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Let p = the product of all the odd integers between 500 and [#permalink]

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12 Jun 2013, 07:11

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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. \(359,999q\)

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. 359,999q

Re: Let p = the product of all the odd integers between 500 and [#permalink]

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04 May 2016, 18:37

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. \(359,999q\)

oh wow..good question..requires some outside the box thinking... p=q/599*601

1/p + 1/q = p+q/pq

first thing: p+q q/599*601 + q = q+q(599*601)/599*601

pq = q^2/599*601

now

[q+q(599*601)/599*601] * [599*601/q^2]

we can simplify by 599*601 we get q+q(599*601)/q^2 we can factor out q in the numerator = q(1+599*601)/q^2 divide both sides by q 1+599*601/q 599*601 = (600-1)(600+1) = 359,999 we add one and get 360,000 now...final step 360,000/q

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. \(359,999q\)

p = (501)(503)(505)...(597) q = (501)(503)(505)...(597)(599)(601) So, q = (p)(599)(601)

Re: Let p = the product of all the odd integers between 500 and [#permalink]

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23 Mar 2017, 04:00

I am struggling a bit with this question. I do not understand how 359,999pq=p∗599∗601=p(600−1)(600+1)=p∗(360,000−1)=359,999p --> p=q359,999p=q359,999 .

This type of questions are just a big confusing in general. Any advice on where to revise this type of questions

I am struggling a bit with this question. I do not understand how 359,999pq=p∗599∗601=p(600−1)(600+1)=p∗(360,000−1)=359,999p --> p=q359,999p=q359,999 .

This type of questions are just a big confusing in general. Any advice on where to revise this type of questions

We applied there \((a-b)(a+b) = a^2 - b^2\), thus \((600-1)(600+1)=600^2 - 1^2=(360,000-1)\).

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 are given that p = the product of the odd integers from 500 to 598, i.e., from 501 to 597 inclusive. We are also given that q = the product of the odd integers from 500 to 602, i.e., 501 to 601 inclusive.

Re: Let p = the product of all the odd integers between 500 and [#permalink]

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16 Apr 2017, 18:46

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

Re: Let p = the product of all the odd integers between 500 and [#permalink]

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09 Jul 2017, 06:23

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. \(359,999q\)

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

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