Data Sufficiency

e-GMAT

For any integer n greater than 1, factorial denotes the product of all the integers from 1 to n, inclusive. It's given that aa and b are two positive integers such that b>a. What is the total number of factors of the largest number that divides the factorials of both a and b?

1) a is the greatest integer for which 3^a is a factor of the product of integers from 1 to 20, inclusive.
2) b is the largest possible number that divides positive integer n, where n^3 is divisible by 96.

OA A

Given two positive integers a and b such that b > a
Find the total number of factors of the largest number which divides the factorial of both a and b . In other words ; what is the value of a?

Statement 1
a is the greatest integer for which $$3^a$$ is a factor for product of integers from 1 to 20 inclusive.
This is asking for how many 3's we can find in 20!
20/3 = 6 remainder 2
20/9 = 2 remainder 2
6 + 2 = 8 hence, a = 8 as 20! can be divided on 3, hence statement 1 is INSUFFICIENT.

Statement 2
b is the largest possible number that divides positive integer n where $$n^3$$ is divisible by 96.
There was no information on the value of a, hence relationship between a and b cannot be established . Statement 2 is INSUFFICIENT.
Statement 1 alone is SUFFICIENT.

$$answer\ is\ Option\ A$$