IMO A

6--->30

X--->100

then x=100*6/30=20

anjaligeorge1 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

Tricky question!

First, we have to understand what "linearly" means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is.

From 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that R increases, S increases by 5.

We know that S is 100. To get from 60 to 100, we went up by 40, or 8 "jumps" of 5; therefore, R will go up by 8 "jumps" of 3.

24 + 8(3) = 24 + 24 = 48: choose (c).

Note that (a) makes no sense, since if S=60 corresponds to R=24, how could S=100 correspond to a lower value for R?

look at it this way

R scale is x axis
S scale is y axis

so points (6,30), (24,60) and (X,100) are on the same line

we need to find X

(60-30)/(24-6) = (100-60)/(X-24)
30/18 = 40/(X-24)
X-24=24
X=48

durgesh79 wrote:look at it this way

R scale is x axis
S scale is y axis

so points (6,30), (24,60) and (X,100) are on the same line

we need to find X

(60-30)/(24-6) = (100-60)/(X-24)
30/18 = 40/(X-24)
X-24=24
X=48

Make sense and easily to be understood