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

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

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18 Feb 2013, 11:50
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Question Stats:

54% (02:16) correct 46% (01:44) wrong based on 138 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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Re: A certain quantity is measured on two different scales,the R [#permalink]

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18 Feb 2013, 12:13
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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, 16:50
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, 19:13
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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?
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Re: A certain quantity is measured on two different scales,the R [#permalink]

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19 Feb 2013, 09:17
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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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Re: A certain quantity is measured on two different scales,the R [#permalink]

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07 Mar 2013, 21:00
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

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

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27 Jun 2014, 09:54
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Re: A certain quantity is measured on two different scales,the R [#permalink]

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06 Sep 2014, 22:41
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.
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Re: A certain quantity is measured on two different scales,the R [#permalink]

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24 Jan 2016, 17:41
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A certain quantity is measured on two different scales,the R   [#permalink] 24 Jan 2016, 17:41
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