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# A certain quantity is measured on two different scales,the R

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Manager
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 184
Concentration: Accounting
GMAT Date: 04-06-2013
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A certain quantity is measured on two different scales,the R [#permalink]

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18 Feb 2013, 12:50
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65% (hard)

Question Stats:

56% (01:33) correct 44% (01:40) wrong based on 308 sessions

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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 the 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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Joined: 02 Sep 2009
Posts: 44421
Re: A certain quantity is measured on two different scales,the R [#permalink]

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18 Feb 2013, 13:13
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mun23 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 the 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

As R increases by 18 (from 6 to 24), S increases by 30 (from 30 to 60). Thus increase of 18 in R corresponds to increase of 30 in S.

Therefore change of 70 in S from 30 (when R is 6) to 100 must correspond to change of 70/30*18=42 in R. Hence, 100 in S corresponds to 6+42=48 in R.

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

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18 Feb 2013, 17:50
Bunuel wrote:
mun23 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 the 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

As R increases by 18 (from 6 to 24), S increases by 30 (from 30 to 60). Thus increase of 18 in R corresponds to increase of 30 in S.

Therefore change of 70 in S from 30 (when R is 6) to 100 must correspond to change of 70/30*18=42 in R. Hence, 100 in S corresponds to 6+42=48 in R.

Sorry Bunuel, i didnt understand both question and concept of this!
How u moved on with this?
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Re: A certain quantity is measured on two different scales,the R [#permalink]

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18 Feb 2013, 20:13
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Consider a line built on R scale.

--------------------------|-----------------------------------|-------------------------------------------
6 24

The increase in value in R scale -=24-6=18 points
Now consider a line built on scale S. For the same increase in value, the increase in S scale is from 30-60 i.e30 points(60-30)

So, we know that an increase of 18 points on R scale corresponds to 30 points on S scale. We need to find our what measurement on R scale corresponds to a value of 100 on S scale.

an increase from 30 to 100 value on S scale= 70 points

R scale S scale
18 point increase= 30 point increase
? = 70 point increase

cross multiply

?=70*18/30=42

Thus, an increase of 70 points on S scale equals an increase of 42 points on R scale. So, the actual value=6+42=48

shanmugamgsn wrote:
Bunuel wrote:
mun23 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 the 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

As R increases by 18 (from 6 to 24), S increases by 30 (from 30 to 60). Thus increase of 18 in R corresponds to increase of 30 in S.

Therefore change of 70 in S from 30 (when R is 6) to 100 must correspond to change of 70/30*18=42 in R. Hence, 100 in S corresponds to 6+42=48 in R.

Sorry Bunuel, i didnt understand both question and concept of this!
How u moved on with this?
Intern
Joined: 15 Jan 2013
Posts: 38
Concentration: Finance, Operations
GPA: 4
Re: A certain quantity is measured on two different scales,the R [#permalink]

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19 Feb 2013, 10:17
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mun23 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 the 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

Since there is a linear relationship between R and S....we can assume R =aS + b (or any other linear equation in terms of R and S)
Now, when R= 6, S= 30....so the equation becomes 6 = 30a + b---(i)
When R = 24, S = 60...so the equation becomes 24 = 60a + b----(ii)
Solving the above two equations we get a = 3/5, b= -12...so the equation becomes R = (3/5)S - 12....now put the value of S =100 in the equation...u'll get the value of R as 48...
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Posts: 21
Re: A certain quantity is measured on two different scales,the R [#permalink]

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07 Mar 2013, 22:00
On scale R when we measure 6 and 24 we measure 30 and 60 respectively on scale S. Therefore an increase in 18 on scale R results in an increase of 30 on scale S.

90 on S (60 + 30) is equivalent to 42 (24 + 18) on R. To get 100 on S we add 10, an increase in 10 on S results in an increase of 6 on R (18*10/30).

42 + 6 = 48

Manager
Joined: 07 Apr 2014
Posts: 130
Re: A certain quantity is measured on two different scales,the R [#permalink]

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06 Sep 2014, 23:41
mun23 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 the 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

24-6 = 18
60-30=30

18:30 --> 6:10 so for every addition of 6 in R scale there will be 10 in S scale.
Intern
Joined: 01 Jun 2013
Posts: 11
A certain quantity is measured on two different scales,the R [#permalink]

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20 Mar 2017, 11:42
mun23 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 the 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

6 > 24 > x
30 > 60 > 100

Through concept of gradient we can solve in less than 30 seconds.
(24-6)/(60-30)=(x-24)/(100-60)
==>x=48
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A certain quantity is measured on two different scales,the R [#permalink]

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16 Aug 2017, 00:49
when
R increased from 6 to 24 ie an increase of 18 points
Than S increased from 30 to 60 ie 30 points.
There is a relationship between increase in R and than subsequent increase in S.
This relationship can be represented as increase in S/R=30/18=5/3
Which means that for every increase in the point of R their will be 5/3 increase in the points of S.
The question asks if S is 100 than what is R.
S has moved from 60 to 100 a increase of 40 points
When S has increased by 40 than let R increase=X
we now have a relationship X*5/3=40
or X=24
Original R=24. Therefore we have 24+24=48
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Joined: 23 Oct 2017
Posts: 65
Re: A certain quantity is measured on two different scales,the R [#permalink]

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06 Jan 2018, 05:33
mun23 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 the 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

----
Since the scales R & S are linearly related we can use y=mx+c, which can be use S=m*R+c
substitute the values (R,S) (6,30) (24,60) to get values of m = 5/3 & c=20
now for S = 100, find R in this equation , 100=(5/3)*R + 20
=> R=48
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Re: A certain quantity is measured on two different scales,the R [#permalink]

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25 Feb 2018, 16:31
Hi All,

The answer choices to this question are 'spread out' enough that you can use a bit of logic to estimate the correct answer.

We're told that the relationship between the values on the R-Scale and S-Scale are LINEAR, which means that as one value increases, the other value will increase by a fixed amount. We're then told the relationship between the R-Scale and S-Scale for two sets of values (6 and 30; 24 and 60). Notice how that when the R-scale value increases from 6 to 24 (an increase of 18), the S-scale value increases from 30 to 60 (an increase of 30). The question asks for the relative R-scale value when the S-scale value is 100.

Since an increase of 30 on the S-scale = an increase of 18 on the R-scale, when we go from 60 to 100 on the S-scale, we're increasing by 40 (a little more than 30)....so the increase on the R-scale should be a little more than 18....

24 + (a bit more than 18)..... = a bit more than 42....

There's only one answer that matches:

[Reveal] Spoiler:
C

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

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07 Mar 2018, 11:12
Let linear relation be S = mR + C, where m is slope, C is S-intercept (when R = 0)
Given: 30 = 6m + C (when R = 6, S = 30)
60 = 24m + C (when R = 24, S = 60)
solving for m and C, we get m = 30/18, C = 20
S = (30/18)R + 20
when S = 100, R = 48
Re: A certain quantity is measured on two different scales,the R   [#permalink] 07 Mar 2018, 11:12
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