SAT data analysis and statistics part 3

Mastering Advanced Math: SAT Test - part 3

The quiz consists of 200 questions, and the user will be presented with a unique set of 10 questions in each session for a diverse experience
Please note that answers cannot be deselected once chosen in the quiz, so make your choices carefully for an optimal testing experience.
Each question is meticulously crafted to mirror the complexity and diversity of problem-solving you'll encounter in the SAT.
Use it as a targeted practice tool to identify and address specific areas of improvement.
Track your progress and see your proficiency grow.

The table above shows the annual salaries for the 24 members of a professional sports team in terms of millions of dollars.
The team signs an additional player to a contract with an annual salary of 7.5 million dollars per year, which brings the sum of the salaries of the 25 players to 69 million dollars. By what amount, in dollars, does the mean increase?

300,000

197,500

It cannot be determined

256,250

None

The scatterplot above shows the profit, by month, for a new company for the first year of operation. A line of best fit is also shown. Using this line, by what dollar amount did the profit in the 18th month exceed the profit in the 13th month?

$7,750

$15,000

$12,500

$5,000

None

In a set of n data values, m represents the median. If each number in the
set is decreased by 3, which expression represents the median of the
revised set of data values?

m-(3/n)

(m-3)/n

m-3

None

Over what interval of time, in minutes, was the jogger’s heart rate
changing at a constant rate?
Refer to the graph above which shows the heart rate,
in beats per minute, of a jogger during a 4-minute interval.

1 to 2

3 to 4

2 to 3

0 to 1

None

The partially completed table above describes the distribution of 200 subjects in a study involving eye color in which there were 4 times as many males with brown eyes as with blue eyes and 7 times as many females with brown eyes as with blue eyes. What percent of the subjects were either male with blue eyes or female with brown eyes?

58%

59%

57%

56%

None

A man drove a car at an average rate of speed of 45 miles per hour for
the first 3 hours of a 7-hour car trip. If the average rate of speed for the
entire trip was 53 miles per hour, what was the average rate of speed in
miles per hour for the remaining part of the trip?

None

Sasha invested $1,200 in a savings account at an annual interest rate of
1.6% compounded annually. She made no further deposits or
withdrawals. To the nearest dollar, how much more money did she
have in the account after 3 years than after 2 years?
write answer only in numbers

Vanessa plans to invest $10,000 for 5 years at an annual interest rate of
6% compounded annually. Which equation could be used to determine
the profit, P, Vanessa earns from her initial investment?

$$P = 10,000\times [5(1.06)-1]$$

$$P = 10,000\times (1.06)^{5}$$

$$P = 10,000\times [(1.06)^{5}+1]$$

$$P = 10,000\times [(1.06)^{5}-1]$$

None

If the average of x, y, and z is 12, what is the average of 3x, 3y, and 3z?

None

10.

The average (arithmetic mean) of a set of seven numbers is 81. If one
of the numbers is discarded, the average of the remaining numbers is
78. What is the value of the number that was discarded?

101

100

None

11.

The lowest value in a set of ordered scores is x and the highest value is
y. If each score is increased by k, then which of the following must be
true of the revised set of scores?
I. The mean is increased by k.
II. The range is k.
III. The median remains unchanged.

I only

II only

I and III

II and III

None

12.

A new fitness class was started at several fitness clubs owned by the same company. The scatterplot shows the total number of people attending the class during the first five months in which the class was offered. The line of
best fit is drawn.
For month 4, the predicted number of people attending the class was approximately what percent greater than the actual number of people attending the class?

20%

15%

36%

30%

None

13.

Some banks charge a fee on savings accounts that are left inactive for
an extended period of time. The equation $y = 5,000(0.98)^{x}$
represents the value, y, of one account that was left inactive for a period of x
years. What is the y-intercept of this equation and what does it
represent?

5,000, the amount of money in the account after x years

0.98, the percent of money in the account initially

0.98, the percent of money in the account after x years

5,000, the amount of money in the account initially

None

14.

The City Tunnel and Bridge Authority in a certain city estimates that
40,000 vehicles currently travel over a certain bridge per year but, due
to highway construction and changing traffic patterns, vehicle traffic
over the bridge will begin to decline by 12% every 5 years. Which of
the following expressions best represents the vehicle traffic projections
for this bridge n years from now?

$$40,000(0.12)^{5n}$$

$$40,000(0.88)^{5n}$$

$$40,000(0.88)^{\frac{n}{5}}$$

$$40,000(0.12)^{\frac{n}{5}}$$

None

15.

The cumulative histogram above shows the distribution of mistakes 28 students in a French language class made on a test. What is the probability that a student selected at random made more than 10 mistakes?

1/4

5/4

7/4

3/4

None

16.

When x is subtracted from 2y, the difference is equal to the average of
x and y. What is the value of x/y?

1/2

2/3

3/2

None

17.

On a test that has a normal distribution of scores, a score of 58 falls
two standard deviations below the mean, and a score of 85 is one
standard deviation above the mean. What is the mean score of this test?

None

18.

The greatest percent of increase in the jogger’s heart rate occurred over
what interval of time, in minutes? Refer to the graph above which shows the heart rate, in beats per minute, of a jogger during a 4-minute interval.

3 to 4

0 to 1

1 to 2

2 to 3

None

19.

Chris plans to purchase a car that loses its value at a rate of 14% per
year. If the intial cost of the car is $27,000, which of the following
equations should Chris use to determine the value, v, of the car after 4
years?

$$v = 27,000 (1.14)^{4}$$

$$ v = 27,000 (0.14)^{4}$$

$$ v = 27,000 (0.86x4)$$

$$ v = 27,000 (0.86)^{4}$$

None

20.

