gmatophobia
PS Question 1 - September 21 The function f(n) is defined as the product of all integers from 1 to n, inclusive, and the function g(n) is defined as the product of all odd integers from 1 to n, inclusive, where n is a positive integer. If p is a prime factor of {f(150)/g(150)} + 1, then which of the following must be true? A. p < 10 B. 10 < p < 25 C. 25 < p < 50 D. 50 < p < 75 E. p > 75 Source:
e-GMAT | Difficulty: Hard
F(150) is basically 150!
When divided by odd factors of g(n), i.e., 150
Remains from 150! are, 150x148x146x.....x2
So, all the odd ones are out and all remaining can be written as a multiple of 2
(2x75)(2x74)......
2 is a prime no.
+1 basically is just remainder
It is the smallest prime divisor, so it has to be greater than 75
Priyanshu2807
(2x75)(2x74)......
Simplified form is 2 with power of 75 x 75! +1
2^75 x 75! + 1