If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2^i * 3^k * 5^m * 7^p, then i + k + m + p = Answers.
A) 4
B) 7
C) 8
D) 11
E) 12

Rationale: given that x = 8 ! = 2 ^ 7 ∗ 3 ^ 2 ∗ 5 ∗ 7 x . hence , x = 2 ^ 7 ∗ 3 ^ 2 ∗ 5 ^ 1 ∗ 7 ^ 1 = 2 ^ i ∗ 3 ^ k ∗ 5 ^ m ∗ 7 p , since i , k , m , and p are positive integers , then we can equate the exponents , so we have that i = 7 , k = 2 , m = 1 , and p = 1 therefore , i + k + m + p = 7 + 2 + 1 + 1 = 11 answer : d .
Answer: D