First Problem

I got an answer that was not in the choices.

To determine if a number is divisible by 9 you add the digits - if the sum is divisible by 9 then the entire number is divisible by 9. If n and n^2 have the same units digit that means the square of the units digit will be the same (this will happen with 0, 1, 5 and 6).

Now we want to be methodical - if the units digit is 0 and the sum of the digits is divisible by 9 we need the other two digits to add to 9 or 18. Be methodical.

If the units digit is 0
Could be 900, 810, 180, 720, 270, 630, 360, or could be 990, 450 or 540 (10 different numbers)

If the units digit is 1
could be 801, 711, 171, 621, 261, 531, 351, 441, or 891, 981 (10 numbers)

If units digit is 5
Could be 405, 315, 135, 225 or 945, 495, 855, 585, 765, 675 ( 10 numbers)

If units digit is 6
could be 306, 216, 126 or 936, 396, 846, 486, 756, 576, 666 ( 10 numbers)

Thus there are 40 numbers (looks like the answer only looked at the numbers that add to 9 - which would be 22)

Hi,

I agree with Becky, except that there are two more possibilities: 450 and 540.

I agree - sorry I missed those two.