Happy Thursday! Here’s a look back at Monday’s GRE Brain Twister!
13! – 11! is divisible by n but not by n^2. What is the range of values of n if n is a prime number?
The first step is to factor this large number: 11!(13×12 – 1) = 11! (155) = 11!(31)(5). We know that n has to be a prime. Be careful though, because n^2 cannot be a factor of the number. Notice how 5, which is a prime, occurs twice in 11! (the number 5 and in the number 10: 5 x 2). The same holds true for the lowest primes, 2 and 3. There are plenty of 2s that can be factored from 11! and a few 3s as well. 7, however, only occurs once in 11!. Therefore, it is the lowest number that fits the criteria and the number 31 that we factored from 155 at the beginning is the highest prime. This gives us 31-7 = 24, answer (B).