A 2-digit number, divisible by 11, is multiplied by 99.

If the 3rd digit is 7, what is the 4-digit product?

Multiplying by 99 is the same as multiplying by 100 and then subtracting the original number.

If the original number is kk, then after multiplying by 99 the product equals

kk00

- kk

This is a 4 digit number, whose digits (in order) are

k, k-1, 9-k, and 10-k

If 9-k = 7 then k = 2 and the digits are 2,1,7 and 8.

Funal answer: 2178