The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is______.
Text Solution
Verified by Experts63
(63)
x y z 
odd number
z= 1,3,5,7,9
x+y+ z = 7, 14, 21 [sum of digit multiple of 7]
= 6, 4, 2, 13, 11, 9, 7, 5, 20, 18, 16, 14, 12
x + y = 6 
(1,5), (2, 4), (3, 3), (4, 2), (5, 1), (6,0)
T.N. = 6
x + y = 4 
(l,3), (2, 2), (3, 1), (4,0)
T.N = 4
x + y = 2 
(1,1),(2,0)
T.N. = 2
x + y = 13 
(4,9), (5,8), (6,7), (7,6), (8,5),(9,4)
T.N. = 6
x + y = 11 
(2,9), (3,8), (4,7), (5,6), (6,5), (6,5), (7,4), (8,3), (9,2)
T.N. = 8
x + y=9 
(l,8),(2,7),(3,8),(4,5),(5,4),....(8,l),(9,0)
T.N. = 9
x + y = 7 
(l,8),(2,5),(3,4),....(8, 1), (7,0)
T.N. = 7
x + y = 5 
(l,4),(2,3),(3, 2), (4,1),(5,0)
T.N. = 5
x + y = 20 
Not possible
x + y = 18 
(9,9) 
T.N. = 1
x + y = 16 
(7,9),(8,8),(9,7) 
T.N. = 3
x + y = 14 
(5,9),(6,8),(7,7),(8,6),(9,5)
T.N. = 5
x + y = 12 
(3,9),(4,8),(5,7),(6,6)....(9,3)
T.N. = 7
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