Author 
Message 
TAGS:

Hide Tags

Director
Joined: 29 Nov 2012
Posts: 685

Let p = the product of all the odd integers between 500 and
[#permalink]
Show Tags
Updated on: 12 Jun 2013, 21:41
Question Stats:
69% (02:37) correct 31% (02:30) wrong based on 413 sessions
HideShow timer Statistics
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. \(359,999q\)
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by fozzzy on 12 Jun 2013, 08:11.
Last edited by fozzzy on 12 Jun 2013, 21:41, edited 2 times in total.




Math Expert
Joined: 02 Sep 2009
Posts: 59730

Re: Let p = the product of all the odd integers between 500 and
[#permalink]
Show Tags
12 Jun 2013, 09:05
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 1/p + 1/q?
A. 1/600q B. 1/359,999q C. 1,200/q D. 360,000/q E. 359,999q \(q=p*599*601=p(6001)(600+1)=p*(360,0001)=359,999p\) > \(p=\frac{q}{359,999}\). \(\frac{1}{p} + \frac{1}{q}=\frac{359,999}{q}+\frac{1}{q}=\frac{3600,000}{q}\). Answer: D.
_________________




VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1010
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: Let p = the product of all the odd integers between 500 and
[#permalink]
Show Tags
12 Jun 2013, 08:18
\(p=501*503*...*597\) \(q=501*503*...*597*599*601\)
\(\frac{1}{p}+\frac{1}{q}=\frac{p+q}{pq}=\frac{p(1+599*601)}{pq}\)
\(\frac{1+599*601}{q}=\frac{360000}{q}\)




Intern
Status: Currently Preparing the GMAT
Joined: 15 Feb 2013
Posts: 28
Location: United States
GPA: 3.7
WE: Analyst (Consulting)

Re: Let p = the product of all the odd integers between 500 and
[#permalink]
Show Tags
12 Jun 2013, 08:33
Let's formalise these expressions a bit : p = the product of all the odd integers between 500 and 598 Meaning that \(p = 501*503*...*597\) (1) Like wise for \(q\) being the product of all the odd integers between 500 and 602, we get, using (1) : \(q = 501*503*...597*599*601 = p*599*601\) (2) Since we are looking to express \(\frac{1}{p} + \frac{1}{q}\) in terms of \(q\), we get from (2) : \(p = \frac{q}{(599*601)}\) So then : \(\frac{1}{p} + \frac{1}{q}\) \(= \frac{1}{q/(599*601)} + \frac{1}{q} = \frac{1}{q} * (599*601 +1)\) Since\(599 = 600  1\) then \(599*601 + 1 = (600  1)*601 + 1 = 360600  601 + 1 = 360599 + 1 = 360000\) Which yields \(\frac{1}{p} + \frac{1}{q}\) = \(\frac{360000}{q}\) Which is answer choice D. Hope that helped



Manager
Joined: 23 May 2013
Posts: 92

Re: Let p = the product of all the odd integers between 500 and
[#permalink]
Show Tags
11 Jan 2014, 21:11
i think we can first simplify, expression 1/p +1/q to 1/q (q/p + 1). This way its easier to visualize that q/p will be only 599*601.



Board of Directors
Joined: 17 Jul 2014
Posts: 2491
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: Let p = the product of all the odd integers between 500 and
[#permalink]
Show Tags
04 May 2016, 19:37
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 = (6001)(600+1) = 359,999 we add one and get 360,000 now...final step 360,000/q answer is D



GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4158
Location: Canada

Re: Let p = the product of all the odd integers between 500 and
[#permalink]
Show Tags
30 Aug 2016, 17:03
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. \(359,999q\) 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)]Answer:
_________________
Test confidently with gmatprepnow.com



Manager
Joined: 16 Jan 2017
Posts: 59

Re: Let p = the product of all the odd integers between 500 and
[#permalink]
Show Tags
23 Mar 2017, 05:00
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



Math Expert
Joined: 02 Sep 2009
Posts: 59730

Re: Let p = the product of all the odd integers between 500 and
[#permalink]
Show Tags
23 Mar 2017, 05:37
vmelgargalan wrote: 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 \((ab)(a+b) = a^2  b^2\), thus \((6001)(600+1)=600^2  1^2=(360,0001)\). Theory on Algebra: http://gmatclub.com/forum/algebra101576.htmlAlgebra  Tips and hints: http://gmatclub.com/forum/algebratips ... 75003.htmlDS Algebra Questions to practice: http://gmatclub.com/forum/search.php?se ... &tag_id=29PS Algebra Questions to practice: http://gmatclub.com/forum/search.php?se ... &tag_id=50Hope it helps.
_________________



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8701
Location: United States (CA)

Re: Let p = the product of all the odd integers between 500 and
[#permalink]
Show Tags
27 Mar 2017, 11:49
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 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. Thus: q = p(599)(601) Now we can evaluate 1/p + 1/q as: 1/p + 1/q = (599)(601)/[p(599)(601)] + 1/q = (599)(601)/q + 1/q = [(599)(601) + 1]/q Notice that (599)(601) = (600  1)(600 + 1) = 600^2  1. Thus, the numerator (599)(601) + 1 becomes 600^2  1 + 1, or simply 600^2. Therefore: 1/p + 1/q = [(599)(601) + 1]/q = 600^2/q = 360,000/q Answer: D
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Director
Joined: 12 Nov 2016
Posts: 694
Location: United States
GPA: 2.66

Re: Let p = the product of all the odd integers between 500 and
[#permalink]
Show Tags
16 Apr 2017, 19:46
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 P =1. Q= (1)(599)(601) = (6001)(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.



Retired Moderator
Joined: 19 Mar 2014
Posts: 915
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5

Re: Let p = the product of all the odd integers between 500 and
[#permalink]
Show Tags
09 Jul 2017, 07:23
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. \(359,999q\) \(p = 501 * 503 * 505 * ............ * 597\) \(q = 501 * 503 * 505 * ......................* 599 * 601\) \(p = \frac{q}{599 * 601}\) \(\frac{1}{p} + \frac{1}{q}\) \(= \frac{1}{q/599 * 601} + \frac{1}{q}\) \(= \frac{599 * 601}{q} + \frac{1}{q}\) \(= \frac{599*601 + 1}{q}\) \(= \frac{(600  1) (600 + 1) + 1}{q}\) \(= \frac{((600)^2 + 600  600  1) + 1}{q}\) \(= \frac{(600)^2}{q}\) \(= \frac{360,000}{q}\) Hence, Answer is D
_________________
"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."
Best AWA Template: https://gmatclub.com/forum/howtoget60awamyguide64327.html#p470475



NonHuman User
Joined: 09 Sep 2013
Posts: 13742

Re: Let p = the product of all the odd integers between 500 and
[#permalink]
Show Tags
27 Jul 2019, 04:27
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: Let p = the product of all the odd integers between 500 and
[#permalink]
27 Jul 2019, 04:27






