I randomly pick an integer p between 1 and 10 inclusive. What is the probability that I choose a p such that there exists an integer q so that p and q satisfy the equation pq - 4p - 2q = 2? Express your answer as a common fraction.
+128400 pq - 4p - 2q = 2
(p - 2)(q -4) = pq -4p - 2q + 8 ......so
pq - 4p - 2q = 2
pq - 4p - 2q + 8 - 8 = 2
(p - 2) (q - 4) - 8 = 2
(p - 2) (q - 4) = 10
When
p = 1, q = -6
p = 3, q = 14
p = 4, q = 9
p = 7, q = 6
So....there are 4 p's that satisfy the equation.....so.....the probability of choosing one of these =
4 / 10 = 2 / 5
