Home / Digital SAT Math Practice Questions: Ratios, rates, proportional relationships

# Digital SAT Math Practice Questions: Ratios, rates, proportional relationships

## SAT MAth Practice questions – all topics

• Problem-solving and Data Analysis Weightage: 15%  Questions: 5-7
• Ratios, rates, proportional relationships, and units
• Percentages
• One-variable data: distributions and measures of centre and spread
• Two-variable data: models and scatterplots
• Probability and conditional probability
• Inference from sample statistics and margin of error
• Evaluating statistical claims: observational studies and Experiments

## SAT MAth and English  – full syllabus practice tests

[Calc]  Question   Easy

In a certain election, the ratio of electoral votes received in Maine by Candidate $$\mathrm{X}$$ to those received by Candidate $$\mathrm{Y}$$ was 3 to 1 . The state of Maine had 4 electoral votes in this election. How many electoral votes did Candidate $$\mathrm{Y}$$ receive in Maine?
A) 1
B) 2
C) 3
D) 4

Ans:A

In the election, the ratio of electoral votes received by Candidate X to those received by Candidate Y in Maine was 3 to 1. Maine had a total of 4 electoral votes.

Let $$X$$ be the number of electoral votes received by Candidate X and $$Y$$ be the number of electoral votes received by Candidate Y. According to the ratio:
$\frac{X}{Y} = 3 \quad \text{and} \quad \frac{X}{Y} = 3 \implies X = 3Y$

The total number of electoral votes is:
$X + Y = 4$

Substitute $$X = 3Y$$ into the total votes equation:
$3Y + Y = 4 \\ 4Y = 4 \\ Y = 1$

[Calc]  Question   Easy

A car’s fuel efficiency is 30 miles per gallon of gasoline. During a trip, the car uses 5 gallons of gasoline. Based on the car’s fuel efficiency, how many miles did the car travel during the trip?
A) 5
B) 6
C) 35
D) 150

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Ans:D

A car has a fuel efficiency of 30 miles per gallon of gasoline. During a trip, the car uses 5 gallons of gasoline. To find out how many miles the car traveled during the trip, we can use the formula:

$\text{Total miles traveled} = \text{Fuel efficiency} \times \text{Gallons of gasoline used}$

Substitute the given values into the formula:
$\text{Total miles traveled} = 30 \, \text{miles/gallon} \times 5 \, \text{gallons}$

Calculate the product:
$\text{Total miles traveled} = 150 \, \text{miles}$

[Calc]  Question   Easy

An object has a mass of 3,300 milligrams. What is the mass of the object in grams? ( 1 gram $$=1,000$$ milligrams)

A. 0.33
B. 3.30
C. 33.00
D. 330.00

Ans:B

To convert milligrams to grams, we divide by $$1,000$$ since $$1$$ gram is equal to $$1,000$$ milligrams.

So, the mass of the object in grams is:

$3,300 \text{ milligrams} \div 1,000 = 3.30 \text{ grams}$

Therefore, the correct answer is option B: $$3.30$$ grams.

[Calc]  Question   Easy

The graph shows the change over time, in milliseconds (ms), in a neuron’s membrane potential, in millivolts ( $$\mathrm{mV}$$ ), during an electrical brain signal known as an action potential. At which of the following times, in $$\mathrm{ms}$$, is the membrane potential closest to negative $$70 \mathrm{mV}$$ ?
A. 2
B. 3
C. 4
D. 5

Ans:D

There will be two  times, in $$\mathrm{ms}$$,when the membrane potential closest to negative $$70 \mathrm{mV}$$

$\text{t= 0 and 5 mV}$

[No-Calc]  Question  Easy

The function m is defined by m(x)=30x+120 What is the slope of the graph of y = m(x) in the xy-plane?

Ans: 30

The slope of a linear function $$m(x)$$ in the form $$m(x) = mx + b$$ is the coefficient of $$x$$, which is $$30$$ in this case. So, the slope of the graph of $$y = m(x)$$ in the $$xy$$-plane is $$30$$.

[Calc]  Question   Easy

𝑘(𝑥) = 260𝑥
The function gives the total amount 𝑘(𝑥), in dollars, Kayla earned after working x weeks at a bookstore. What is the total amount Kayla earned, in dollars, after working 10 weeks at the bookstore?
A. 2,600
B. 2,610
C. 2,626
D. 2,860

Ans: A

The function $$k(x) = 260x$$ represents the total amount $$k(x)$$, in dollars, Kayla earned after working $$x$$ weeks at a bookstore. We need to find the total amount earned after working 10 weeks.

