Sat practice Test #8 Answer Explanations

Choice D is correct. Since density is mass per unit volume, the mass 
is the density times volume. The volume of a right rectangular prism is 
the product of the lengths of the sides. Therefore:
mass = (2.8 grams per cubic centimeter) ×
(30 centimeters × 40 centimeters × 50 centimeters)
mass = (2.8 grams per cubic centimeter) × (60,000 cubic centimeters)
mass = 168,000 grams
Choice A is incorrect and may result from adding, instead of 
multiplying, the lengths of the sides to find the volume. Choice B is 
incorrect and may result from the same error as in choice A, as well as 
a place value error. Choice C is incorrect and may result from a place 
value error when finding the volume.
QUESTION 16
Choice B is correct. A total of 150 adults received the sugar pill. 
Of those, 33 reported contracting a cold. Therefore, 33 
_ 
150 , or the 
equivalent 11 
_ 
50 , is the proportion of adults receiving a sugar pill who 
reported contracting a cold.

---

Choice A is incorrect. This is the proportion of adults receiving a 
sugar pill and contracting a cold to all adults contracting a cold
( 
33 
_ 
54
)
.
Choice C is incorrect. This is the proportion of adults who reported 
contracting a cold to all the participants in the study
( 
54 
_ 
300 =
9 
_ 
50
)
. 
Choice D is incorrect. This is the proportion of adults who received a 
sugar pill and reported contracting a cold to all the participants in the 
study
( 
33 
_ 
300 =
11 
_ 
100
)
.
QUESTION 17
Choice A is correct. The mode is the data value with the highest 
frequency. So for the data shown, the mode is 18. The median is the 
middle data value when the data values are sorted from least to 
greatest. Since there are 20 ages ordered, the median is the average of 
the two middle values, the 10th and 11th, which for these data are both 
19. Therefore, the median is 19. The mean is the sum of the data values 
divided by the number of the data values. So for these data, the mean is
(18 × 6) + (19 × 5) + (20 × 4) + (21 × 2) + (22 × 1) + (23 × 1) + (30 × 1)
_
______
20 
= 20. 
Since the mode is 18, the median is 19, and the mean is 20,
mode < median < mean.
Choice B and D are incorrect because the mean is greater than the 
median. Choice C is incorrect because the median is greater than
the mode.
Alternate approach: After determining the mode, 18, and the 
median, 19, it remains to determine whether the mean is less than 
19 or more than 19. Because the mean is a balancing point, there is 
as much deviation below the mean as above the mean. It is possible 
to compare the data to 19 to determine the balance of deviation above 
and below the mean. There is a total deviation of only 6 below 19 
(the 6 values of 18); however, the data value 30 alone deviates by 11 
above 19. Thus the mean must be greater than 19.
QUESTION 18