It sounds easy but i can't find the answer 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

A linear relation is represented by following equation: y = mx + b We are familiar with it in co-ordinate geometry, basically the R and S scale are the X and Y axes. So: r = ms + b where m = slope and b is the intercept on r axis We get two equations by substituting the numbers given: 60 = 30 m + b (1) 24 = 60 m + b (2) Solving these 2 equations we get m = 3/5 and b = -12 So equation is r = 3/5 s -12 Substituting s = 100, R = 48 (Answer - C)

6/30 = 1/5 and 24/60 = 2/5, so then number x over 90 = 3/5 and x = 54. This means that the next number over 100 will have to be a little lower than this. The best choice is 48.

roy_priya wrote:basically the R and S scale are the X and Y axes. I give props to Roy for his clever analysis on that. Good job.

I certainly agree with beeparoo, that was an excellent approach by roy. Way to use algebra.

I think the answer should be 60 Since R and S are linearly related, we can take them as X and Y cordinates ie. X value (R) : x1 = 6 and x2= 24 and Y value (S): y1 = 30 and y2 = 60 so the slope of a line passing these point (X,Y) will be: y2 - y1 / x2 - x1 = 60-30/ 24-6 = 30/18 = 5 / 3 so new equation is: y = mx + c y = 100, so x= y/m = 100 * 3 /5 = 60