Author 
Message 
TAGS:

Hide Tags

EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15929
Location: United States (CA)

Random Pack 1, Question 3 Three circles with radii...
[#permalink]
Show Tags
Updated on: 27 Oct 2015, 21:38
Question Stats:
22% (02:24) correct 78% (01:56) wrong based on 265 sessions
HideShow timer Statistics
QUANT 4PACK SERIES Problem Solving Pack 1 Question 3 Three circles with radii...Three circles with radii of 2 cm, 3 cm and 5 cm, respectively are on the same plane. If the centers of the three circles are all on the same line and each circle is tangent to at least one of the other two circles, then what is the shortest possible distance, in cm, between the center of the largest circle and the center of the smallest circle? A) 0 B) 1 C) 3 D) 7 E) 13 48 Hour Window Answer & Explanation WindowEarn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Quant 4Pack series
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Manager
Joined: 11 Sep 2013
Posts: 104

Re: Random Pack 1, Question 3 Three circles with radii...
[#permalink]
Show Tags
23 Oct 2015, 00:25
EMPOWERgmatRichC wrote: RANDOM 4PACK SERIES Pack 1 Question 3 Three circles with radii...Three circles with radii of 2 cm, 3 cm and 5 cm, respectively are on the same plane. If the centers of the three circles are all on the same line and each circle is tangent to at least one of the other two circles, then what is the shortest possible distance, in cm, between the center of the largest circle and the center of the smallest circle? A) 0 B) 1 C) 3 D) 7 E) 13 48 Hour Window Answer & Explanation WindowEarn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Random 4Pack series A) 0 when the center of the largest is that of the smallest => both these circle must be tangent with the second big one => This situation cannot happen => Cross out this ans B) 1 This situation cannot satisfy the biggest adn the smallest are both tangent with the second one. Hope you can imagine this situation in ur head => Cross out this C) 3 => the biggest is tangent with the smallest and the smallest is inside the biggest => Both these circle can be tangent with the second one => THIS SITUATION CAN HAPPEN => CHOOSE THIS ANSWER Because the question asks the shortest distance so I will not check the ans D, E Ans: C



CEO
Joined: 20 Mar 2014
Posts: 2552
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Random Pack 1, Question 3 Three circles with radii...
[#permalink]
Show Tags
Updated on: 29 Oct 2015, 03:49
EMPOWERgmatRichC wrote: RANDOM 4PACK SERIES Pack 1 Question 3 Three circles with radii...Three circles with radii of 2 cm, 3 cm and 5 cm, respectively are on the same plane. If the centers of the three circles are all on the same line and each circle is tangent to at least one of the other two circles, then what is the shortest possible distance, in cm, between the center of the largest circle and the center of the smallest circle? A) 0 B) 1 C) 3 D) 7 E) 13 48 Hour Window Answer & Explanation WindowEarn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Random 4Pack series As this question asks us to find the smallest value, we will start from the top and keep eliminating answers. Option A: 0, this is not possible as this would mean that the smallest and largest circles are concentric and hence both can not be tangent to each other or to the 3rd circle. Eliminate. Option B: 1, The figure above shows 1 possible arrangement. We can clearly see that the distance AB must be less than the radius of the smallest circle (=2), making 1 as the correct answer. No need to spend time on other options. B is the correct answer.
Attachments
102915 64032 AM.jpg [ 14.28 KiB  Viewed 5045 times ]
Originally posted by ENGRTOMBA2018 on 23 Oct 2015, 04:58.
Last edited by ENGRTOMBA2018 on 29 Oct 2015, 03:49, edited 1 time in total.
Updated the attached picture



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15929
Location: United States (CA)

Re: Random Pack 1, Question 3 Three circles with radii...
[#permalink]
Show Tags
26 Oct 2015, 16:29
Hi All, Physically drawing the circles that are described in this prompt will likely help you to visualize the work that needs to be done (the math itself is just arithmetic, but you have to keep track of what the question asks for  the SMALLEST possible distance between the two centers). We're told that the 3 centers of the 3 circles have to be on the SAME line and that each of the 3 circles is tangent to at least one of the other two circles. Thus, there aren't that many different ways to arrange the 3 circles. Attachment:
3 circles answer GC.png [ 67.36 KiB  Viewed 5153 times ]
Placing the 2cm circle INSIDE the 3cm circle creates three equal 2cm wide 'pieces.' The two 2cm radii of the smallest circle would take up 4 cm of space on the mediumsized circle's diameter, leaving 2cm of excess space. Placing the 3cmwiththe2cmcircleinsideit INSIDE the 5cm circle now allows us to compare the largest radius (5cm) to the three 2cm 'pieces' in the smaller two circles. The center of the smallest circle is now 4cm from the edge of the largest circle. Since the radius of the largest circle is 5cm, the distance between those 2 centers is 5cm  4cm = 1cm. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 29 Mar 2015
Posts: 20

