Question

If j, k, and n are consecutive integers such that 0<j<k<n and the units (ones) digit of the product is 9, what is the units digit of k?

I thought of setting the product of x and x+2 to something but didn't know what..

I thought of pairs that get to a unit digit of 9 (1&9, 1&29, 7&7,..) but didn't know what to do.

The key says the answer is 0. How?

Answer 1

wait a minute. If you multiply j*k*n and any of them ends in zero, the product will also end in zero.

Also, if the three are consecutive integers, then at least one of them must be even, so the product cannot end in 9.