Sat practice Test #8 Answer Explanations

Choice D is correct. The two data sets have the same range. The 
first data set has a range of 88 − 56 = 32, and the second data set 
has a range of 112 − 80 = 32. Alternatively, it can be seen visually 
that the ranges are the same because the two dot plots are aligned, 
the scales of the graphs are the same, and the graphs have the same 
width. The two data sets have different standard deviations. Both 
dot plots show distributions that have a mean near the center value 
of the dot plot. The first dot plot shows most values clustered near 
the mean, while the second dot plot shows most values farther from 
the mean. Therefore, the standard deviations of the two data sets are 
not equal—the data represented by the second dot plot has a greater 
standard deviation.
Choices A, B, and C are incorrect because they incorrectly assert
either that the standard deviations are the same or that the ranges
are different.
QUESTION 29
Choice B is correct. Since the machine copies at a constant rate, 
the relationship between p, the number of sheets of paper remaining, 
and m, the time in minutes since the machine started printing, is 
modeled by a linear equation. The initial number of sheets of paper 
is given as 5,000. It is also given that the machine used 30% of those 
5,000 sheets in 20 minutes, so it used 0.30 × 5,000 = 1,500 sheets in 
20 minutes. Therefore, the number of sheets used per minute is 
1,500
_ 
20 = 75. To determine the number of sheets of paper used 
m minutes after the machine started printing, multiply 75 by m, which 
gives 75m. Therefore, a linear equation modeling this relationship is 
the number of sheets remaining equals the initial number of sheets of 
paper minus the number of sheets of paper used m minutes after the 
machine started printing, which is p = 5,000 − 75m.
Choice A is incorrect and may be the result of using the given number 
of minutes, 20, as the rate at which the copy machine uses paper. 
However, the rate is 75, not 20, sheets per minute. Choices C and D are 
incorrect because they aren’t linear equations; they assume that the 
copy machine prints at a nonconstant rate.
QUESTION 30