Answer:
The sum of all single-digit replacements for z is 12
Step-by-step explanation:
* Lets explain how to solve the problem
- The number is divisible by 6 if it divisible by 2 and 3
- Any even number divisible by 2
- The number is divisible by 3 is the sum of its digits divisible by 3
* Now lets solve the problem
- The number 24,z38 is divisible by 6
- We need to find all the possible values of z which keep the number
divisible by 6
∵ Lets add the sum of the digits without z
∵ 2 + 4 + 3 + 8 = 17
∵ 18 is the nearest number to 17
∵ 18 is divisible by 3
∴ Add 17 by 1 to get 18
∴ z = 1
- Lets check the number
∵ The number is 24,138
∵ 24,138 ÷ 6 = 4023
∴ The number is divisible by 6
∵ 21 is the next number after 18 and divisible by 3
∴ We must add 17 by 4 to get 21
∴ z = 4
- Lets check the number
∵ The number is 24,438
∵ 24,438 ÷ 6 = 4073
∴ The number is divisible by 6
∵ 24 is the next number after 18 and divisible by 3
∴ We must add 17 by 7 to get 24
∴ z = 7
- Lets check the number
∵ The number is 24,738
∵ 24,738 ÷ 6 = 4123
∴ The number is divisible by 6
- There is no other value for z because if we take the next number
of 24 divisible by 3 it will be 27 , then we must add 17 by 10 but
10 not a single digit
∴ The possible values of z are 1 , 4 , 7
∴ The sum of them = 1 + 4 + 7 = 12
∴ The sum of all single-digit replacements for z is 12
