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GMAT Set 7 Q10

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GMAT Set 7 Q10

by Abhijit K » Thu Feb 19, 2015 1:49 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 Rscale
corresponds to a measurement of 100 on the S-scale?
A. 20
B. 36
C. 48
D. 60
E. 84
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by GMATGuruNY » Thu Feb 19, 2015 4:34 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
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 = (S₂ - S�)/(R₂ - R�) = (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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by [email protected] » Thu Feb 19, 2015 11:30 am
Hi Abhijit K,

The answer choices to this question are 'spread out' enough that you can use a bit of logic to estimate the correct answer.

We're told that the relationship between the values on the R-Scale and S-Scale are LINEAR, which means that as one value increases, the other value will increase by a fixed amount.

We're then told the relationship between the R-Scale and S-Scale for two sets of values (6 and 30; 24 and 60). Notice how that when the R-scale value increases from 6 to 24 (an increase of 18), the S-scale value increases from 30 to 60 (an increase of 30). The question asks for the relative R-scale value when the S-scale value is 100.

Since an increase of 30 the S-scale = an increase of 18 on the R-scale, when we go from 60 to 100 on the S-scale, we're increasing by 40 (a little more than 30)....so the increase on the R-scale should be a little more than 18....

24 + (a bit more than 18)..... = a bit more than 42....

There's only one answer that matches:

Final Answer: C

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