Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

In a certain business, production index p is directly [#permalink]

Show Tags

06 May 2008, 23:49

4

This post received KUDOS

32

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

59% (02:10) correct
41% (01:22) wrong based on 1183 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

Show Tags

07 May 2008, 00:31

1

This post received KUDOS

1

This post was BOOKMARKED

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

Show Tags

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.

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.

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]

Show Tags

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

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

Show Tags

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.

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]

Show Tags

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).

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]

Show Tags

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?

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.
_________________

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

Show Tags

05 Oct 2015, 06:01

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).

Hi Krishna/Bunuel,

Can you explain why the constant k could be different? I took constant k for both the proportionalities and marked answer D.
_________________

Kindly support by giving Kudos, if my post helped you!

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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: p = c1*e - (i) where c1 is a constant and e = c2*i - (ii) where c2 is a constant

Required: p = ? when i = 70 p = c1*e = c1*c2*i p = c1*c2*70 - (iii) Hence we need to find the value of c1 and c2

Statement 1: e=0.5 whenever i=60 From (ii), 0.5 = c2*60 Clearly we cannot solve for c1 INSUFFICIENT

Statement 2: p=2.0 whenever i=50 From (i), 2 = c1*50 and we know that p = c1*70

Dividing both the equations, 2/p = 50/70 Hence we can solve for p SUFFICIENT

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).

Hi Krishna/Bunuel,

Can you explain why the constant k could be different? I took constant k for both the proportionalities and marked answer D.

Let me ask you the flip question: why do you think both constants would have the same value?

"In a certain business, production index p is directly proportional to efficiency index e," - say, p = 2e so when e doubles, p becomes four times etc

"e is in turn directly proportional to investment i." - Now how does this imply that e = 2i? We could very well have e = 3i or e = i/2 etc

We are not given that whatever the relation is between p and e, the relation has to be the same between e and i too.
_________________

In a certain business, production index p is directly [#permalink]

Show Tags

01 Aug 2016, 22:16

Superhuman wrote:

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

Stimulus tell us that p∝e∝i p=k1*e=k2*i {where k1 and k2 are proportionality constant for e and i respectively } (1) e = 0.5 whenever i = 60 p∝k1*0.5∝k2*60 We do not know what the proportionally constant k1 and k2 are; there is no way to calculate them either. INSUFFICIENT

(2) p = 2.0 whenever i = 50 2=k2*50 k2 =2/50 Since we know k2 we can figure out any relation between p and k SUFFICIENT

ANSWER B
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016.

gmatclubot

In a certain business, production index p is directly
[#permalink]
01 Aug 2016, 22:16

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...

The words of John O’Donohue ring in my head every time I reflect on the transformative, euphoric, life-changing, demanding, emotional, and great year that 2016 was! The fourth to...