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

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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

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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.

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). _________________

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 _________________

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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 _________________

Re: OG - proportional index [#permalink]
25 May 2014, 07:49

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.

Hi Bunuel,

When you break it down like that, it makes complete sense but I made the following error. Can you please clarify why this isn't true?

\(\frac{p}{e}\) = \(\frac{e}{i}\)

\(\frac{p}{.5}\) = \(\frac{.5}{60}\) and solve for p. If the ratios are proportional, shouldn't .5/60 give me a relationship for p/e since I already know E? This led me to choose "D" as the answer choice.

Re: OG - proportional index [#permalink]
25 May 2014, 09:56

Expert's post

russ9 wrote:

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.

Hi Bunuel,

When you break it down like that, it makes complete sense but I made the following error. Can you please clarify why this isn't true?

\(\frac{p}{e}\) = \(\frac{e}{i}\)

\(\frac{p}{.5}\) = \(\frac{.5}{60}\) and solve for p. If the ratios are proportional, shouldn't .5/60 give me a relationship for p/e since I already know E? This led me to choose "D" as the answer choice.

Thanks

Directly proportional means that as one amount increases, another amount increases at the same rate.

We are told that p is directly proportional to e and e is directly proportional to i. But it does NOT mean that the rate of increase, constant of proportionality, (x in my solution) for p and e is the same as the rate of increase, constant of proportionality, (y in my solution) for e and i.

Or simply put, we have that \(\frac{p}{e}=x\) and \(\frac{e}{i}=y\) but we cannot say whether x=y, so we cannot say whether \(\frac{p}{e}=\frac{e}{i}\).

Re: In a certain business, production index p is directly [#permalink]
10 Jun 2015, 02:32

VeritasPrepKarishma 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.

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).

Re: In a certain business, production index p is directly [#permalink]
10 Jun 2015, 20:27

2

This post received KUDOS

Expert's post

francoimps wrote:

VeritasPrepKarishma 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.

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).

I would arrive with the solution: p/e = k and e/i = k hence, pi/e = k is the joint variation.

Why does this problem differ?

Thanks

Joint variation gives you the relation between 2 quantities keeping the third (or more) constant. p will vary inversely with i if and only if e is kept constant.

Think of it this way, if p increases, e increases. But we need to keep e constant, we will have to decrease i to decrease e back to original value. So an increase in p leads to a decrease in i to keep e constant. But if we don't have to keep e constant, an increase in p will lead to an increase in e which will increase i.

Here, we are not given that e needs to be kept constant. So we will not use the joint variation approach. _________________

Re: In a certain business, production index p is directly [#permalink]
10 Jun 2015, 20:43

VeritasPrepKarishma wrote:

Joint variation gives you the relation between 2 quantities keeping the third (or more) constant. p will vary inversely with i if and only if e is kept constant.

Think of it this way, if p increases, e increases. But we need to keep e constant, we will have to decrease i to decrease e back to original value. So an increase in p leads to a decrease in i to keep e constant. But if we don't have to keep e constant, an increase in p will lead to an increase in e which will increase i.

Here, we are not given that e needs to be kept constant. So we will not use the joint variation approach.

Hi Karishma,

Thanks for your reply.

How will I know whether the question asks that a certain variable needs to be kept constant?

The question above, "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?" seems similar to the question on your blog post, "x varies directly with y and y varies inversely with z."

What should I explicitly look for to determine whether the issue is joint variation or not?

Re: In a certain business, production index p is directly [#permalink]
10 Jun 2015, 22:10

1

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francoimps wrote:

VeritasPrepKarishma wrote:

Joint variation gives you the relation between 2 quantities keeping the third (or more) constant. p will vary inversely with i if and only if e is kept constant.

Think of it this way, if p increases, e increases. But we need to keep e constant, we will have to decrease i to decrease e back to original value. So an increase in p leads to a decrease in i to keep e constant. But if we don't have to keep e constant, an increase in p will lead to an increase in e which will increase i.

Here, we are not given that e needs to be kept constant. So we will not use the joint variation approach.

Hi Karishma,

Thanks for your reply.

How will I know whether the question asks that a certain variable needs to be kept constant?

The question above, "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?" seems similar to the question on your blog post, "x varies directly with y and y varies inversely with z."

What should I explicitly look for to determine whether the issue is joint variation or not?

It will be told that the third variable has to be kept constant.

Note how the independent question is framed in my post: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical M present and inversely proportional to the concentration of chemical N present. If the concentration of chemical N is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical M required to keep the reaction rate unchanged?

You need relation between N and M when reaction rate is constant. _________________

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