Question

Let p = the product of all the odd integers between 500 and 598, and let q = the product of all the odd integers between 500 and 602. In terms of q , what is the value of 1/p+1/q ?

A) 1/600q
B) 1/359,999q
C) 1,200/q
D) 360,000/q
E) 359,999/q

Answer 1

`p=501\cdot503\cdot\cdots\cdot597`

`q=\underbrace{501\cdot503\cdot\cdots\cdot597}_p\cdot599\cdot601`

So we have
`q=359,999p`. Then

`\frac1p+\frac1q=(359,999)/(359,999p)+\frac1q=\frac{359,999+1}q=\frac{360,000}q`

and the answer is D.