The average of the test scores of a group of x students is 76 and the
average of the test scores of a group of y students is 90. When the
scores of the two groups of students are combined, the average test
score is 85. What is the value of x/y?

7/4

2/3

5/9

4/7

None

21.

The gas tank in a car holds a total of 16 gallons of gas. The car travels 75 miles on 4 gallons of gas. If the gas tank is full at the beginning of a trip, which graph represents the rate of change in the amount of gas in the tank?

Graph A

Graph C

Graph D

Graph B

None

22.

Refer to the above table, which summarizes the results of a
survey of the student body of a high school about club membership in which each student enrolled in the high school enumerated the clubs in which they were members.

If a student is selected at random, what is the probability that the student is either a 9th grade student or belongs to 3 or more clubs?

0.4

0.8

0.7

0.6

None

23.

Given a starting population of 100 bacteria, the formula b(t) = 100(2^t)
can be used to determine the number of bacteria, b, after t periods of
time. If each time period is 15 minutes long, how many minutes will it
take for the population of bacteria to reach 51,200?
write answer only in numbers

24.

If 2a + b = 7 and b + 2c = 23, what is the average of a, b, and c?

7.5

12.25

None

25.

Refer to the above table, which summarizes the results of a
survey of the student body of a high school about club membership in which each student enrolled in the high school enumerated the clubs in which they were members.

If 28% of the students who are enrolled in this school belong to at least two clubs, how many students who are enrolled in this school did not participate in the survey?

100

300

400

200

None

26.

The breakdown of a sample of a chemical compound is represented by
the function $p(n) = 300(0.5)^{n}$ , where p(n) represents the number of
milligrams of the substance that remains at the end of n years. Which of
the following is true?
I. 300 represents the number of milligrams of the substance that
remains after the first year.
II. 0.5 represents the fraction of the starting amount by which the
substance gets reduced by the end of each year.
III. Each year the substance gets reduced by one-half of 300.

I and III only

II only

II and III only

I only

None

27.

Two health clubs offer different membership plans. The accompanying graph represents the total yearly cost of belonging to Club A and Club B for one year. The yearly cost includes a membership fee plus a fixed monthly charge. By what amount does the monthly charge for Club A exceed the monthly charge for Club B?

7.50

12.50

5.00

10.00

None

28.

The table above shows the annual salaries for the 24 members of a professional sports team in terms of millions of dollars.
If each player’s salary is increased by 10%, which of the following statistics does not increase by 10%?

all increase by 10%

mean

median

mode

None

29.

Susan received grades of 78, 93, 82, and 76 on four math exams. What
is the lowest score she can receive on her next math exam and have an
average of at least 85 on the five exams?

None

30.

The graph above shows the average daily temperature during a particular week in January in a certain city. Which statement best describes the temperature data in the graph above?

mean < mode

median = mode

median = mean

mean = mode

None

31.

Based on the cumulative histogram above, what percent of the total number of swimmers swam between 200 and 249 yards?

30%

20%

40%

15%

None

32.

The yearly growth in the number of fast food restaurants in a certain
retail chain can be modeled by the function f(n) = 5 + 8n. According to
this model which statement is true?

The retail chain opened with 13 restaurants.

5 is the starting number of restaurants; 8 is the number of restaurants added each year after the first year.

The y-intercept of the graph of function f shows the year in which the retail chain made a zero profit.

8 is the initial number of restaurants; 5 is the number of restaurants added each year after the first year

None

33.

Which survey is most likely to have the least bias?

surveying the members of a football team to determine the most watched TV sport

surveying a sample of people leaving a library to determine the average number of books a person reads in a year

surveying a sample of people leaving a gym to determine the average number of hours a person exercises per week

surveying a sample of people leaving a movie theater to determine which flavor of ice cream is the most popular

None

34.

If $ a_{n}$ represents the nth term of the sequence 54,18,6, ..., and $ a_{1}$
represents the first term, then $ a_{n}$ =

$$54(\frac{1}{3})^{n}$$

$$6(\frac{1}{3})^{n}$$

$$54(\frac{1}{3})^{n-1}$$

$$6(\frac{1}{3})^{n-1}$$

None

35.

The owner of a small computer repair business has one employee, who
is paid an hourly rate of $22. The owner estimates his weekly profit
using the function P(x) = 8,600 – 22x. In this function, x represents the
number of

customers served per week.

computers repaired per week.

employee’s hours worked per week.

days worked per week.

None

36.

What percent of the people surveyed saw either an action or a science fiction movie?
Refer to the graph above that summarizes a survey of a
group of 250 people who were randomly selected when leaving a multiplex movie theater and asked what type of movie they had seen.

None

37.

The tables above give the distribution of grades for 21 students in two different college mathematics classes. For purposes of making statistical calculations,
A = 4, B = 3, C = 2, D = 1, and F = 0. Which of the following statements is true about the data shown for these two
classes?
I. The standard deviation of grades is greater for class X.
II. The standard deviation of grades is greater for class Y.
III. The median letter grade is the same for classes X and Y.

I and III only

I only

II and III only

II only

None

38.

The bar graph above shows the verbal and math SAT scores for five students labeled A through E. If a scatterplot of the data in the bar graph is made such that the math SAT score for each student is plotted along the x-axis and their verbal SAT score is plotted along the y-axis, how many of the data points would lie above the line y = x?

None

39.

The graph above shows how $250,000 is invested.
After 20% of the amount that is invested in technology stocks is
reinvested in health stocks, how much money is invested in health
stocks?

$77,500

$45,000

$65,000

$39,000

None

40.

The average of a, b, c, and d is p. If the average of a and c is q, what is
the average of b and d in terms of p and q?

2p+q

2p-q

2q - p

2q + p

None

Time's up