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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.

 Jan 11, 2019
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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

 

 

 

cool cool cool

 Jan 11, 2019
edited by CPhill  Jan 11, 2019

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