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Question ID 0f1d42fd
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Ratios, rates, Hard
and Data Analysis proportional
relationships, and
units
ID: 0f1d42fd
The density of a certain type of wood is kilograms per cubic meter. A sample of this type of wood is
in the shape of a cube and has a mass of kilograms. To the nearest hundredth of a meter, what is
the length of one edge of this sample?
A.
B.
C.
D.
ID: 0f1d42fd Answer
Correct Answer: B
Rationale
Choice B is correct. It’s given that the density of a certain type of wood is 353 kilograms per cubic meter (kg/m3 ), and a
sample of this type of wood has a mass of 345 kg. Let 𝑥 represent the volume, in m3 , of the sample. It follows that the
353 kg 345 kg 345
relationship between the density, mass, and volume of this sample can be written
= , or 353 = . Multiplying both sides of this equation by 𝑥 yields 353𝑥 = 345. Dividing both sides of
1 m3 𝑥 m3 𝑥
345 345
as
this equation by 353 yields 𝑥 = m3 . Since it’s given that the sample of
353 353
. Therefore, the volume of this sample is
for a cube, 𝑉 = 𝑠3 , where 𝑉 represents the volume, in m3 , and 𝑠 represents the length, in m, of one edge of the cube.
this type of wood is a cube, it follows that the length of one edge of this sample can be found using the volume formula
345 345 345
for 𝑉 in this formula yields = 𝑠3 . Taking the cube root of both sides of this equation yields 3 =𝑠
353 353 √353
Substituting
, or 𝑠 ≈ 0 . 99. Therefore, the length of one edge of this sample to the nearest hundredth of a meter is 0.99.
Choices A, C, and D are incorrect and may result from conceptual or calculation errors.
Question Difficulty: Hard
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Question ID 7989c1bb
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Ratios, rates, Hard
and Data Analysis proportional
relationships, and
units
ID: 7989c1bb
A certain town has an area of square miles. What is the area, in square yards, of this town?
A.
B.
C.
D.
ID: 7989c1bb Answer
Correct Answer: D
Rationale
Choice D is correct. Since the number of yards in 1 mile is 1,760, the number of square yards in 1 square mile is
(1,760)(1,760) = 3,097,600. Therefore, if the area of the town is 4.36 square miles, it is 4.36(3,097,600) = 13,505,536, in
square yards.
Choice A is incorrect and may result from dividing the number of yards in a mile by the square mileage of the town.
Choice B is incorrect and may result from multiplying the number of yards in a mile by the square mileage of the town.
Choice C is incorrect and may result from dividing the number of square yards in a square mile by the square mileage
of the town.
Question Difficulty: Hard
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Question ID 6baeb1d2
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Percentages Hard
and Data Analysis
ID: 6baeb1d2
of the items in a box are green. Of those, are also rectangular. Of the green rectangular items,
are also metal. Which of the following is closest to the percentage of the items in the box that are
not rectangular green metal items?
A.
B.
C.
D.
ID: 6baeb1d2 Answer
Correct Answer: C
Rationale
Choice C is correct. It's given that 37 % of the items in a box are green. Let 𝑥 represent the total number of items in the
37
𝑥, or 0.37𝑥, items in the box are green. It's also given that of those, 37 % are also rectangular.
100
37
box. It follows that
(0.37𝑥), or 0.1369𝑥, items in the box are green rectangular items. It's also given that of the green
100
42
Therefore,
rectangular items, 42 % are also metal. Therefore, (0.1369𝑥), or 0.057498𝑥, items in the box are rectangular green
100
metal items. The number of the items in the box that are not rectangular green metal items is the total number of items
are not rectangular green metal items is 𝑥 − 0.057498𝑥, or 0.942502𝑥. The percentage of items in the box that are not
in the box minus the number of rectangular green metal items in the box. Therefore, the number of items in the box that
rectangular green metal items is the percentage that 0.942502𝑥 is of 𝑥. If 𝑝 % represents this percentage, the value of 𝑝
0.942502𝑥
is 100( ), or 94.2502. Of the given choices, 94.25 % is closest to the percentage of items in the box that are not
𝑥
rectangular green metal items.
Choice A is incorrect and may result from conceptual or calculation errors.
Choice B is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors.
