SOLUTION: Hello, I need help with the following math problem: I randomly pick an integer {{{ p }}} between {{{ 1 }}} and {{{ 10 }}} inclusive. What is the probability that I choose a

Question 1046465: Hello,
I need help with the following math problem:
I randomly pick an integer between and inclusive. What is the probability that I choose a such that there exists an integer so that and satisfy the equation ? Express your answer as a common fraction.
Thank you,
Nicole
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
pq - 4p - 2q = 2 if and only if (p-2)(q-4) = 10. If p-2 is any factor of 10 (incl. negative factors) then there will exist an integer q such that the equation holds, and if p-2 is not a factor of 10, then there is no such q.

Possible values of p: 1, 3, 4, 7 --> probability = 4/10 = 2/5
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