05:47