A six digit number x3479y is divisible by 9 and 11. Find the possible values of (x, y).
Answers
Given : A six digit number x3479y is divisible by 9 and 11.
To find : Possible Values of ( x , y )
Solution:
A number is divisible by 9
if sum of digits is divisible by 9
x + 3 + 4 + 7 + 9 + y
= 23 + x + y
27 & 36 divisible by 9
=> x + y = 4 or x + y = 13
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
x - 3 + 4 - 7 + 9 - y
= x - y + 3
0 & 11 are divisible by 11
=> x - y = - 3 or x- y = 8
x + y = 4 , x - y = - 3 => x = 1/2 , y = 7/2 ( not possible)
x + y = 4 , x- y = 8 => x = 6 & y = - 2 (not possible)
x + y = 13 x - y = - 3 => x = 5 & y = 8
x + y = 13 x - y = 8 => x = 21/2 & y = 5/2 ( not possible)
x = 5 & y = 8 are possible values
534798 is divisible by 9 and 11.
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