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

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Re: In a certain business, production index p is directly proportional to  [#permalink]

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New post 24 Aug 2018, 08:03
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.

Answer: B.

Hope it's clear.



2 = 50
x = 70

Cross Multiply
x = 2.8

is it correct approach ? if not why ?
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Re: In a certain business, production index p is directly proportional to  [#permalink]

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New post 24 Aug 2018, 08:37
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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In a certain business, production index p is directly proportional to  [#permalink]

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New post 24 Aug 2018, 08:40
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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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New post 25 Aug 2018, 05:18
s8kadian wrote:
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  [#permalink]

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New post 06 Nov 2018, 18:21
I agree with this solution, and that is how i interpret Joint variations, However according to the Joint variations article
If x is proportional to y and y is proportional z, then x is inversely proportional to z
x/y=k
y/z=k

Shouldnt
x/yz =constant
and not

xz/y = constant

The article says otherwise.
I cannot tell the difference
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Re: In a certain business, production index p is directly proportional to &nbs [#permalink] 06 Nov 2018, 18:21

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