Re: Random Pack 1, Question 3 Three circles with radii...
[#permalink]
Show Tags
28 Oct 2015, 19:37
Engr2012 wrote: EMPOWERgmatRichC wrote: RANDOM 4PACK SERIES Pack 1 Question 3 Three circles with radii...Three circles with radii of 2 cm, 3 cm and 5 cm, respectively are on the same plane. If the centers of the three circles are all on the same line and each circle is tangent to at least one of the other two circles, then what is the shortest possible distance, in cm, between the center of the largest circle and the center of the smallest circle? A) 0 B) 1 C) 3 D) 7 E) 13 48 Hour Window Answer & Explanation WindowEarn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Random 4Pack series As this question asks us to find the smallest value, we will start from the top and keep eliminating answers. Option A: 0, this is not possible as this would mean that the smallest and largest circles are concentric and hence both can not be tangent to each other or to the 3rd circle. Eliminate. Option B: 1, Attachment: 102315 75225 AM.jpg The figure above shows 1 possible arrangement. We can clearly see that the distance AB must be less than the radius of the smallest circle (=2), making 1 as the correct answer. No need to spend time on other options. B is the correct answer. Engr2012I'm not sure if this is just one of those days and I'm missing something completely here. But according to your drawing, the smallest circle A would enclose the center of the largest circle B when A is placed inside B and A is tangent to B. I'm wondering how this is possible since the diameter of A is 4 and the radius of B is 5? The center of point B should never be inside circle A when A is tangent to B. I do agree that the answer is B though.



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8425
GPA: 3.82

Re: Random Pack 1, Question 3 Three circles with radii...
[#permalink]
Show Tags
29 Oct 2015, 01:28
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer. Three circles with radii of 2 cm, 3 cm and 5 cm, respectively are on the same plane. If the centers of the three circles are all on the same line and each circle is tangent to at least one of the other two circles, then what is the shortest possible distance, in cm, between the center of the largest circle and the center of the smallest circle? A) 0 B) 1 C) 3 D) 7 E) 13 Let the center of the largest circle be A, that of second large be B and that of the smallest circle be C. Since we should find the shortest possible distance between the centers. The smallest circle should be inside of the largest circle, moreover if the smallest circle is tangential to the largest circle, the distance between A and C would be 3. But let’s consider another possibility : Inside of circle A the circle B is tangential to circle A and inside B the circle C is tangential to circle B at the other side of tangent point of A and B. Then the distance between A and C is 1. So the answer is (B).
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 1 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



CEO
Joined: 20 Mar 2014
Posts: 2552
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Random Pack 1, Question 3 Three circles with radii...
[#permalink]
Show Tags
29 Oct 2015, 03:48
Marchewski wrote: Engr2012 wrote: EMPOWERgmatRichC wrote: RANDOM 4PACK SERIES Pack 1 Question 3 Three circles with radii...Three circles with radii of 2 cm, 3 cm and 5 cm, respectively are on the same plane. If the centers of the three circles are all on the same line and each circle is tangent to at least one of the other two circles, then what is the shortest possible distance, in cm, between the center of the largest circle and the center of the smallest circle? A) 0 B) 1 C) 3 D) 7 E) 13 48 Hour Window Answer & Explanation WindowEarn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Random 4Pack series As this question asks us to find the smallest value, we will start from the top and keep eliminating answers. Option A: 0, this is not possible as this would mean that the smallest and largest circles are concentric and hence both can not be tangent to each other or to the 3rd circle. Eliminate. Option B: 1, Attachment: The attachment 102315 75225 AM.jpg is no longer available The figure above shows 1 possible arrangement. We can clearly see that the distance AB must be less than the radius of the smallest circle (=2), making 1 as the correct answer. No need to spend time on other options. B is the correct answer. Engr2012I'm not sure if this is just one of those days and I'm missing something completely here. But according to your drawing, the smallest circle A would enclose the center of the largest circle B when A is placed inside B and A is tangent to B. I'm wondering how this is possible since the diameter of A is 4 and the radius of B is 5? The center of point B should never be inside circle A when A is tangent to B. I do agree that the answer is B though. Good catch. I drew the figure in a hurry without realising that it is not possible. I have updated the figure. But the answer still remains = 1 as is mentioned by Rich in his post above.
Attachments
102915 64032 AM.jpg [ 14.28 KiB  Viewed 5032 times ]



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: Random Pack 1, Question 3 Three circles with radii...
[#permalink]
Show Tags
19 Nov 2018, 13:31
EMPOWERgmatRichC wrote: Three circles with radii of 2 cm, 3 cm and 5 cm, respectively are on the same plane. If the centers of the three circles are all on the same line and each circle is tangent to at least one of the other two circles, then what is the shortest possible distance, in cm, between the center of the largest circle and the center of the smallest circle?
A) 0 B) 1 C) 3 D) 7 E) 13
The correct answer is (B), indeed. Regards, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net




Re: Random Pack 1, Question 3 Three circles with radii...
[#permalink]
19 Nov 2018, 13:31






