How many even 3 digit integers greater than 700 with distinct non zero

Let us try for an approximate answer since the values in the choices are far apart by relaxing some constraints.

The last digit can change in 4 ways
The middle digit can change in 8 ways
The first digit can change in 3 ways

This is 4*8*3 = 96 only even with relaxation of constraints. Choices A,B and C can be eliminated

There are some more numbers which will not be included.

when first digit is 7, second digit cannot be 7. So the possibilities reduce to 4*8*2 + 4*7*1=92
Similarly when first digit is 9, second digit cannot be 9 and the possibilities reduce by 4 more = 88.

The number of possibilities will be less than 88 because when first digit is 8, there are other impossible numbers.

So now we can pick the answer as E