Question

Not understood the answer of the question

If x and y are 2 digits of number 653xy wich is divisible by 80. Find x+y =

Answer 1

There are so many method to solve this problem.I am going to solve this problem using two different methods

1st Method

If a number is divisible by a number, is it always divisible by factors of that number.

Since 10 is a factor of 80, 653xy is divisible by 10.

Divisibility by 10 rule last digit must be zero

It means last digit,y =0

Rewriting 653xy as 653x0. Since 8 is a factor of 80, 653x0 is divisible by 8. It means last three digits 3x0 is divisible by 8. Hence, x is 2 or 6

if x=2, number is 65320. But this is not divisible by 80
if x=6, number is 65360 which is divisible by 80

Therefore number is 65360 with x=6 and y=0.
x+y = 6+0 = 6

Alternative Solution

65300/80 = 816 with remainder = 20.
Therefore, 65300 + 60 = 65360 is divisible by 80.

In this case xy = 60. There are no other values of xy which makes 653xy divisible by 80 (If we add another 80 to 65360, number becomes 65440 which cannot be taken)

Hence, x+y = 6+0 = 6