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In a certain business, production index p is directly

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In a certain business, production index p is directly [#permalink] New post 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
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Mar 2012, 13:05, edited 1 time in total.
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Re: OG - proportional index [#permalink] New post 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

thus B
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Re: OG - proportional index [#permalink] New post 07 May 2008, 06:22
i say B as well, unless im missing something.

From stat 1, you know relationship btwn e and i, but you dont know what it is btwn p and e ... so insuff.

From stat 2, you are given the relationship btwn p and i, and from the stem you know what i is. so suff.
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Re: OG - proportional index [#permalink] New post 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.
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Re: OG - proportional index [#permalink] New post 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.

Answer: B.

Hope it's clear.
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Re: OG - proportional index [#permalink] New post 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).
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Re: OG - proportional index [#permalink] New post 29 Nov 2010, 20:54
Thanks Karishma and Bunuel very helpful explanations.
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Re: In a certain business, production index p is directly [#permalink] New post 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] New post 17 May 2013, 08:02
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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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Re: OG - proportional index [#permalink] New post 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.

Thanks
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Re: OG - proportional index [#permalink] New post 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}.

Hope it's clear.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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