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

It is currently 06 Dec 2019, 18:05

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

In the above figure, the area of circle A is 144π and the area of circ

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59587
In the above figure, the area of circle A is 144π and the area of circ  [#permalink]

Show Tags

New post 25 Jun 2015, 04:40
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:11) correct 25% (01:37) wrong based on 96 sessions

HideShow timer Statistics

Image
In the above figure, the area of circle A is 144π and the area of circle B is 169π. If point x (not shown above) lies on circle A and point y (not shown above) lies on circle B, what is the range of the possible lengths of line xY.

A) 0 to 169π^2
B) 0 to 144
C) 0 to 25
D) 0 to 50
E) 5 to 144

Source: Platinum GMAT
Kudos for a correct solution.
Attachment:
00022-1.gif
00022-1.gif [ 4.41 KiB | Viewed 2582 times ]

_________________
Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 816
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User
Re: In the above figure, the area of circle A is 144π  [#permalink]

Show Tags

New post 25 Jun 2015, 05:27
Circle A has a Diameter of 24
Circle B has a Diameter of 26

Shortest line, if both points lie in the middle where the circles tangent = 0. If both points lie on the outer bounds, then the longest line would be their diameters 26 + 24 = 50.

Answer D.
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
In the above figure, the area of circle A is 144π and the area of circ  [#permalink]

Show Tags

New post 25 Jun 2015, 05:52
Bunuel wrote:
Image
In the above figure, the area of circle A is 144π and the area of circle B is 169π. If point x (not shown above) lies on circle A and point y (not shown above) lies on circle B, what is the range of the possible lengths of line xY.

A) 0 to 169π^2
B) 0 to 144
C) 0 to 25
D) 0 to 50
E) 5 to 144

Source: Platinum GMAT
Kudos for a correct solution.
Attachment:
00022-1.gif


Area of Circle = πr^2

Area of Circle A = 144π = πr^2
i.e. Radius of Circle A = 12

Area of Circle B = 169π = πr^2
i.e. Radius of Circle B = 13

Maximum Length of XY = Diameter of A + Diameter of B = 2(12+13) = 50
Minimum Length of XY = 0 (When the Two circles are tangent to each other)

Answer: Option
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Director
Director
avatar
P
Joined: 21 May 2013
Posts: 633
Re: In the above figure, the area of circle A is 144π and the area of circ  [#permalink]

Show Tags

New post 25 Jun 2015, 06:57
1
Bunuel wrote:
Image
In the above figure, the area of circle A is 144π and the area of circle B is 169π. If point x (not shown above) lies on circle A and point y (not shown above) lies on circle B, what is the range of the possible lengths of line xY.

A) 0 to 169π^2
B) 0 to 144
C) 0 to 25
D) 0 to 50
E) 5 to 144

Source: Platinum GMAT
Kudos for a correct solution.
Attachment:
00022-1.gif


Area of circle A=144pie
Therefore, radius=12 and diameter=24
Similarly, radius of circle B=13 and diameter=26
If both the points X and Y lie on the same point, distance=0
For max distance, we need to add the distance of diameters=24+26=50
Answer D
Manager
Manager
avatar
S
Joined: 26 Dec 2012
Posts: 144
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)
Re: In the above figure, the area of circle A is 144π and the area of circ  [#permalink]

Show Tags

New post 25 Jun 2015, 09:45
Area of A = 144pie = pie r^2 =? r=12; d=24
Area of B=169pie=pie R^2 => R=13; D=26
Minimum length of length of xy = 0, where both A and B touches
Maximum length of XY = d+D=50,
Hence range of length of xy = 0 to 50

Hence answer is D
Thanks,
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59587
Re: In the above figure, the area of circle A is 144π and the area of circ  [#permalink]

Show Tags

New post 29 Jun 2015, 05:24
Bunuel wrote:
Image
In the above figure, the area of circle A is 144π and the area of circle B is 169π. If point x (not shown above) lies on circle A and point y (not shown above) lies on circle B, what is the range of the possible lengths of line xY.

A) 0 to 169π^2
B) 0 to 144
C) 0 to 25
D) 0 to 50
E) 5 to 144

Source: Platinum GMAT
Kudos for a correct solution.
Attachment:
The attachment 00022-1.gif is no longer available


Platinum GMAT Official Solution:

The shortest distance of line xy will occur when x and y are at the same point (i.e., the point where the two circles come together). In this instance, the line xy will be 0 units long.

In order to determine the longest possible distance for xy, we must first recall that the longest line across a circle is the circle's diameter. In other words, it is impossible to construct a line from one point on a circle to another point on the same circle that is longer than the circle's diameter.

The longest distance of line xy will occur when x and y are at exact opposite sides of the two circles. In other words, when x is at the far left of A and y is at the far right of B. More technically, line xy will be the combined diameter of circles A and B. This makes sense given that the diameter of a circle is the longest possible line from one point on the circle to another point on the same circle.

Image

Since the length of xy is the length of the diameter of A plus the diameter of B, we need to find the diameter of each circle.
Area of A = 144π = πr^2
rA = 12 = radius of circle A
dA = 2(12) = 24 = diameter of circle A

Area of B = 169π = πr^2
rB = 13 = radius of circle B
dB = 2(13) = 26 = diameter of circle B

Maximum distance of xy = 24 + 26 = 50.

Answer: D.

Attachment:
00022-2.gif
00022-2.gif [ 4.61 KiB | Viewed 2359 times ]

_________________
GMAT Club Bot
Re: In the above figure, the area of circle A is 144π and the area of circ   [#permalink] 29 Jun 2015, 05:24
Display posts from previous: Sort by

In the above figure, the area of circle A is 144π and the area of circ

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne