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Three circles with radii of 1, 2, and 3, lie on the same plane. Do any
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29 Jul 2015, 14:42
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69% (02:00) correct 31% (01:50) wrong based on 182 sessions
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Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any
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30 Jul 2015, 01:07
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. Option A



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Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any
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30 Jul 2015, 01:24
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 formedHeight 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 suffStatement 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
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Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any
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17 Aug 2015, 08:10
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. 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.
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Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any
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17 Aug 2015, 08:21
Bunuel wrote: 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. 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. Similar questions to practice: theradiioftwocirclesare2inchesand4inchesrespecti154443.htmlwhatarethecoordinatesofpointa154298.htmlifthreecircleshavingradii12and3respectivelylieo54757.htmlifxandyarepointsinaplaneandxliesinsidethe135194.html (OG13) acertaincircularareahasitscenteratpointpandhas101485.html (GMAT Prep) circlecisinthexyplanewhatistheareaofthecircle99766.htmlinthefigureshownthecirclehascenteroandradius107309.htmlonthenumberlineshowniszerohalfwaybetweenrands89015.htmlistheradiusofthecirclegreaterthan105060.htmlifpointxisinsideacirclewithcenteroandradius2is102751.htmlifaandcarepointsinaplanecisthecenterofcircle133325.htmltherearethreecircleswithradii24and5respectively154408.htmlHope it helps.
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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any
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12 Nov 2017, 19:11
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Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any
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