Find the number of five-digit positive integers, n, that satisfy the following conditions:
(a) the number n is divisible by 5,
(b) the first and last digits of n are equal, and
(c) the sum of the digits of n is divisible by 5.

Solution

The number takes a form of 5 ext{x,y,z}5, in which 5|x+y+z. Let x and y be arbitrary digits. For each pair of x,y, there are exactly two values of z that satisfy the condition of 5|x+y+z. Therefore, the answer is 10*10*2=200

Question

Find the number of five-digit positive integers, n, that satisfy the following conditions:
(a) the number n is divisible by 5,
(b) the first and last digits of n are equal, and
(c) the sum of the digits of n is divisible by 5.

Solution

The number takes a form of 5	ext{x,y,z}5, in which 5|x+y+z. Let x and y be arbitrary digits. For each pair of x,y, there are exactly two values of z that satisfy the condition of 5|x+y+z. Therefore, the answer is 10*10*2=200

anonymous · Answer

I don't understand "For each pair of x,y, there are exactly two values of z that satisfy the condition of 5|x+y+z." If I set x=2, y=5 or any combination thereof, z could be anything from 0-9 as well.