R and S scale

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Amrabdelnaby: Master | Next Rank: 500 Posts; Posts: 137; Joined: Fri Nov 13, 2015 11:01 amFollowed by: 2 members; Thanked: 1 times

by Amrabdelnaby » Sun Jan 10, 2016 4:25 pm

A certain quantity is measured on 2 different scales, R scale and S scale that are related linearly. Measurements on R scale of 6 and 24 corresponds to measurements on the S scale of 30 and 60, respectively.what measurement on the R scale corresponds to measurement of 100 on the S scale?

20
36
48
60
84

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jan 10, 2016 4:26 pm

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

Since the relationship between R and S is linear, any pair of points (R,S) must yield the same slope.

Given points are (6,30), and (24,60).
Slope = (Sâ‚‚ - Sâ‚�)/(Râ‚‚ - Râ‚�) = (60-30)/(24-6) = 30/18 = 5/3.

(6,30) and (R,100) must yield the same slope.
(100-30)/(R-6) = 5/3.
70/(R-6) = 5/3.
Cross-mulitplying, we get:
5R-30 = 210.
R = 48.

The correct answer is C.

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chetan.sharma: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Sun Dec 27, 2015 7:03 amFollowed by: 1 member; Thanked: 8 times

by chetan.sharma » Mon Jan 11, 2016 11:34 pm

Amrabdelnaby wrote:A certain quantity is measured on 2 different scales, R scale and S scale that are related linearly. Measurements on R scale of 6 and 24 corresponds to measurements on the S scale of 30 and 60, respectively.what measurement on the R scale corresponds to measurement of 100 on the S scale?

20
36
48
60
84

hi,
30 on S = 6 on R..
60 on S = 24 on R..
so an inrease of 30 on S = 18 on R...
NOW 100 is 40 more than 60..
so lets check
As increase of 30 on S = 18 on R
increase of 1 on S = 18/30 on R
increase of 40 on S = 18*40/30 or 24 on R..
so the value on R =24+24=48..
C

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