Find the sum of the greatest and the smallest number which may replace k in the number 8130k36 so that the number is divisible by 8.

A number is divisible by 8 if the number formed by its last three digits is divisible by 8. For the number 8130k36, the last three digits form the number k36.
Since k is a single-digit integer (0≤k≤9), let's test values of k from 0 to 9 to see when k36 is divisible by 8:

If k=0: 036=36 (Not divisible by 8)

If k=1: 136÷8=17 (Divisible!) ⟹ Smallest value of k=1

If k=2: 236 (Not divisible by 8)

If k=3: 336÷8=42 (Divisible!)

If k=4: 436 (Not divisible by 8)

If k=5: 536÷8=67 (Divisible!)

If k=6: 636 (Not divisible by 8)

If k=7: 736÷8=92 (Divisible!)

If k=8: 836 (Not divisible by 8)

If k=9: 936÷8=117 (Divisible!) ⟹ Greatest value of k=9

The possible values for k are 1,3,5,7,9.

Sum of the greatest and smallest values=9+1=10