Substitute $$x = 10$$ into the function:

$k(10) = 260 \times 10 = 2600$

So, the total amount Kayla earned after working 10 weeks is $$2600$$ dollars.

[Calc]  Question   Easy

The ratio of Jupiter’s diameter to Saturn’s diameter is approximately 1.2 to 1. The diameter of Jupiter is 143,000 kilometers. What is the diameter, to the nearest ten thousand kilometers, of Saturn?
A. 24,000
B. 83,000
C. 120,000
D. 170,000

Ans: C

Ratio of Jupiter’s diameter to Saturn’s diameter is 1.2 to 1
Diameter of Jupiter: 143,000 kilometers

Let $$d$$ be the diameter of Saturn. According to the ratio:

$\frac{\text{Diameter of Jupiter}}{\text{Diameter of Saturn}} = 1.2$

So, we have:

$\frac{143,000}{d} = 1.2$

Solve for $$d$$:

$d = \frac{143,000}{1.2}$

Calculate $$d$$:

$d = \frac{143,000}{1.2} = 119,166.67 \approx 120,000 \text{ kilometers}$

[Calc]  Question  Easy

If $$\frac{x-3}{7}=\frac{x-3}{9}$$ , the value of 𝑥 − 3 is between which of the following pairs of values?
A. -7 and -9
B. -1 and 1
C. 2.5 and 3.5
D. 6.75 and 9.25

Ans: B

To find the value of $$x-3$$, let’s first cross multiply the equation $$\frac{x-3}{7} = \frac{x-3}{9}$$:

$9(x-3) = 7(x-3)$

Expanding both sides:

$9x – 27 = 7x – 21$

Now, let’s solve for $$x$$:

$9x – 7x = -21 + 27$
$2x = 6$
$x = 3$

Now that we know $$x = 3$$, we can substitute it back into the equation to find $$x – 3$$:

$x – 3 = 3 – 3 = 0$

So, the value of $$x – 3$$ is $$0$$. Therefore, the correct answer is option B, $$-1$$ and $$1$$.

[Calc]  Question   Foundation

$$20 d+0.7 m=235$$
Shelly spent $$\ 235$$ to rent a moving van. The equation above shows the relationship between the number of days she rented the van, $$d$$, and the number of miles she drove the van, $$m$$. If she rented the van for 3 days, how many miles did she drive the van?
A) 118
B) 250
C) 307
D) 421

Ans:B

$20d + 0.7m = 235$
We know that Shelly rented the van for 3 days ($$d = 3$$). We need to find the number of miles ($$m$$) she drove.

Substitute $$d = 3$$ into the equation:
$20(3) + 0.7m = 235$

$60 + 0.7m = 235$

$0.7m = 175$

$m = \frac{175}{0.7} = 250$

So, Shelly drove 250 miles.

[Calc]  Question  Foundation

An automobile uses 27 pints of fuel for every 63 miles traveled. How many pints of fuel does the automobile use to travel 7 miles?
A) 16
B) 9
C) 4
D) 3

Ans:D

To find out how many pints of fuel the automobile uses to travel 7 miles, we set up a proportion based on the given information:

$\frac{27 \text{ pints}}{63 \text{ miles}} = \frac{x \text{ pints}}{7 \text{ miles}}$

Cross-multiply and solve for $$x$$:
$27 \times 7 = 63 \times x$

$189 = 63x$

$x = \frac{189}{63} = 3$

So, the automobile uses 3 pints of fuel to travel 7 miles.

[Calc]  Question Easy

When the temperature of water is 25 degrees Celsius, sound travels through the water at a constant speed of about 1,500 meters per second. At the same temperature, about how far, in meters, would sound travel through the water in 15 seconds?

A) 37,500

B) 22,500

C) 375

D) 100

B) 22,500

To determine how far sound would travel through water in 15 seconds at a speed of 1,500 meters per second:

Use the formula for distance:
$\text{Distance} = \text{Speed} \times \text{Time}$

Substitute the given values into the formula:
$\text{Distance} = 1500 \, \text{meters/second} \times 15 \, \text{seconds}$
$\text{Distance} = 22,500 \, \text{meters}$

[Calc]  Question  Easy

Dakota and Alex work as babysitters. For each babysitting job, Dakota charges $$\ 10$$ per hour plus a flat fee of $$\ 5$$ for travel expenses. Alex charges $$\ 8$$ per hour plus an additional fee of $$\ 4$$ per child.

