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 ?

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) (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

RELATED QUESTIONS
Right now I'm working on a PSAT Practice Booklet and I'm not sure how to solve it.... (answered by jim_thompson5910)
Two positive integers j and k satisfy the relation jRk if and only if {{{j=k^2+1}}}. If... (answered by solver91311)
|Angles J and K are complementary. If J= x-9 and K= x=5, what is the measure of each... (answered by tommyt3rd)
If n and k are integers whose product is 400, which of the following statements... (answered by Edwin McCravy)
If we find I=J and J>K then which of the following is true? IJ... (answered by MathLover1)
Conditional proof M->(K->L) (L\/N) -> J Therefore, M-> (K->J) That's supposed to be (answered by math_helper)
a b c d e f g h i j k l m n o p q r (answered by ewatrrr)
if j is chosen at random from the set { 4,5.6 }and k is chosen at random from the set {... (answered by robertb)
If j and k are integers and j+k = 2j +4, which of the following must be true ? I.... (answered by richwmiller,hokies)