What is the maximum number of points of intersection of

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Wed Jun 20, 2018 2:40 am

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What is the maximum number of points of intersection of two circles that have unequal radii?

(A) none
(B) 1
(C) 2
(D) 3
(E) infinite

The OA is the option C.

Is not D the correct choice? Could anyone explain this PS question to me? Thanks.

Source: Beat The GMAT — Problem Solving | Wed Jun 20, 2018 2:40 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Jun 20, 2018 5:34 am

VJesus12 wrote:What is the maximum number of points of intersection of two circles that have unequal radii?

(A) none
(B) 1
(C) 2
(D) 3
(E) infinite

With a quick sketch....

....we can get 2 points of intersection.

With the exception of a formal proof, we're left on our own accord to find a situation with more than 2 points of intersection.
If we can't identify such a situation, we must go with C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Thu Jun 21, 2018 4:11 pm

VJesus12 wrote:What is the maximum number of points of intersection of two circles that have unequal radii?

(A) none
(B) 1
(C) 2
(D) 3
(E) infinite

Two circles with unequal radii can intersect in three ways:

1) The smaller circle is completely inside the larger circle.

2) The two circles are tangent to each other.

3) The two circles intersect like the ones in a Venn diagram.

The number of points of intersection of these three ways are 0, 1, and 2, respectively. Thus, 2 is the maximum number of intersections.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Fri Jun 22, 2018 2:44 pm

The maximum number of points of intersection is 2.
Point of intersection is 0,1 and 2 but the maximum number of intersection is only 2.

Regards!

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