Dakota and Alex have different babysitting jobs where each will be babysitting 4 children for the same amount of time. If they charge the same total amount, in dollars, for their respective jobs, how many hours will each spend babysitting?
A) 2.0
B) 3.0
C) 5.5
D) 10.5

C

Let’s first calculate the total charge for each babysitter.

For Dakota:
Charge per hour: $$\10$$
Flat fee for travel expenses: $$\5$$
Number of children: 4

Total charge for Dakota:
$Total_{\text{Dakota}} = (\text{Charge per hour} \times \text{Number of hours}) + \text{Flat fee for travel expenses}$
$Total_{\text{Dakota}} = (10 \times \text{Number of hours}) + 5$

For Alex:
Charge per hour: $$\8$$
Additional fee per child: $$\4$$
Number of children: 4

Total charge for Alex:
$Total_{\text{Alex}} = (\text{Charge per hour} \times \text{Number of hours}) + (\text{Additional fee per child} \times \text{Number of children})$
$Total_{\text{Alex}} = (8 \times \text{Number of hours}) + (4 \times 4)$
$Total_{\text{Alex}} = (8 \times \text{Number of hours}) + 16$

Since both babysitters charge the same total amount for their respective jobs, we can set their total charges equal to each other and solve for the number of hours:

$10 \times \text{Number of hours} + 5 = 8 \times \text{Number of hours} + 16$

Solve for the number of hours:
$2 \times \text{Number of hours} = 16 – 5$
$2 \times \text{Number of hours} = 11$
$\text{Number of hours} = \frac{11}{2}$
$\text{Number of hours} = 5.5$

Thus, each babysitter will spend $$5.5$$ hours babysitting.

$\boxed{C) \, 5.5}$

[Calc]  Question Easy

Dakota and Alex work as babysitters. For each babysitting job, Dakota charges $$\ 10$$ per hour plus a flat fee of $$\ 5$$ for travel expenses. Alex charges $$\ 8$$ per hour plus an additional fee of $$\ 4$$ per child.

Which graph shows the relationship between the time, in hours, that Dakota spends babysitting and the amount, in dollars, Dakota charges for each babysitting job?

B

[Calc]  Question  Easy

A digital artist resized a rectangular image. The ratio of the length to the width of the image did not change. The width of the new image is 3 times as long as the original width. If L is the length of the original image, which expression represents the length of the new image in terms of L ?

A) $$\frac{L}{3}$$

B) L-3

C) 3L

D) L+3

C) 3L

To find the expression for the length of the new image given that the width of the new image is 3 times as long as the original width and the ratio of length to width remains the same:

Let the original width be $$W$$ and the original length be $$L$$. The original ratio is:
$\frac{L}{W}$

Let the new width be $$3W$$. Since the ratio of length to width does not change, the new length $$L_{\text{new}}$$ must satisfy:
$\frac{L_{\text{new}}}{3W} = \frac{L}{W}$

Solve for the new length $$L_{\text{new}}$$:
$L_{\text{new}} = 3L$

[Calc]  Question  Easy

4, 5, 5, 6, 7, 8, 8, 9, 9, 9, 10

Eleven employees at a company were selected at random to participate in a survey. The survey included a question that asked the participants to rate their work satisfaction on a scale from 1 to 10. The list shows the eleven ratings of the participants.

What is the ratio of the number of participants who gave a rating of 6 or higher to the number of participants who gave a rating lower than 6 ?

A) 3 to 8

B) 8 to 3

C) 8 to 11

D) 11 to 8

B) 8 to 3

To determine the ratio of the number of participants who gave a rating of 6 or higher to those who gave a rating lower than 6, we first count the participants in each category.

Given the list of ratings:
$4, 5, 5, 6, 7, 8, 8, 9, 9, 9, 10$

We categorize them as follows:

Ratings of 6 or higher: 6, 7, 8, 8, 9, 9, 9, 10
Ratings lower than 6: 4, 5, 5

Now, we count the number of participants in each category:

Number of participants with ratings 6 or higher:
$6, 7, 8, 8, 9, 9, 9, 10$
There are 8 participants in this category.

Number of participants with ratings lower than 6:
$4, 5, 5$
There are 3 participants in this category.

Next, we find the ratio of the number of participants who gave a rating of 6 or higher to the number of participants who gave a rating lower than 6:

$\text{Ratio} = \frac{\text{Number of participants with ratings 6 or higher}}{\text{Number of participants with ratings lower than 6}} = \frac{8}{3}$

Thus, the ratio is $$8$$ to $$3$$.

