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by j_shreyans » Sun Apr 26, 2015 4:18 am
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)159,999q
C)1,200/q
D)360,000/q
E)359,999q

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by GMATGuruNY » Sun Apr 26, 2015 5:40 am
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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by Brent@GMATPrepNow » Sun Apr 26, 2015 5:40 am
Abhijit K 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 1/p + 1/q ?

A.1/600q
B.1/359999q
C.1200/q
D.360000/q
E.359999q
p = (501)(503)(505)...(597)
q = (501)(503)(505)...(597)(599)(601)
So, q = (p)(599)(601)

So, 1/p + 1/q = 1/p + 1/(p)(599)(601) [replaced q with (p)(599)(601)]
= (599)(601)/(p)(599)(601) + 1/(p)(599)(601) [found common denominator]
= [(599)(601) + 1]/(p)(599)(601)
= 360,000/(p)(599)(601)
= 360,000/q [since q = (p)(599)(601)]
= D

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Brent
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