Which of the following numbers is divisible by 36 ?

For a number to be divisible by 36, it must be simultaneously divisible by both 4 and 9 (since 36=4×9 and gcd(4,9)=1).
Divisibility rule of 4: The last two digits of the number must be divisible by 4.

Divisibility rule of 9: The sum of all digits of the number must be divisible by 9.

Let's test each option:

Option A: 1542

Last two digits: 42 (not divisible by 4)

Option B: 96272

Last two digits: 72 (divisible by 4, 18×4=72)

Sum of digits: 9+6+2+7+2=26 (not divisible by 9)

Option C: 55512

Last two digits: 12 (divisible by 4, 3×4=12)

Sum of digits: 5+5+5+1+2=18 (divisible by 9)

Since it is divisible by both 4 and 9, it is divisible by 36.

Option D: 8840

Last two digits: 40 (divisible by 4)

Sum of digits: 8+8+4+0=20 (not divisible by 9)