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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

70% (01:30) correct
30% (01:24) wrong based on 155 sessions

HideShow timer Statistics

Three circles with radii of 1, 2, and 3, lie on the same plane. Do any of these circles intersect or lie within another?

(1) If you connect the centers of the circles, an equilateral triangle with the height of 2√3 will be formed. (2) The distance between the centers of any two circles is less than 6.

Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any [#permalink]

Show Tags

30 Jul 2015, 02:07

Bunuel wrote:

Three circles with radii of 1, 2, and 3, lie on the same plane. Do any of these circles intersect or lie within another?

(1) If you connect the centers of the circles, an equilateral triangle with the height of 2√3 will be formed. (2) The distance between the centers of any two circles is less than 6.

Kudos for a correct solution.

St 1: An equilateral triangle with height 2\(\sqrt{3}\) , then

the side of the triangle a = ( \(\sqrt{3}\) / 2 ) * a = 2 \(\sqrt{3}\)

=> a = 4, which implies that circles with radii 3 and 2 must intersect each other to form a side of eq. triangle = 4.

Hence Sufficient.

St 2: Distance between any two centers < 6

if the distance between any two circles is less than 5, we can confirm that circles with radii 3 and 2 intersect each other.

But since the distance is < 6, then we cannot decide if they intersect each other. Hence not sufficient.

Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any [#permalink]

Show Tags

30 Jul 2015, 02:24

1

This post received KUDOS

Bunuel wrote:

Three circles with radii of 1, 2, and 3, lie on the same plane. Do any of these circles intersect or lie within another?

(1) If you connect the centers of the circles, an equilateral triangle with the height of 2√3 will be formed. (2) The distance between the centers of any two circles is less than 6.

Kudos for a correct solution.

IMO: A

Statement 1: If you connect the centers of the circles, an equilateral triangle with the height of 2√3 will be formed Height of an equilateral triangle with side "a' = √3/2*a 2√3 = √3/2 *a a= 4

If distance between any two centers is 4 For Circles with radius 1 and 2 --> do not intersect For Circles with radius 1 and 3 --> Touch each other externally For Circles with radius 2 and 3 --> intersect Hence suff

Statement 2 : The distance between the centers of any two circles is less than 6.

Maximum distance between any two circles touching externally will be when circle with radius 2 and circle with radius 3 = 5 Thus If distance between them is below 5 --> intersect Equal to 5 --> touch externally >5 --> do not intersect

Given condition distance < 6. So we get different answers for d=5.5 or 5 or 4 Hence not suff _________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos ¯\_(ツ)_/¯

Three circles with radii of 1, 2, and 3, lie on the same plane. Do any of these circles intersect or lie within another?

(1) If you connect the centers of the circles, an equilateral triangle with the height of 2√3 will be formed. (2) The distance between the centers of any two circles is less than 6.

Kudos for a correct solution.

800score Official Solution:

From Statement (1), we can determine how the circles are positioned relative to each other, because we know the distances between the centers. Therefore, we could establish whether any two of the circles intersect each other or one lies within another. Thus Statement (1) is sufficient. You do NOT need to do any further analysis of Statement (1).

Statement (2) is not sufficient. Imagine the two different situations: all the centers coincide; the centers are the vertices of an equilateral triangle with sides 5.5 . The first situation would answer the original question positively, the second one – negatively. Only if the distance was less than or equaled 5 could we guarantee the positive answer.

Remember that, in Data Sufficiency questions, it is not necessary to solve the problem, it is only necessary to establish whether or not we have sufficient information to do so.

Since Statement (1) is sufficient, and Statement (2) is not, the correct answer is A.
_________________

Three circles with radii of 1, 2, and 3, lie on the same plane. Do any of these circles intersect or lie within another?

(1) If you connect the centers of the circles, an equilateral triangle with the height of 2√3 will be formed. (2) The distance between the centers of any two circles is less than 6.

Kudos for a correct solution.

800score Official Solution:

From Statement (1), we can determine how the circles are positioned relative to each other, because we know the distances between the centers. Therefore, we could establish whether any two of the circles intersect each other or one lies within another. Thus Statement (1) is sufficient. You do NOT need to do any further analysis of Statement (1).

Statement (2) is not sufficient. Imagine the two different situations: all the centers coincide; the centers are the vertices of an equilateral triangle with sides 5.5 . The first situation would answer the original question positively, the second one – negatively. Only if the distance was less than or equaled 5 could we guarantee the positive answer.

Remember that, in Data Sufficiency questions, it is not necessary to solve the problem, it is only necessary to establish whether or not we have sufficient information to do so.

Since Statement (1) is sufficient, and Statement (2) is not, the correct answer is A.

Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any [#permalink]

Show Tags

12 Nov 2017, 20:11

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.
_________________