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In a certain business, production index p is directly [#permalink]
06 May 2008, 23:49

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Difficulty:

25% (low)

Question Stats:

65% (02:01) correct
34% (01:11) wrong based on 155 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

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

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.

Re: OG - proportional index [#permalink]
29 Nov 2010, 00:45

6

This post received KUDOS

Expert's post

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.

Re: OG - proportional index [#permalink]
29 Nov 2010, 05:41

1

This post received KUDOS

Expert's post

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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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.
_________________

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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.
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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

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
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