If j, k, and n are consecutive integers such that 0<j<k<n and the units (ones) digit of the product jn is 9, what is the units digit of k ?
There are only a few ways you can make a product have a units digit of 9. Either both numbers you’re multiplying have to be 3, or one has to be 1 and one has to be 9. Since we’re dealing with consecutive integers, j and n can’t both end in 3, so they’re going to have to end in 1 and 9.
It’s important to remember that although we only really care about the units digits in this problem, we’re dealing with numbers that might (or in fact, must) be 2 or more digits. That’s why you can have k′s units digit be 0.
Say j=19, k=20, and n=21. Then jn=(19)(21)=399 (units digit is 9), and the units digit of k=0.
Hence option A is correct.