keatross wrote:
Going to need some help on this one for sure (and I do not understand the solution posted)....
I tried to find a pattern between the sizes of f(n) and g(n) given their properties. Didn't really result in much I could use.
I did, however, notice that g(n) will have to skip half of the #s from 1-150, which is 75. Using this I kind of theorized that f(n) will be 75(x all even numbers) times larger than g(n). [E] was my guess as a result, but it was a complete shot in the dark.
i hope this will be clearer
f(150) = 1x2x3x4x5x....150 (product of all integers between 1-150 inclusive)
g(150) = 1x3x5x7x9...149 (product of all odd integers between 1-150)
\(\frac{f(150)}{g(150)}\) = 2x4x6x8x10....150
=> 2^75 (1*2*3*4*...75) [take 2 common from all the terms. There are 75 terms therefore 2^75]
Prime Factor for \(\frac{f(150)}{g(150)}\) = all prime factors from 1 to 75
Since two consecutive terms have no prime factors common , Prime Factor for \(\frac{f(150)}{g(150)}+ 1\) will not have any term between 1 and 75
Therefore p>75