If “62x2365y” is an eight-digit number divisible by 72, then find the value of ‘x^2 + y^2 – xy’.OPTIONS 36 32 40 28

To find the value of 'x^2 + y^2 – xy', we first need to understand that a number is divisible by 72 if and only if it is divisible by both 8 and 9 (since 72 is the product of 8 and 9).

1. For a number to be divisible by 8, the last three digits must be divisible by 8. So, '65y' must be divisible by 8. The only possible values of 'y' that satisfy this condition are 2 and 6.

2. For a number to be divisible by 9, the sum of its digits must be divisible by 9. So, '6 + 2 + x + 2 + 3 + 6 + 5 + y' must be divisible by 9. This simplifies to 'x + y + 24' must be divisible by 9.

3. If 'y' is 2, then 'x + 2 + 24' must be divisible by 9, which means 'x' must be 1 or 10. But 'x' can't be 10 because it's a single digit, so 'x' must be 1.

4. If 'y' is 6, then 'x + 6 + 24' must be divisible by 9, which means 'x' must be 7.

5. So, the possible pairs of (x, y) are (1, 2) and (7, 6).

6. Substituting these values into the expression 'x^2 + y^2 – xy' gives us '1^2 + 2^2 – 12 = 1 + 4 - 2 = 3' and '7^2 + 6^2 – 76 = 49 + 36 - 42 = 43'.

7. Neither of these values match any of the options given, so there seems to be a mistake in the question or the options.