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# In a certain business, production index p is directly proportional to

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Director
Joined: 09 Mar 2016
Posts: 863
Re: In a certain business, production index p is directly proportional to  [#permalink]

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24 Aug 2018, 09:03
Bunuel wrote:
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.

2 = 50
x = 70

Cross Multiply
x = 2.8

is it correct approach ? if not why ?
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Manager
Joined: 05 Nov 2015
Posts: 70
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In a certain business, production index p is directly proportional to  [#permalink]

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24 Aug 2018, 09:40
1
VeritasKarishma , Bunuel -- is below approach correct ?

What is p if i = 70?

(1) e = 0.5 whenever i = 60 --> no P , n no relation between e & P is established, hence insufficient
(2) p = 2.0 whenever i = 50

(2) if i = 10 --> P = 2/10
if i = 70 --> P = 2/10 *7 --> p=2.8
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Re: In a certain business, production index p is directly proportional to  [#permalink]

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25 Aug 2018, 06:18
VeritasKarishma , Bunuel -- is below approach correct ?

What is p if i = 70?

(1) e = 0.5 whenever i = 60 --> no P , n no relation between e & P is established, hence insufficient
(2) p = 2.0 whenever i = 50

(2) if i = 10 --> P = 2/10
if i = 70 --> P = 2/10 *7 --> p=2.8

Yes it is fine but you first need to deduce that p is directly proportional to i to solve it this way.
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Re: In a certain business, production index p is directly proportional to &nbs [#permalink] 25 Aug 2018, 06:18

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