Bunuel wrote:
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?
A. 79
B. 83
C. 88
D. 89
E. 91
Are You Up For the Challenge: 700 Level QuestionsTo get maximum possible difference between two scores, we need the smallest score and the greatest score such that each is made up by multiplying exactly two distinct prime factors and such that they have no prime factors in common.
We need to find the greatest score which is made up of 2 prime factors only.
100 = 2*50
99 = 9*11
98 = 2*49
97 = prime (only 1 prime factor)
96 = 32*3
95 = 5*19 (the score with exactly 2 prime factors)
Then we can make the smallest such score by multiplying the 2 smallest prime numbers 2 and 3 since 95 has neither 2 nor 3 as a factor.
Smallest score = 2*3 = 6
Difference between them = 95 - 6 = 89
Answer (D)