Expert: Paul Klarreich - 2/8/2007

Question
If J, K, N are consecutive integers such that O<J<K<N and the units (ones) digit of the product JN is 9. What is the units digit of K?
A. 0  B. 1  C. 2  D. 3  E. 4

Answer
Questioner:   Beth
Category:  Calculus
 
Subject:  pre calc
Question:  If J, K, N are consecutive integers such that O<J<K<N and the units (ones) digit of the product JN is 9. What is the units digit of K?
A. 0  B. 1  C. 2  D. 3  E. 4
..............................................
Hi, Beth,

I don't know whether this really belongs in the Calculus section; as you noted, it's precalc -- VERY pre.

Still....   This is more a puzzle than a problem.

If the units digit of a product is 9, then the two integers are clearly odd.  So the possibilities are:

1.  J,N mod 10 = 1,3;  product mod 10 = 3
2.  J,N mod 10 = 3,5;  product mod 10 = 5
3.  J,N mod 10 = 5,7;  product mod 10 = 5
4.  J,N mod 10 = 7,9;  product mod 10 = 3
5.  J,N mod 10 = 9,1;  product mod 10 = 9

Looks as if (5) is the choice.  Then K must end in a zero.