Answer:
Explanation:
To find the possible values of x in the four-digit number 7x45y that is divisible by 9 and leaves a remainder of 2 when divided by 4, we can use the divisibility rule for 9 and the remainder theorem for 4.
1. Divisibility rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
Since the number 7x45y is divisible by 9, the sum of its digits must also be divisible by 9. We can find the sum of the digits by adding 7 + x + 4 + 5 + y.
2. Remainder theorem for 4: A number leaves a remainder of 2 when divided by 4 if its last two digits form a number that is divisible by 4.
Since the number 7x45y leaves a remainder of 2 when divided by 4, the last two digits, 5 and y, must form a number that is divisible by 4. This means that y can only be 2, 6, or 0 (since 52, 56, and 50 are divisible by 4).
Now, let's combine these conditions to find the possible values of x:
- If y is 2: The possible values of x are 1, 4, 7 since 7 + x + 4 + 5 + 2 = 18 (divisible by 9).
- If y is 6: The possible values of x are 0, 3, 6, 9 since 7 + x + 4 + 5 + 6 = 22 (divisible by 9).
- If y is 0: The possible values of x are 2, 5, 8 since 7 + x + 4 + 5 + 0 = 16 (divisible by 9).
Therefore, the possible values of x are 1, 4, 7, 0, 3, 6, 9, 2, 5, 8.