the 'connection' between any two positive integers a and b : product of a and b
-positive integer 'y' is less than '20'
-'connection' between 'y' and 6=1/1
$$ratio=\frac{1}{1}=\operatorname{lcm}\ and\ product\ are\ equal$$
$$This\ means\ 1\ is\ the\ only\ common\ factor\ between\ 'y'\ and\ '6'$$
$$\sin ce\ '6'\ has\ 2\ factors\ \left[2\ and\ 3\right]$$
''y'' can have values as all those numbers which are not multiples of 2 and 3, and less than 2
$$y=\left\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19\right\}$$
$$Therefore,\ y=\left\{1,5,7,11,13,17,19\right\}$$
$$Hence,\ y\ has\ 7\ possible\ values$$
option A<i class="em em-innocent"></i>

BTGmoderatorRO wrote:The "connection" between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24/96 = 1/4

The positive integer y is less than 20 and the connection between y and 6 is equal to 1/1. How many possible values of y are there?
A. 7
B. 8
C. 9
D. 10
E. 11

We need to determine each integer y less than 20 whose LCM with 6 is identical to the product of that integer y and 6. That is, each of these values has to be relatively prime to 6. So they are 1, 5, 7, 11, 13, 17 and 19 for a total of 7 values.

(Recall that relatively prime numbers share no common factor besides 1. For example, 6 and 11 are relatively prime because the only factor they share in common is 1.)

Answer: A