For divisibility by 3 , sum of digits must be divisible by 3 , ∴2+3+k+5+6+7+k=23+2k Since, (23+2k) is divisible by 3 ∴23+2k=27 ⇒27−23=2k ⇒2k=4 ⇒k=2 ∴ Possible value of k=2 Next possible values of k=5,8 ∴ Sum of all possible values of k=2+5+8=15