Which digits should come in the place of x and y, respectively, if the number 62684xy is divisible by both 8 and 5?

Question

Accepted Answer

To find digits x and y such that the number 62684xy is divisible by both 8 and 5, we use the divisibility rules for 8 and 5.

1. Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5. So, y can be 0 or 5.

2. Divisibility by 8: A number is divisible by 8 if the last three digits form a number divisible by 8.

The last three digits here are 4xy.

Since y must be 0 or 5, check both cases:

- If y = 0, last three digits are 4x0.
- If y = 5, last three digits are 4x5.

Check divisibility by 8 for each:

For y = 0:
- Try x = 0: 400 ÷ 8 = 50 (divisible)
- x = 1: 410 ÷ 8 = 51.25 (not divisible)
- x = 2: 420 ÷ 8 = 52.5 (not divisible)
- x = 3: 430 ÷ 8 = 53.75 (not divisible)
- x = 4: 440 ÷ 8 = 55 (divisible)

For y = 5:
- 4x5 will be 405, 415, 425, 435, 445, etc., none of which are divisible by 8 because 405 ÷ 8 = 50.625, 415 ÷ 8 = 51.875, etc.

So y must be 0, and x can be 0 or 4 for divisibility by 8.

Given the options, only x=4 and y=0 is provided and correct.

Hence, the digits are x = 4 and y = 0.

Answer

Answer

Answer