Question

The sum of all possible values of \( K \) such that a 5-digit number 90K68 is divisible by 8 will be:

• A. 21
• B. 23
• C. 25
• D. 26

Hint:

When checking divisibility by 8, focus on the last three digits of the number.

Answer 1

The Correct Option is C

We are given a 5-digit number \( 90K68 \). For the number to be divisible by 8, the last three digits (i.e., \( K68 \)) must be divisible by 8. Let’s check the values of \( K \) such that \( K68 \) is divisible by 8. - For \( K = 0 \), \( 068 \div 8 = 8.5 \) (not divisible). - For \( K = 1 \), \( 168 \div 8 = 21 \) (divisible). - For \( K = 2 \), \( 268 \div 8 = 33.5 \) (not divisible). - For \( K = 3 \), \( 368 \div 8 = 46 \) (divisible). - For \( K = 4 \), \( 468 \div 8 = 58.5 \) (not divisible). - For \( K = 5 \), \( 568 \div 8 = 71 \) (divisible). - For \( K = 6 \), \( 668 \div 8 = 83.5 \) (not divisible). - For \( K = 7 \), \( 768 \div 8 = 96 \) (divisible). - For \( K = 8 \), \( 868 \div 8 = 108.5 \) (not divisible). - For \( K = 9 \), \( 968 \div 8 = 121 \) (divisible). The possible values of \( K \) are 1, 3, 5, 7, and 9. The sum of these values is: \[ 1 + 3 + 5 + 7 + 9 = 25 \] Thus, the correct answer is \( \boxed{25} \).