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.1/359999q
C.1200/q
D.360000/q
E.359999*q
p =
(501)(503)...(595)(597).
q =
(501)(503)...(595)(597)(599)(601).
Notice the OVERLAP between p and q.
Implication:
q =
(p)(599)(601).
Since the answer choices are IN TERMS OF A VARIABLE, we can PLUG IN any values for p and q such that q = (p)(599)(601).
Let p =1.
Then q = (1)(599)(601) = (600-1)(600+1) = 360000 - 1 = 359999.
Thus:
1/p + 1/q = 1/1 + 1/359999 = 359999/359999 + 1/359999 = 360000/359999. This is our target.
Now plug q = 359999 into the answers to see which yields our target of 360000/359999.
A quick scan of the answers reveals that only
D works:
360000/q = 360000/359999.
The correct answer is
D.
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