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

$\dfrac1p+\dfrac1q=\dfrac{359,999}{359,999p}+\dfrac1q=\dfrac{359,999+1}q=\dfrac{360,000}q$

and the answer is D.