If the four-digit number $463y$ is divisible by 7, then what is the value of $y$?

Question

Accepted Answer

**Solution:**

1. The divisibility rule for 7 states that a number is divisible by 7 if the difference between the number formed by the first three digits and twice the last digit is divisible by 7.

2. Here, the number is $463y$, where the first three digits form the number 463 and the last digit is $y$.

3. Applying the rule:
   $$463 - 2 	imes y$$

4. We check each option:
   - For $y=4$: $$463 - 2 	imes 4 = 463 - 8 = 455$$
     - $455 \div 7 = 65$ (no remainder), so divisible by 7.

- For $y=6$: $$463 - 2 	imes 6 = 463 - 12 = 451$$
     - $451 \div 7 = 64$ remainder 3, not divisible.

- For $y=3$: $$463 - 2 	imes 3 = 463 - 6 = 457$$
     - $457 \div 7 = 65$ remainder 2, not divisible.

- For $y=5$: $$463 - 2 	imes 5 = 463 - 10 = 453$$
     - $453 \div 7 = 64$ remainder 5, not divisible.

**Answer:** The value of $y$ is $4$.

Answer

Answer

Answer