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A certain quantity is measured on two different scales, the

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A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?

(A) 20
(B) 36
(C) 48
(D) 60
(E) 84
[Reveal] Spoiler: OA

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Last edited by Bunuel on 02 Oct 2012, 00:23, edited 1 time in total.
Renamed the topic and edited the question.

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Re: Number Properties: [#permalink]

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appy001 wrote:
Two measure standards R and S. 24 and 30 measured with R are 42 and 60 when they are measured with S, respectively. If 100 is acquired with S, what would its value be measured with R?


This not a good question. In order to calculate R for S=100 we must know how are the scales of R ans S related.

If they are related linearly, then we would have: \(42=24m+b\) and \(60=30m+b\). The question: if \(100=Rm+b\), then \(R=?\)

Solving system of equations for \(m\) and \(b\) --> \(m=3\) and \(b=-30\) --> substituting these values in \(100=Rm+b\) --> \(R=\frac{130}{3}\).


But if they are not related linearly and for example are related like: \(S=\frac{m}{R}+b\), then we would have \(42=\frac{m}{24}+b\) and \(60=\frac{m}{30}+b\). The question: if \(100=\frac{m}{R}+b\), then \(R=?\)

Solving system of equations for \(m\) and \(b\) --> \(m=-2160\) and \(b=132\) --> substituting these values in \(100=\frac{m}{R}+b\) --> \(R=\frac{135}{2}\).

Hope it's clear.
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Re: Number Properties: [#permalink]

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appy001 wrote:
Two measure standards R and S. 24 and 30 measured with R are 42 and 60 when they are measured with S, respectively. If 100 is acquired with S, what would its value be measured with R?


Please don't paraphrase questions - by not using the actual wording of the question, a LOT gets lost in translation. As written, the question is completely unanswerable.

Also, please provide answer choices, so we can discuss not only pure algebra, but the key alternative strategies that will get you a great score on test day.

Using my magical powers, I'll post the actual question:

Quote:
A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?
(A) 20
(B) 36
(C) 48
(D) 60
(E) 84


First, we have to understand what "linearly" means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is.

From 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that R increases, S increases by 5.

We know that S is 100. To get from 60 to 100, we went up by 40, or 8 "jumps" of 5; therefore, R will go up by 8 "jumps" of 3.

24 + 8(3) = 24 + 24 = 48: choose (c).

Note that (a) makes no sense, since if S=60 corresponds to R=24, how could S=100 correspond to a lower value for R?

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Re: Number Properties: [#permalink]

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New post 27 Jun 2010, 19:21
Thanks a lot to both of you. :)
This question really made me MAD...thanx for correcting the question & providing the solution.
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New post 27 Jun 2010, 21:34
nice explanation skovinsky and buneul

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Measure Standard Problem [#permalink]

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New post 28 Jul 2010, 21:11
Hi,

Is there a systematic approach to solve this problem ?

Two measure standards R and S. 24 and 30 measured with R are 42 and 60 when they are measured with S, respectively. If 100 is acquired with S, what would its value be measured with R?


regards,
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Re: Measure Standard Problem [#permalink]

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New post 29 Jul 2010, 02:14
Clearly no.
The data can be translated as you have only two points of the function R=R(S).
The only case that you can determine the value of R corresponding to S=100 is that R varies linearly with S.
Hope that I'm right.
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Two different measurement standards ! [#permalink]

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New post 14 Dec 2010, 05:43
Two measure standards R and S. 24 and 30 measured with R are 42 and 60 when they are measured with S, respectively. If 100 is acquired with S, what would its value be measured with R?

Request you to please help with concept !!!

OA is not available.
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Re: A certain quantity is measured on two different scales, the [#permalink]

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Re: A certain quantity is measured on two different scales, the [#permalink]

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New post 16 May 2016, 14:25
are questions of this sort actually asked on GMAT? I doubt it highly
Correct answer is option C spend a good 4 minutes to deduce the logic won't be able to explain it apologies

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Linear equations so:
30= 6x+b (x variable, b contant)
60= 24x+b

solving these two-- b= 20, x= 5/3
100= 5/3 (x)+ 20
80= 5/3 (x)
x= 48

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Re: A certain quantity is measured on two different scales, the [#permalink]

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appy001 wrote:
A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?

(A) 20
(B) 36
(C) 48
(D) 60
(E) 84


Think of the graphical approach here.

Related linearly means that their relation represents a line. e.g. x and y co-ordinates are related linearly on a line segment. We know how to deal with lines.

So think of it as two points (6, 30) and (24, 60) lying on a line. So what will be (r, 100) on the same line?
We see that an increase of 18 in x co-ordinate causes an increase of 30 in y co-ordinate. So y increases by 30/18 = 5/3 for every 1 point increase in x co-ordinate.
From 60 to 100, the increase in y co-ordinate is 40. So x co-ordinate will increase from 24 to 24 + 40*(3/5) = 48.

Answer (C)
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Re: A certain quantity is measured on two different scales, the [#permalink]

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appy001 wrote:
A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?

(A) 20
(B) 36
(C) 48
(D) 60
(E) 84



R scale and S are linearly related i.e, y = mx + c, and y is the S scale and x is the R scale.
Given,
30 = m*6 + C
60 = m*24 + C
Solving these 2 equation for m and C gives, m =\(\frac{5}{3}\) and C = 20

so solve for S scales of 100

100 = \(\frac{5}{3}\) * x + 20
x = 48

Answer is C)


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Re: A certain quantity is measured on two different scales, the [#permalink]

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Re: A certain quantity is measured on two different scales, the   [#permalink] 05 Sep 2017, 18:29
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