If j, k, and n are consecutive integers such that 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 . Either both numbers you’re multiplying have to be , or one has to be and one has to be . Since we’re dealing with consecutive integers, and can’t both end in , so they’re going to have to end in and .
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 or more digits. That’s why you can have units digit be .
Say , , and . Then (units digit is ), and the units digit of .
Hence option A is correct.