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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  [#permalink]

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New post Updated on: 17 Dec 2013, 08:27
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Question Stats:

64% (01:03) correct 36% (01:07) wrong based on 285 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 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-quantity-is-measured-on-two-different-scales-the-r-147469.html

Originally posted by Jcpenny on 11 Nov 2008, 20:11.
Last edited by Bunuel on 17 Dec 2013, 08:27, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: measurement--27  [#permalink]

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New post 11 Nov 2008, 20:56
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Jcpenny 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


Note that scales are related "linearly"

y = mx + c
30 = m*6 + c
60 = m*24 + c

solving m =5/3, c =20

100 = 5/3 * x + 20

80 * 3/5 = x therefore x =48

C.
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Re: measurement--27  [#permalink]

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New post 11 Nov 2008, 21:44
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Because these scales are related linearly, we need to figure out the "slope" which will then be able to tell us how much one scale changes with 1 unit of movement on the other one.

The R-scale moves 18 (from 6 to 24 is 24-6=18) for every 30 (30 to 60 is 60-30=30) that the S-Scale moves. This is a 18/30 slope, or 3/5 slope.

Lets check to see if this is indeed the right slope.

R=6, S=30
R=9, S=35
R=12, S=40
R=15, S=45
R=18, S=50
R=21, S=55
R=24, S=60 <---Just like it should

If we're going to 100 from 60, that's a difference of 40, and if we go in increments of 5, that's 40/5 increments, or 8 increments, so on the other scale that goes in increments of 3, it's 8 * 3=24 more units, or 48 on the R-Scale = 100 on the S-Scale. Answer C.

alpha_plus_gamma wrote:
Jcpenny 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


Note that scales are related "linearly"

y = mx + c
30 = m*6 + c
60 = m*24 + c

solving m =5/3, c =20

100 = 5/3 * x + 20

80 * 3/5 = x therefore x =48

C.

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Re: measurement--27  [#permalink]

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New post 11 Nov 2008, 22:34
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Jcpenny 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



(60-30)/(24-6)= (100-60)/(x-24)

--> x-24 = 40*18/30 =24
-->x=48

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

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New post 17 Dec 2013, 08:28
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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

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-quantity-is-measured-on-two-different-scales-the-r-147469.html
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Re: A certain quantity is measured on two different scales, the  [#permalink]

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New post 29 Jul 2018, 12:44
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