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26 Jul 2006, 11:21
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how many distinct values can x/y have if x and y are both integers from 1 to 10?
(A) 63 (B) 65 (C) 67 (D) 69 (E) 71
Here's how i got it :
Please provide an alternative approach :
(1,1),(1,2), (1,3),(1,4), (1,5),(1,6), (1,7),(1,8), (1,9),(1,10)
(2,1),(2,2), (2,3),(2,4), (2,5),(2,6), (2,7),(2,8), (2,9),(2,10)
(3,1),(3,2), (3,3),(3,4), (3,5),(3,6), (3,7),(3,8), (3,9),(3,10)
(4,1),(4,2), (4,3),(4,4), (4,5),(4,6), (4,7),(4,8), (4,9),(4,10)
(5,1),(5,2), (5,3),(5,4), (5,5),(5,6), (5,7),(5,8), (5,9),(5,10)
(6,1),(6,2), (6,3),(6,4), (6,5),(6,6), (6,7),(6,8), (6,9),(6,10)
(7,1),(7,2), (7,3),(7,4), (7,5),(7,6), (7,7),(7,8), (7,9),(7,10)
(8,1),(8,2), (8,3),(8,4), (8,5),(8,6), (8,7),(8,8), (8,9),(8,10)
(9,1),(9,2), (9,3),(9,4), (9,5),(9,6), (9,7),(9,8), (9,9),(9,10)
(10,1),(10,2), (10,3),(10,4), (10,5),(10,6), (10,7),(10,8), (10,9),(10,10)
100 - 23 = 67
Ans : C
(A) 63 (B) 65 (C) 67 (D) 69 (E) 71
Here's how i got it :
Please provide an alternative approach :
(1,1),(1,2), (1,3),(1,4), (1,5),(1,6), (1,7),(1,8), (1,9),(1,10)
(2,1),(2,2), (2,3),(2,4), (2,5),(2,6), (2,7),(2,8), (2,9),(2,10)
(3,1),(3,2), (3,3),(3,4), (3,5),(3,6), (3,7),(3,8), (3,9),(3,10)
(4,1),(4,2), (4,3),(4,4), (4,5),(4,6), (4,7),(4,8), (4,9),(4,10)
(5,1),(5,2), (5,3),(5,4), (5,5),(5,6), (5,7),(5,8), (5,9),(5,10)
(6,1),(6,2), (6,3),(6,4), (6,5),(6,6), (6,7),(6,8), (6,9),(6,10)
(7,1),(7,2), (7,3),(7,4), (7,5),(7,6), (7,7),(7,8), (7,9),(7,10)
(8,1),(8,2), (8,3),(8,4), (8,5),(8,6), (8,7),(8,8), (8,9),(8,10)
(9,1),(9,2), (9,3),(9,4), (9,5),(9,6), (9,7),(9,8), (9,9),(9,10)
(10,1),(10,2), (10,3),(10,4), (10,5),(10,6), (10,7),(10,8), (10,9),(10,10)
100 - 23 = 67
Ans : C
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alimad
Brute force
I got 71.
some fractions you might forget to subtract
1/2 =2/4 =3/6.........
1/3=3/6........
1/4=2/8
1/5 = 2/10
2/3= 4/6
3/4=6/8
4/5=8/10
26 Jul 2006, 11:58
Kudos
Bookmarks
I stand corrected : Here's my latest findings :
(1,1),(1,2), (1,3),(1,4), (1,5),(1,6), (1,7),(1,8), (1,9),(1,10) = 0
(2,1),(2,2), (2,3),(2,4), (2,5),(2,6), (2,7),(2,8), (2,9),(2,10) = 5
(3,1),(3,2), (3,3),(3,4), (3,5),(3,6), (3,7),(3,8), (3,9),(3,10) = 3
(4,1),(4,2), (4,3),(4,4), (4,5),(4,6), (4,7),(4,8), (4,9),(4,10) = 5
(5,1),(5,2), (5,3),(5,4), (5,5),(5,6), (5,7),(5,8), (5,9),(5,10) = 2
(6,1),(6,2), (6,3),(6,4), (6,5),(6,6), (6,7),(6,8), (6,9),(6,10) = 7
(7,1),(7,2), (7,3),(7,4), (7,5),(7,6), (7,7),(7,8), (7,9),(7,10) = 1
(8,1),(8,2), (8,3),(8,4), (8,5),(8,6), (8,7),(8,8), (8,9),(8,10) = 5
(9,1),(9,2), (9,3),(9,4), (9,5),(9,6), (9,7),(9,8), (9,9),(9,10) = 3
(10,1),(10,2), (10,3),(10,4), (10,5),(10,6), (10,7),(10,8), (10,9),(10,10) = 36
Total = 37 – 100 = 63
(1,1),(1,2), (1,3),(1,4), (1,5),(1,6), (1,7),(1,8), (1,9),(1,10) = 0
(2,1),(2,2), (2,3),(2,4), (2,5),(2,6), (2,7),(2,8), (2,9),(2,10) = 5
(3,1),(3,2), (3,3),(3,4), (3,5),(3,6), (3,7),(3,8), (3,9),(3,10) = 3
(4,1),(4,2), (4,3),(4,4), (4,5),(4,6), (4,7),(4,8), (4,9),(4,10) = 5
(5,1),(5,2), (5,3),(5,4), (5,5),(5,6), (5,7),(5,8), (5,9),(5,10) = 2
(6,1),(6,2), (6,3),(6,4), (6,5),(6,6), (6,7),(6,8), (6,9),(6,10) = 7
(7,1),(7,2), (7,3),(7,4), (7,5),(7,6), (7,7),(7,8), (7,9),(7,10) = 1
(8,1),(8,2), (8,3),(8,4), (8,5),(8,6), (8,7),(8,8), (8,9),(8,10) = 5
(9,1),(9,2), (9,3),(9,4), (9,5),(9,6), (9,7),(9,8), (9,9),(9,10) = 3
(10,1),(10,2), (10,3),(10,4), (10,5),(10,6), (10,7),(10,8), (10,9),(10,10) = 36
Total = 37 – 100 = 63
