fozzzy wrote:
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 \(\frac{1}{p}\)+ \(\frac{1}{q}\)?
A. \(\frac{1}{600q}\)
B. \(\frac{1}{359,999q}\)
C. \(\frac{1,200}{q}\)
D. \(\frac{360,000}{q}\)
E. \(359,999q\)
We can solve this question using algebra:
p =
(501)(503)...(595)(597).
q =
(501)(503)...(595)(597)(599)(601).
The overlap between P and Q implies that
q = (p)(599)(601)
We could do this with another set of numbers (p is the odd integers between 2 and 8, q is the odd integers between 2 and 12)
p= 3 x 5 x 7
q=3 x 5 x 7 x 9 x 11
105= p (11)(9)
Anyways
The answer choices are in terms of a variable so are result must be in the form of P+q/pq
P =1.
Q= (1)(599)(601) = (600-1)(600+1) = 360000 - 1 = 359999.
Therefore
1/p + 1/q = 1/1 + 1/359999 = 359999/359999 + 1/359999 = 360000/359999 = p + q/ q=
Plug in q = 359999 into the answers to see which equals 360000/359999.
360000/q = 360000/359999.
Thus D.