[Calc]  Question Easy

It is estimated that humans begin REM sleep 90 minutes after falling asleep. Based on this estimate, how many seconds after falling asleep do humans begin REM sleep?

A)3,600

B)5,400

C)8,100

D)9,000

B)5,400

To find out how many seconds after falling asleep humans begin REM sleep, we need to convert 90 minutes into seconds.

1 minute = 60 seconds

Therefore, 90 minutes is:
$90 \, \text{minutes} \times 60 \, \text{seconds/minute} = 5400 \, \text{seconds}$

So, humans begin REM sleep 5400 seconds after falling asleep.

[Calc]  Question Easy

Two people sweep the floor. The table gives their sweeping rates, in square yards per minute ($$yd^2$$/min).

If each person sweeps the floor for 5 minutes, how much greater of an area, in square yards, does Eric sweep than Jeremy?

A)20

B)60

C)80

D)140

A)20

To determine how much greater an area Eric sweeps than Jeremy, we first calculate the area each person sweeps.

Jeremy’s sweeping rate is 12 square yards per minute, and he sweeps for 5 minutes:
$\text{Area swept by Jeremy} = 12 \, \text{yd}^2/\text{min} \times 5 \, \text{min} = 60 \, \text{yd}^2$

Eric’s sweeping rate is 16 square yards per minute, and he sweeps for 5 minutes:
$\text{Area swept by Eric} = 16 \, \text{yd}^2/\text{min} \times 5 \, \text{min} = 80 \, \text{yd}^2$

The difference in the area swept by Eric compared to Jeremy is:
$80 \, \text{yd}^2 – 60 \, \text{yd}^2 = 20 \, \text{yd}^2$

So, Eric sweeps 20 square yards more than Jeremy.

[Calc]  Question Easy

A limestone stalactite grew in length at a rate of $$\frac{1}{8}$$ millimeter per year. At this rate, how many years would it take for this stalactite to grow a total of 4.0 millimeters?

32

If the limestone stalactite grows at a rate of $$\frac{1}{8}$$ of a millimeter per year, then in $$1$$ year it grows $$\frac{1}{8}$$ millimeters.

To find out how many years it takes for the stalactite to grow a total of $$4.0$$ millimeters, we can set up the equation:
$\text{total growth} = \text{growth per year} \times \text{number of years}$
$4.0 = \frac{1}{8} \times \text{number of years}$
Solving for the number of years:
$\text{number of years} = 4.0 \times 8 = 32$

So, it would take $$32$$ years for the stalactite to grow $$4.0$$ millimeters.

[Calc]  Questions  Easy

In 2015, the city of Miami had a population of 441,000 people and an area of 36 square miles. What was the population density of Miami, in people per square mile, in 2015?
A) 10,750
B) 12,250
C) 14,250
D) 16,750

Ans: B

To find the population density of Miami in 2015, we use the formula for population density:
$\text{Population Density} = \frac{\text{Population}}{\text{Area}}$

Given:
Population = 441,000 people
Area = 36 square miles

Using the formula:
$\text{Population Density} = \frac{441,000 \text{ people}}{36 \text{ square miles}}$

Perform the division:
$\text{Population Density} = 12,250 \text{ people per square mile}$

Therefore, the population density of Miami in 2015 was:
$\boxed{12,250}$

[Calc]  Question Easy

The line graph shows the number of space shuttle launches by the United States from 1981 through 1986.

During which year of this time period was the number of space shuttle launches the greatest?
A) 1982
B) 1983
C) 1984
D) 1985

D

[Calc]  Question Easy

In 1855, Louis Remme traveled trom Sacramento, California, to Portland, Oregon, stopping to rest for only 10 hours of the 143 hours it took him to reach Portland. If his average speed while traveling without resting was 5 miles per hour, how many miles did Louis Remme travel?
A) 665
B) 705
C) 715
D) 765

A

Question

Ewan writes 30 manuscripts and wants to get them published. What is the minimum cost, in dollars, for professional review of Ewan’s manuscripts?

1. 7,500
2. 11,850
3. 13,125
4. 18,750

A

Question

Water quality managers estimate that a population of algae initially covered $$x$$ square miles of water in a nearby river. After a period of time, the algae grew to cover 375% of its original area. Which of the following expressions represents the area of water, in square miles, that the algae covered after this period of time?

