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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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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 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.

Concentration: Entrepreneurship, International Business

GMAT 1: 440 Q33 V13

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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.

Answer: C.

Sorry Bunuel, i didnt understand both question and concept of this! How u moved on with this?
_________________

GMAT - Practice, Patience, Persistence Kudos if u like

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.

Answer: C.

Sorry Bunuel, i didnt understand both question and concept of this! How u moved on with this?

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...

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).

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

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27 Jun 2014, 10:54

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

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06 Sep 2014, 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.

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

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24 Jan 2016, 18:41

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

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24 Feb 2017, 04:42

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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

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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