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23 Mar 2020, 02:42
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
25% (02:22) correct
75%
(02:26)
wrong
based on 121
sessions
History
Date
Time
Result
Not Attempted Yet
An entomologist noticed 15 ants crawling on his table. Exactly 13 of them were male and 2 were female. He noticed that they were crawling on the table in a random order such that no three of them were ever in the same straight line. Suddenly, three of the male ants start following one of the female ants such that, all four of them were in a single line. Then the maximum number of distinct straight lines that the entomologist can draw passing through any two ants is
A. 44
B. 56
C. 99
D. 100
E. 105
Are You Up For the Challenge: 700 Level Questions
A. 44
B. 56
C. 99
D. 100
E. 105
Are You Up For the Challenge: 700 Level Questions
23 Mar 2020, 02:58
Kudos
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Bunuel
Note that, we can form only 1 straight line by selecting any 2 ants out of 4 ants
Case 1: When 2 ants are from 11 other ants. Number of st. lines possible = \(11c_2 = 55\)
Case 2: When 1 ant is from 11 ants and the other is from 4 ants in a st. line. Number of st. lines possible = \(11c_1*4c_1 = 44\)
Case 3: When 2 ants are from 4 ants in a st. line; Number of st. lines possible = \(1\) ONLY
--> Total straight lines = 55 + 44 + 1 = 100
Option D
General Discussion
23 Mar 2020, 03:07
Kudos
Bookmarks
the maximum number of distinct straight lines that the entomologist can draw passing through any two ants, when four of 15 ants are in a single line
= 15C2 - 4C2 +1
= 105-6+1
=100
= 15C2 - 4C2 +1
= 105-6+1
=100
Bunuel