1. 0.375$$x$$
2. 3.75$$x$$
3. 37.5$$x$$
4. 375$$x$$

B

Question

The distance between two locations on a map is 6 centimeters (cm). If $1 \mathrm{~cm}$ on the map corresponds to an actual distance of 15 miles, what is the actual distance, in miles, between the two locations?
A. 0.4
B. 2.5
C. 90
D. 150

Ans: C

Question

$2 n+6=14$

A tree had a height of 6 feet when it was planted. The equation above can be used to find how many years $n$ it took the tree to reach a height of 14 feet. Which of the following is the best interpretation of the number 2 in this context?
A. The number of years it took the tree to double its height
B. The average number of feet that the tree grew per year
C. The height, in feet, of the tree when the tree was 1 year old
D. The average number of years it take similar trees to grow 14 feet

Ans: B

Questions

$T=1,000+18 h$ In the equation above, $T$ represents Brittany’s total take-home pay, in dollars, for her first week of work, where $h$ represents the number of hours she worked that week and 1,000 represents a sign-on bonus. If Brittany’s total take-home pay was $\$ 1,576$, for how many hours was Brittany paid for her first week of work? A. 16 B. 32 C. 55 D. 88 ▶️Answer/Explanation Ans: B Questions Juliet rented a car for one day from a company that charges$\$80$ per day plus $\$ 0.15$per mile driven. If she was charged a total of$\$98$ for the rental and mileage, for how many miles of driving was Juliet charged? (Assume there is no tax.)
A. 15
B. 120
C. 533
D. 633

Ans: B

Questions

.Makayla is planning an event in a 5,400-square-foot room. If there should be at least 8 square feet per person, what is the maximum number of people that could attend this event?
A. 588
B. 675
C. 15,274
D. 43,200

Ans: B

Questions

Tanya earns $\$ 13.50$per hour at her part-time job. When she works$z$hours, she earns$13.50 z$dollars. Which of the following expression gives the amount, in dollars, Tanya will earn if she works$3 z$hours? A.$3(13.50 z)$B.$3+13.50 z$C.$3 z+13.50 z$D.$13.50(z+3)$▶️Answer/Explanation Ans: A Question A teacher has signed up for a program that automatically delivers books for the classroom library. The classroom library currently consists of 48 books. If the program delivers 12 books a month, how many books will the classroom library consist of after 5 months? A. 240 B. 108 C. 65 D. 60 ▶️Answer/Explanation Ans: B Question In normal weather conditions, a particular type of jet burns an average of 2.4 gallons of fuel per nautical mile flown. The distance from New York to Los Angeles is about 2,100 nautical miles. Approximately how many gallons of fuel will the jet burn for a trip from New York to Los Angeles in normal weather conditions? A. 900 B. 1,200 C. 5,000 D. 7,000 ▶️Answer/Explanation Ans: C Questions If the ratio of$0.5: x$is equivalent to$1.5: 2.25$, what is the value of$x ?$A. 0.75 B. 1.6875 C. 3 D. 3.25 ▶️Answer/Explanation Ans: A Questions Based on the table above, what fraction of the flights for Airline A were delayed? 1. $$\frac{700}{1,850}$$ 2. $$\frac{861 }{1,561}$$ 3. $$\frac{861}{2,890}$$ 4. $$\frac{2,029}{2,890}$$ ▶️Answer/Explanation Ans: C Questions A physician prescribes a treatment in which a patient takes 2 teaspoons of a medication every 6 hours for 5 days. According to the prescription, how many teaspoons of the medication should the patient take in a 24-hour period? A. 4 B. 6 C. 8 D. 40 ▶️Answer/Explanation Ans: C Question . At her summer job, Paula earns the same amount of money for each hour she works. If she earns$\$240$ for working 20 hours, how much does she earn for 5 hours?
A. $\$ 12$B.$\$50$
C. $\$ 60$D.$\$100$

Ans: C

Question

Yuna sold boxes of cookies and bags of candy. The ratio of the number of boxes of cookies she sold to the number of bags of candy she sold was 2 to 1 . If Yuna sold 8 boxes of cookies, how many bags of candy did she sell?
A. 4
B. 8
C. 10
D. 16

Ans: A

Question

At a snack bar, each medium drink costs $\$ 1.85$and each large drink costs$c$more dollars than a medium drink. If 5 medium drinks and 5 large drinks cost a total of$\$20.50$, what is the value of $c$ ?
A. 0.45
B. 0.40
C. 0.30
D. 0.25