Find the maximum value of (x + y) if 7x52y4 is divisible

Solution

ATQ, A number is divisible by 12 if it is divisible by both 3 and 4. A number is divisible by 4 when last two digits of the number are divisible by 4. y4 is divisible by 4 when y = 0, 2, 4, 6 or 8. Since we have to find maximum value, so y = 8. A number is divisible by 3 when sum of its digits is divisible by 3. So, (7 + x + 5 + 2 + 8 + 4) = (26 + x) must be divisible by 3. So, x = 1, 4 or 7. Since we have to find maximum value, so x = 7. Therefore, required value = 7 + 8 = 15.