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# In a certain business, production index p is directly

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In a certain business, production index p is directly [#permalink]  06 May 2008, 23:49
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64% (02:02) correct 35% (01:15) wrong based on 130 sessions
In a certain business, production index p is directly proportional to efficiency index e, which is in turn directly proportional to investment i. What is p if i = 70?

(1) e = 0.5 whenever i = 60
(2) p = 2.0 whenever i = 50
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Mar 2012, 13:05, edited 1 time in total.
Edited the question
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Re: OG - proportional index [#permalink]  07 May 2008, 00:31
we need P when i is some value...

we know p is dependent on e and e is dependent on i

In a certain business, production index p is directly proportional to efficiency index e, which is in turn directly proportional to investment i. What is p if i = 70?

1) e = 0.5 whenever i = 60 -> does not give the value or relation between e and P thus insufficient
2) p = 2.0 whenever i = 50 -> gives the relation between p and i thus we can find p when i=70

thus B
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Re: OG - proportional index [#permalink]  07 May 2008, 06:22
i say B as well, unless im missing something.

From stat 1, you know relationship btwn e and i, but you dont know what it is btwn p and e ... so insuff.

From stat 2, you are given the relationship btwn p and i, and from the stem you know what i is. so suff.
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Re: OG - proportional index [#permalink]  28 Nov 2010, 18:50
Would p be directly proportional to i as well if e is proportional to p? I am thinking it should be, however the constant proportion will be different between p and e and e and i and thus entirely separate between p and i? thanks.
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Re: OG - proportional index [#permalink]  29 Nov 2010, 00:45
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gettinit wrote:
Would p be directly proportional to i as well if e is proportional to p? I am thinking it should be, however the constant proportion will be different between p and e and e and i and thus entirely separate between p and i? thanks.

a is directly proportional to b means that as the absolute value of b gets bigger, the absolute value of a gets bigger too, so there is some non-zero constant x such that a=xb;

So if a is directly proportional to b (a=xb), then vise-versa is also correct: b is directly proportional to a (b=\frac{1}{x}*a as the absolute value of a gets bigger, the absolute value of b gets bigger too).

a is inversely proportional to b means that as the absolute value of b gets bigger, the absolute value of a gets smaller, so there is some non-zero constant constant y such that a=\frac{y}{b}.

So if a is inversely proportional to b (a=\frac{y}{b}), then vise-versa is also correct: b is inversely proportional to a (b=\frac{y}{a} as the absolute value of a gets bigger, the absolute value of b gets smaller).

As for the question:
In a certain business, production index p is directly proportional to efficiency index e, which is in turn directly proportional to investment i. What is p if i = 70?

Given: p=ex and e=iy (for some constants x and y), so p=ixy. Question: p=70xy=? So, basically we should find the value of xy.

(1) e = 0.5 whenever i = 60 --> as e=iy then 0.5=60y --> we can find the value of y, but still not sufficient.
(2) p = 2.0 whenever i = 50 --> as p=ixy then 2=50xy --> we can find the value of xy. Sufficient.

Hope it's clear.
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Re: OG - proportional index [#permalink]  29 Nov 2010, 05:41
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gettinit wrote:
Would p be directly proportional to i as well if e is proportional to p? I am thinking it should be, however the constant proportion will be different between p and e and e and i and thus entirely separate between p and i? thanks.

production index p is directly proportional to efficiency index e,
implies p = ke (k is the constant of proportionality)

e is in turn directly proportional to investment i

implies e = mi (m is the constant of proportionality. Note here that I haven't taken the constant of proportionality as k here since the constant above and this constant could be different)

Then, p = kmi (km is the constant of proportionality here. It doesn't matter that we depict it using two variables. It is still just a number)

e.g. if p = 2e and e = 3i
p = 6i will be the relation. 6 being the constant of proportionality.

So if you have i and need p, you either need this constant directly (as you can find from statement 2) or you need both k and m (statement 1 only gives you m).
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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Manager Joined: 13 Jul 2010 Posts: 172 Followers: 1 Kudos [?]: 13 [0], given: 7 Re: OG - proportional index [#permalink] 29 Nov 2010, 20:54 Thanks Karishma and Bunuel very helpful explanations. Intern Joined: 05 Mar 2013 Posts: 48 Location: India Concentration: Entrepreneurship, Marketing GMAT Date: 06-05-2013 GPA: 3.2 Followers: 1 Kudos [?]: 13 [0], given: 14 In a certain business production index p is directly [#permalink] 16 May 2013, 08:03 In a certain business, production index P is directly proportional to efficiency index E,which is in turn directly proportional to investment index i ,What is P if i = 70.? (1) e = 0.5 whenever i = 60. (2) p = 2.0 whenever i = 50. _________________ "Kudos" will help me a lot!!!!!!Please donate some!!! Completed Official Quant Review OG - Quant In Progress Official Verbal Review OG 13th ed MGMAT IR AWA Structure Yet to do 100 700+ SC questions MR Verbal MR Quant Verbal is a ghost. Cant find head and tail of it. Math Expert Joined: 02 Sep 2009 Posts: 16817 Followers: 2774 Kudos [?]: 17576 [0], given: 2225 Re: In a certain business production index p is directly [#permalink] 16 May 2013, 08:12 Expert's post SrinathVangala wrote: In a certain business, production index P is directly proportional to efficiency index E,which is in turn directly proportional to investment index i ,What is P if i = 70.? (1) e = 0.5 whenever i = 60. (2) p = 2.0 whenever i = 50. Merging similar topics. Please refer to the solutions above. _________________ Intern Joined: 05 Mar 2013 Posts: 48 Location: India Concentration: Entrepreneurship, Marketing GMAT Date: 06-05-2013 GPA: 3.2 Followers: 1 Kudos [?]: 13 [0], given: 14 Re: In a certain business, production index p is directly [#permalink] 16 May 2013, 08:17 If P id directly proportional to E then what is the relation between them? Is it only P = E * x Or can it also be P = E*x + y. In both the cases P is directly proportional to E. As in the question the author doesn't mention anything about the values of the variables when either of them is zero, it leads to a confusing situation. Please Clarify _________________ "Kudos" will help me a lot!!!!!!Please donate some!!! Completed Official Quant Review OG - Quant In Progress Official Verbal Review OG 13th ed MGMAT IR AWA Structure Yet to do 100 700+ SC questions MR Verbal MR Quant Verbal is a ghost. Cant find head and tail of it. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4028 Location: Pune, India Followers: 857 Kudos [?]: 3613 [0], given: 144 Re: In a certain business, production index p is directly [#permalink] 17 May 2013, 08:02 Expert's post SrinathVangala wrote: If P id directly proportional to E then what is the relation between them? Is it only P = E * x Or can it also be P = E*x + y. In both the cases P is directly proportional to E. As in the question the author doesn't mention anything about the values of the variables when either of them is zero, it leads to a confusing situation. Please Clarify It is P = E*k only. It cannot be P = E*k + m Directly proportional means that if one doubles, other doubles too. If one becomes half, other becomes half too. It doesn't happen in case you add a constant. P = 2E + 1 If E = 5, P = 11 If E = 10, P = 21 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Re: In a certain business, production index p is directly   [#permalink] 17 May 2013, 08:02
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