A class of students appeared in two different tests of quantitative ability both of which were scored out of 100. The scores of each student in each test could be expressed as a product of two distinct prime numbers. If a student’s scores in the two tests did not have any common prime factors, what is the maximum possible difference between his two scores?  Choose one.
A) 79  B) 83  C) 88  D) 89  E) 91
I started by listing out the primes   2,3,5,7,11,13,17,19,23,29,31,37   Then I tried to maximize the score--we know the minimum score will be 6 as the product has to be between two distinct primes.   Our max score is 100 so lets try to get as close to 100 as possible. 19*5=95   95-6= 
<gadget id="calculator">95-6</gadget>
<output>89</output>
89   ANSWER:89
<result>D</result>
A class of students appeared in two different tests of quantitative ability both of which were scored out of 100. The scores of each student in each test could be expressed as a product of two distinct prime numbers. If a student’s scores in the two tests did not have any common prime factors, what is the maximum possible difference between his two scores?