if the number A3640548981270644B is divisible 99 then ordered pair of digits ( A,B) is
Answers
Given : the number A3640548981270644B is divisible 99
To Find : ordered pair of digits ( A,B)
Solution:
Number divisible by 99 would be divisible by 9 and 11
Number is divisible by 9 if sum of digits is divisible by 9
A3640548981270644B
A + 3 + 6 + 4 + 0 + 5 + 4 + 8 + 9 + 8 + 1 + 2 + 7 + 0 + 6 + 4 + 4 + B
= 71 + A + B
72 , 81 , 90 are divisible by 9
Hence A + B = 1 or A + B = 10 ( A + B can not be 19 as max sum is 18)
Number is Divisible by 11 if
subtract and then add the digits in an alternating pattern from left to right
and number got should be divisible by 11
A -3 + 6 - 4 + 0 - 5 + 4- 8 + 9 - 8 + 1 - 2 + 7 - 0 + 6 - 4 + 4 - B
= 3 + A - B
=> A - B = - 3
or A - B = 8
A + B = 1 A - B = - 3 => 2A = - 2 => A = - 1 not possible
A + B = 1 , A - B = 8 => 2A = 9 => A = 9/2 not possible
A + B =10 A - B = - 3 => 2A = 7 => A = 7/2 not possible
A + B = 10 A - B = 8 => 2A = 18 => A = 9 and B = 1
( 9 , 1) is the required order pair
936405489812706441 is divisible 99
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