If an integer n is to be selected at random from 1 to 100, inclusive, what is probability n(n+1) will be divisible by 32? Choose one.
A) 2 / 7
B) 3 / 7
C) 1 / 16
D) 1 / 14
E) 1 / 12

Rationale: "because n ( n + 1 ) is always an even product of even * odd or odd * even factors , there is a probability of 1 that that it will be divisible by 2 , and , thus , a probability of 1 / 2 that it will be divisible by 4 and , thus , a probability of 1 / 4 that it will be divisible by 8 and , thus , a probability of 1 / 8 that it will be divisible by 16 and , thus , a probability of 1 / 16 that it will be divisible by 32 1 * 1 / 16 = 1 / 16 answer : c"
Answer: C