SOLUTION: If J, K, and N are consecutive integers such that 0 < J < K < N and the unit's (ones) digit of the product JN is 9, what is the unit's digit of K ?

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Question 55323: If J, K, and N are consecutive integers such that 0 < J < K < N and the unit's (ones) digit of the product JN is 9, what is the unit's digit of K ?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
If J, K, and N are consecutive integers such that 0 < J < K < N 
and the unit's (one's) digit of the product JN is 9, what is the unit's
digit of K 

Since JN ends in 9, then either

1. J and N both end in 3

Or

2. One of J, N ends in 9 and the other ends in 1

They can't both end in 3 because N is 2 more than J, and if
one of them ended in 3 the other would either have to end 
in either 1 or 5.  So case 1 is out.

So case 2 is the only possibility. 

J can't end in 1 because since N=J+2 that would make N end
in 3, not 9

So J must end in 9 and N, being 2 more than J, must end in 1.

So K, being 1 less than a number ending in 1, and 1 more than
a number ending in 9, must end in 0.

That's the answer, 0, since the unit's digit is the last digit.

Edwin