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

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VP
Joined: 09 Mar 2016
Posts: 1229
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 ?
Manager
Joined: 05 Nov 2015
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Location: India
Re: In a certain business, production index p is directly proportional to  [#permalink]

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24 Aug 2018, 09:37
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
Manager
Joined: 05 Nov 2015
Posts: 60
Location: India
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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Posts: 9869
Location: Pune, India
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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Karishma
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Re: In a certain business, production index p is directly proportional to  [#permalink]

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06 Nov 2018, 19:21
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
SVP
Joined: 03 Jun 2019
Posts: 1882
Location: India
Re: In a certain business, production index p is directly proportional to  [#permalink]

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21 Aug 2019, 04:21
Superhuman wrote:
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

Given: In a certain business, production index p is directly proportional to efficiency index e, which is in turn directly proportional to investment i.

Asked: What is p if i = 70?

p = k1 * e
e = k2 * i
p = k1 * k2 * i = k * i where k = k1 * k2

p = 70 k = 70 k1 * k2 if i = 70

(1) e = 0.5 whenever i = 60
e = k2 * i
.5 = k2 * 60
k2 = .5/60 = 1/120
Since k1 is unknown
NOT SUFFICIENT

(2) p = 2.0 whenever i = 50
p = k* i
2 = k * 50
k = 2/ 50 = 1/25
p = 70 k = 70 /25 = 2.8
SUFFICIENT

IMO B
SVP
Joined: 03 Jun 2019
Posts: 1882
Location: India
Re: In a certain business, production index p is directly proportional to  [#permalink]

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21 Aug 2019, 04:23
vishaldd01 wrote:
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

SVP
Joined: 03 Jun 2019
Posts: 1882
Location: India
Re: In a certain business, production index p is directly proportional to  [#permalink]

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21 Aug 2019, 04:24
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.

s8kadian see how p is directly proportional to i in my solution
Re: In a certain business, production index p is directly proportional to   [#permalink] 21 Aug 2019, 04:24

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