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about:srcdoc Page 1 of 43
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Question ID 0f1d42fd
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Ratios, rates, Hard
and Data Analysis proportional
relationships, and
units
ID: 0f1d42fd
The density of a certain type of wood is kilograms per cubic meter. A sample of this type of wood is
in the shape of a cube and has a mass of kilograms. To the nearest hundredth of a meter, what is
the length of one edge of this sample?
A.
B.
C.
D.
ID: 0f1d42fd Answer
Correct Answer: B
Rationale
Choice B is correct. It’s given that the density of a certain type of wood is 353 kilograms per cubic meter (kg/m3 ), and a
sample of this type of wood has a mass of 345 kg. Let 𝑥 represent the volume, in m3 , of the sample. It follows that the
353 kg 345 kg 345
relationship between the density, mass, and volume of this sample can be written
= , or 353 = . Multiplying both sides of this equation by 𝑥 yields 353𝑥 = 345. Dividing both sides of
1 m3 𝑥 m3 𝑥
345 345
as
this equation by 353 yields 𝑥 = m3 . Since it’s given that the sample of
353 353
. Therefore, the volume of this sample is
for a cube, 𝑉 = 𝑠3 , where 𝑉 represents the volume, in m3 , and 𝑠 represents the length, in m, of one edge of the cube.
this type of wood is a cube, it follows that the length of one edge of this sample can be found using the volume formula
345 345 345
for 𝑉 in this formula yields = 𝑠3 . Taking the cube root of both sides of this equation yields 3 =𝑠
353 353 √353
Substituting
, or 𝑠 ≈ 0 . 99. Therefore, the length of one edge of this sample to the nearest hundredth of a meter is 0.99.
Choices A, C, and D are incorrect and may result from conceptual or calculation errors.
Question Difficulty: Hard
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Question ID 7989c1bb
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Ratios, rates, Hard
and Data Analysis proportional
relationships, and
units
ID: 7989c1bb
A certain town has an area of square miles. What is the area, in square yards, of this town?
A.
B.
C.
D.
ID: 7989c1bb Answer
Correct Answer: D
Rationale
Choice D is correct. Since the number of yards in 1 mile is 1,760, the number of square yards in 1 square mile is
(1,760)(1,760) = 3,097,600. Therefore, if the area of the town is 4.36 square miles, it is 4.36(3,097,600) = 13,505,536, in
square yards.
Choice A is incorrect and may result from dividing the number of yards in a mile by the square mileage of the town.
Choice B is incorrect and may result from multiplying the number of yards in a mile by the square mileage of the town.
Choice C is incorrect and may result from dividing the number of square yards in a square mile by the square mileage
of the town.
Question Difficulty: Hard
about:srcdoc Page 3 of 43
, 5/29/24, 10:31 PM
Question ID 6baeb1d2
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Percentages Hard
and Data Analysis
ID: 6baeb1d2
of the items in a box are green. Of those, are also rectangular. Of the green rectangular items,
are also metal. Which of the following is closest to the percentage of the items in the box that are
not rectangular green metal items?
A.
B.
C.
D.
ID: 6baeb1d2 Answer
Correct Answer: C
Rationale
Choice C is correct. It's given that 37 % of the items in a box are green. Let 𝑥 represent the total number of items in the
37
𝑥, or 0.37𝑥, items in the box are green. It's also given that of those, 37 % are also rectangular.
100
37
box. It follows that
(0.37𝑥), or 0.1369𝑥, items in the box are green rectangular items. It's also given that of the green
100
42
Therefore,
rectangular items, 42 % are also metal. Therefore, (0.1369𝑥), or 0.057498𝑥, items in the box are rectangular green
100
metal items. The number of the items in the box that are not rectangular green metal items is the total number of items
are not rectangular green metal items is 𝑥 − 0.057498𝑥, or 0.942502𝑥. The percentage of items in the box that are not
in the box minus the number of rectangular green metal items in the box. Therefore, the number of items in the box that
rectangular green metal items is the percentage that 0.942502𝑥 is of 𝑥. If 𝑝 % represents this percentage, the value of 𝑝
0.942502𝑥
is 100( ), or 94.2502. Of the given choices, 94.25 % is closest to the percentage of items in the box that are not
𝑥
rectangular green metal items.
Choice A is incorrect and may result from conceptual or calculation errors.
Choice B is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors.
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