Question ID 3f236a64
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Ratios, rates,
and Data Analysis proportional
relationships, and
units
ID: 3f236a64
x y
1 4
3 12
5 20
40 k
In the table above, the ratio of y to x for each ordered pair is
constant. What is the value of k ?
A. 28
B. 36
C. 80
D. 160
ID: 3f236a64 Answer
Correct Answer: D
Rationale
Choice D is correct. Since the ratio of y to x is constant for each ordered pair in the table, the first row can be used to
determine that the ratio of y to x is 4 to 1. The proportion can be used to solve for k. Multiplying each side of the
equation by 40 yields .
Choice A is incorrect. This is the value of y when the value of x is 7, not 40. Choice B is incorrect and may result from
subtracting 4 from 40 instead of multiplying 40 by 4. Choice C is incorrect and may result from incorrectly setting up the
proportion.
Question Difficulty: Easy
,Question ID 8705ecba
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Percentages
and Data Analysis
ID: 8705ecba
The cost of a certain shirt is $20 before a 5% sales tax is added. What is the total
cost, including sales tax, to purchase the shirt?
A. $20.05
B. $20.50
C. $21.00
D. $25.00
ID: 8705ecba Answer
Correct Answer: C
Rationale
Choice C is correct. The total cost to purchase the shirt is the $20 cost of the shirt plus the 5% sales tax. The value of the 5%
sales tax on the $20 shirt is equivalent to , or $1. Therefore, the total cost to purchase the shirt is , or
$21.
Choice A is incorrect and may result from neglecting to multiply by $20 when finding the value of the sales tax. Choice B is
incorrect and may result from dividing by 10, instead of by 100, and then neglecting to multiply by $20 when finding the sales
tax. Choice D is incorrect and may result from interpreting the sales tax of 5% as $5.
Question Difficulty: Easy
, Question ID f8f79e11
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Inference from
and Data Analysis sample statistics
and margin of error
ID: f8f79e11
A park ranger asked a random sample of visitors how far they hiked during their
visit. Based on the responses, the estimated mean was found to be 4.5 miles, with
an associated margin of error of 0.5 miles. Which of the following is the best
conclusion from these data?
A. It is likely that all visitors hiked between 4 and 5 miles.
B. It is likely that most visitors hiked exactly 4.5 miles.
C. It is not possible that any visitor hiked less than 3 miles.
D. It is plausible that the mean distance hiked for all visitors is between 4 and 5 miles.
ID: f8f79e11 Answer
Correct Answer: D
Rationale
Choice D is correct. The given estimated mean has an associated margin of error because from sample data, the population
mean can’t be determined precisely. Rather, from the sample mean, an interval can be determined within which it’s plausible
that the population’s mean is likely to lie. Since the estimated mean is 4.5 miles with an associated margin of error of 0.5
miles, it follows that between miles and miles, or between 4 and 5 miles, is plausibly the mean distance
hiked for all visitors.
Choices A, B, and C are incorrect. Based on the estimated mean, no determination can be made about the number of miles
hiked for all visitors to the park.
Question Difficulty: Medium
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Ratios, rates,
and Data Analysis proportional
relationships, and
units
ID: 3f236a64
x y
1 4
3 12
5 20
40 k
In the table above, the ratio of y to x for each ordered pair is
constant. What is the value of k ?
A. 28
B. 36
C. 80
D. 160
ID: 3f236a64 Answer
Correct Answer: D
Rationale
Choice D is correct. Since the ratio of y to x is constant for each ordered pair in the table, the first row can be used to
determine that the ratio of y to x is 4 to 1. The proportion can be used to solve for k. Multiplying each side of the
equation by 40 yields .
Choice A is incorrect. This is the value of y when the value of x is 7, not 40. Choice B is incorrect and may result from
subtracting 4 from 40 instead of multiplying 40 by 4. Choice C is incorrect and may result from incorrectly setting up the
proportion.
Question Difficulty: Easy
,Question ID 8705ecba
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Percentages
and Data Analysis
ID: 8705ecba
The cost of a certain shirt is $20 before a 5% sales tax is added. What is the total
cost, including sales tax, to purchase the shirt?
A. $20.05
B. $20.50
C. $21.00
D. $25.00
ID: 8705ecba Answer
Correct Answer: C
Rationale
Choice C is correct. The total cost to purchase the shirt is the $20 cost of the shirt plus the 5% sales tax. The value of the 5%
sales tax on the $20 shirt is equivalent to , or $1. Therefore, the total cost to purchase the shirt is , or
$21.
Choice A is incorrect and may result from neglecting to multiply by $20 when finding the value of the sales tax. Choice B is
incorrect and may result from dividing by 10, instead of by 100, and then neglecting to multiply by $20 when finding the sales
tax. Choice D is incorrect and may result from interpreting the sales tax of 5% as $5.
Question Difficulty: Easy
, Question ID f8f79e11
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Inference from
and Data Analysis sample statistics
and margin of error
ID: f8f79e11
A park ranger asked a random sample of visitors how far they hiked during their
visit. Based on the responses, the estimated mean was found to be 4.5 miles, with
an associated margin of error of 0.5 miles. Which of the following is the best
conclusion from these data?
A. It is likely that all visitors hiked between 4 and 5 miles.
B. It is likely that most visitors hiked exactly 4.5 miles.
C. It is not possible that any visitor hiked less than 3 miles.
D. It is plausible that the mean distance hiked for all visitors is between 4 and 5 miles.
ID: f8f79e11 Answer
Correct Answer: D
Rationale
Choice D is correct. The given estimated mean has an associated margin of error because from sample data, the population
mean can’t be determined precisely. Rather, from the sample mean, an interval can be determined within which it’s plausible
that the population’s mean is likely to lie. Since the estimated mean is 4.5 miles with an associated margin of error of 0.5
miles, it follows that between miles and miles, or between 4 and 5 miles, is plausibly the mean distance
hiked for all visitors.
Choices A, B, and C are incorrect. Based on the estimated mean, no determination can be made about the number of miles
hiked for all visitors to the park.
Question Difficulty: Medium
