S and R scale

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Mon May 21, 2012 3:18 am

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

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Source: Beat The GMAT — Problem Solving | Mon May 21, 2012 3:18 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon May 21, 2012 3:23 am

GmatKiss 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

An easy way to proceed is to consider the R and S-scales as X and Y-axes respectively.
Then the coordinates are (6, 30), (24, 60), and (x, 100) all lie in the same line.
Then (60 - 30)/(24 - 6) = (100 - 30)/(x - 6)
3/18 = 7/(x - 6)
3(x - 6) = 126
x - 6 = 42 or x = 48

The correct answer is C.

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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 » Mon May 21, 2012 3:26 am

GmatKiss 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

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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kullayappayenugula: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Thu Dec 01, 2011 2:59 am; Thanked: 4 times

by kullayappayenugula » Mon May 21, 2012 3:27 am

Hi,

Obsereve the pattern in the scale

R-scale of 6 and 24 correspond to S-scale of 30 and 60

We can generate the below scale comparison
6 -> 30
12 ->40
18 ->50
24 ->60 We can see the 6 point on r is equal to 10 on s

Now, we can dedue what 100 would be on r scale as below.

30->70
36->80
42->90
48->100

Therefore the 100 on S scale equals to 48 on R scale.

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Mon May 21, 2012 3:53 am

An easy way to proceed is to consider the R and S-scales as X and Y-axes respectively.
Then the coordinates are (6, 30), (24, 60), and (x, 100) all lie in the same line

Best, even if we go by graphical method.

Thanks Anurag

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