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 = (599)(601)p
p = q/(599*601).
Since the answer choices are IN TERMS OF A VARIABLE, we can PLUG IN any values for p and q such that p = q/(599*601).
Let q=1.
Then p = 1/(599*601), implying that 1/p = 599*601 = (600-1)(600+1) = 360000 - 1.
Thus:
1/p + 1/q = (360000 - 1) + 1/1 = 360000. This is our target.
Now plug q=1 into the answers to see which yields our target of 360000.
A quick scan of the answers reveals that only
D works:
360000/q = 360000/1 = 360000.
The correct answer is
D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
