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12 Jun 2019, 23:55
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D
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Difficulty:
35%
(medium)
Question Stats:
60% (01:05) correct
40%
(01:36)
wrong
based on 116
sessions
History
Date
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What is the maximum number of points that 10 circles of different radii intersect?
(A) 24
(B) 26
(C) 33
(D) 90
(E) 100
(A) 24
(B) 26
(C) 33
(D) 90
(E) 100
firas92
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Joined: 16 Jan 2019
Last visit: 02 Dec 2024
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Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
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13 Jun 2019, 00:13
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A circle can intersect another circle at a maximum of 2 points
So circle 1 intersects the 9 other circles at 2 points each. Therefore, total number of intersections of circle 1 is 9*2=18
Circle 2 intersects with 8 other circles (excluding its intersection with circle 1).Therefore, total number of intersections of circle 2 is 8*2=16
Similarly 7*2 for Circle 3
Following this pattern, total number of intersections = (9+8+7+6+5+4+3+2+1)*2 = 90
Answer is (D)
So circle 1 intersects the 9 other circles at 2 points each. Therefore, total number of intersections of circle 1 is 9*2=18
Circle 2 intersects with 8 other circles (excluding its intersection with circle 1).Therefore, total number of intersections of circle 2 is 8*2=16
Similarly 7*2 for Circle 3
Following this pattern, total number of intersections = (9+8+7+6+5+4+3+2+1)*2 = 90
Answer is (D)
27 Jan 2022, 04:43
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Bunuel
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Hope it helps.
