Find the largest value of k such that a 6-digit number 450k1k is divisible by 3.
- A7
- B9
- C8
- D6
Solution & Step-by-step Explanation
For a number to be divisible by 3, the sum of its digits must be a multiple of 3.
Sum of digits=4+5+0+k+1+k=10+2k
Since k is a single-digit number, k∈{0,1,2,…,9}. We need to find the largest possible value of k such that 10+2k is divisible by 3.
Let's test the largest single digits for k:
If k=9: Sum=10+2(9)=28 (not divisible by 3)
If k=8: Sum=10+2(8)=26 (not divisible by 3)
If k=7: Sum=10+2(7)=24 (divisible by 3 ✓)
Thus, the largest value of k is 7.
Sum of digits=4+5+0+k+1+k=10+2k
Since k is a single-digit number, k∈{0,1,2,…,9}. We need to find the largest possible value of k such that 10+2k is divisible by 3.
Let's test the largest single digits for k:
If k=9: Sum=10+2(9)=28 (not divisible by 3)
If k=8: Sum=10+2(8)=26 (not divisible by 3)
If k=7: Sum=10+2(7)=24 (divisible by 3 ✓)
Thus, the largest value of k is 7.