# Digital SAT Math Practice Questions – Advanced : 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   Hard

The Sun’s mass is $$1.989 \times 10^{30}$$ kilograms, and $$0.04 \%$$ of its total mass is sulfur. If the total mass of sulfur in the Sun is $$s \times 10^{30}$$ kilograms, what is the value of $$s$$ ?
A) 0.0007956
B) 0.007956
C) 0.07956
D) 0.7956

Ans:A

Given that $$0.04 \%$$ of the Sun’s total mass is sulfur, we can express this mathematically as:
$0.04 \% = \frac{s}{1.989 \times 10^{30}}$

To find $$s$$, multiply both sides by $$1.989 \times 10^{30}$$:
$s = 0.0004 \times 1.989 \times 10^{30}$

Calculate the value:
$s = 0.0004 \times 1.989 \times 10^{30} = 0.0007956 \times 10^{30}$

So, the value of $$s$$ is $$0.0007956 \times 10^{30}$$, which is equivalent to $$7.956 \times 10^{27}$$.

$\boxed{\text{A) 0.0007956}}$

[Calc]  Question   Hard

If $$\frac{x}{y}=8$$ and $$\frac{2 x}{t y}=160$$, what is the value of $$t$$ ?

Ans: 0.1,1 / 10

$$\frac{x}{y} = 8$$ and $$\frac{2x}{ty} = 160$$

From the first equation, we can express $$x$$ in terms of $$y$$:
$x = 8y$

Substitute $$x = 8y$$ into the second equation:
$\frac{2(8y)}{ty} = 160$

Simplify:
$\frac{16y}{ty} = 160$

Multiply both sides by $$ty$$ to isolate $$t$$:
$16y = 160ty$

Divide both sides by $$160y$$:
$\frac{16}{160} = t$

Simplify:
$\frac{1}{10} = t$

[Calc]  Question  Hard

If $$\frac{2}{3} p+4=10$$, what is the value of $$3 p ?$$

27

Given the equation:
$\frac{2}{3}p + 4 = 10$

We need to solve for $$p$$ and subsequently determine the value of $$3p$$.

First, isolate $$p$$:
$\frac{2}{3}p + 4 = 10$
Subtract 4 from both sides:
$\frac{2}{3}p = 6$
Multiply both sides by $$\frac{3}{2}$$ to solve for $$p$$:
$p = 6 \times \frac{3}{2}$
$p = 9$

Now, calculate $$3p$$:
$3p = 3 \times 9$
$3p = 27$

Thus, the value of $$3p$$ is:
$\boxed{27}$

[Calc]  Question  Hard

$p=\frac{2}{n}+3$

The given equation relates the numbers $$p$$ and $$n$$, where $$n$$ is not equal to 0 and $$p>3$$. Which equation correctly expresses $$n$$ in terms of $$p$$ ?
A) $$n=\frac{p}{2}-3$$
B) $$n=\frac{p}{2}+3$$
C) $$n=\frac{2}{p-3}$$
D) $$n=-\frac{2}{p+3}$$

C

The given equation is:
$p = \frac{2}{n} + 3$
We need to express $$n$$ in terms of $$p$$.

First, subtract 3 from both sides to isolate the fraction:
$p – 3 = \frac{2}{n}$

Next, take the reciprocal of both sides:
$\frac{1}{p – 3} = \frac{n}{2}$

Finally, multiply both sides by 2:
$n = \frac{2}{p – 3}$

$\boxed{C}$

[Calc]  Question   Hard

The bar graph above shows the total number of scheduled flights and the number of delayed flights for five airlines in a one-month period. Values have been rounded to the nearest 1000 flights.

According to the graph, for the airline with the greatest number of delayed flights, what fraction of the total number of scheduled flights for the airline were delayed?

Ans:.375 or 3/8

The airline with the greatest number of delayed flights is Airline B with 15,000 delayed flights.

From the graph, the total number of scheduled flights for Airline B is 40,000 .

The fraction of delayed flights is:
$\frac{\text { Number of Delayed Flights }}{\text { Total Number of Scheduled Flights }}=\frac{15,000}{40,000}=\frac{3}{8}$

Therefore, the fraction of the total number of scheduled flights for Airline B that were delayed is: $$\frac{3}{8}$$

[Calc]  Question  Hard

$C(x)=\frac{5}{9}(x-32)$

The function $$C$$ gives the temperature, in degrees Celsius, that corresponds to a temperature of $$x$$ degrees Fahrenheit. If a temperature increased by 19.8 degrees Fahrenheit, how much did the temperature increase in degrees Celsius? (Disregard the degree symbol when entering your answer.)

11

Given the function $$C(x) = \frac{5}{9}(x – 32)$$, which converts Fahrenheit to Celsius, let’s find how much the temperature increased in degrees Celsius when it increased by 19.8 degrees Fahrenheit.

$\text{Increase in Fahrenheit} = 19.8$

Now, let’s use the conversion formula to find the increase in Celsius:

$\text{Increase in Celsius} = \frac{5}{9} \times \text{Increase in Fahrenheit}$

$\text{Increase in Celsius} = \frac{5}{9} \times 19.8$

$\text{Increase in Celsius} \approx \frac{5}{9} \times 19.8$

$\text{Increase in Celsius} \approx 11$

So, the temperature increased by approximately $$\boxed{11}$$ degrees Celsius.

[Calc]  Question  Hard

The expression $0.7 x$ represents the result of decreasing a positive quantity $x$ by what percent?
A) $70 \%$
B) $30 \%$
C) $7 \%$
D) $3 \%$

B

[Calc]  Question  Hard

When Arban walks from home to class, he burns 4.2 calories per minute, and when he rides his bike from home to class, he burns 5.1 calories per minute. If Arban spent a total of 2 hours walking and bicycling from home to class in a week and burned a total of 531 calories, how many minutes did he spend walking?

90

Question

In 2007, US economists gathered data about money collected for the arts, entertainment, and recreation industries in eight states. The ratio of money collected in all eight states to the money collected in the state of Florida was 11 to 8. If a total of $$x$$ dollars was collected in all eight states, which expression represents the total amount of money, in dollars, collected in Florida?

1. $$\frac{8x}{11}$$
2. $$\frac{11x}{8}$$
3. 8
4. 11

A

Question

A quantity is decreased by 45 % of its value. The resulting value is $$x$$. Which expression gives the value of the original quantity in terms of $$x$$?

1. $$\frac{x}{0.45}$$
2. $$\frac{x}{0.55}$$
3. $$\frac{x}{1.45}$$
4. $$\frac{x}{1.55}$$

B

Question

The ratio of students to teachers in a high school is 18 to 1. If the school has 105 teachers, how many students does it have?

1890

Question

$P=686 q$

The formula above gives the theoretical power $P$, in kilowatts $(\mathrm{kW})$, available from water falling from a certain height in terms of its flow rate, $q$, in cubic meters per second. What is the flow rate, in cubic meters per second, of water falling from the same height with a theoretical power of $1,029,000 \mathrm{~kW}$ ?

Ans: 1500

Questions

$I=\frac{V}{R}$

The formula above is Ohm’s law for an electric circuit with current $I$, in amperes, potential difference $V$, in volts, and resistance $R$, in ohms. A circuit has a resistance of 500 ohms, and its potential difference will be generated by $n$ six-volt batteries that produce a total potential difference of $6 n$ volts. If the circuit is to have a current of no more than 0.25 ampere, what is the greatest number, $n$, of six-volt batteries that can be used?

Ans: 20

Questions

Anna was 99 centimeters tall the day she turned 3 years old, and she was 106.5 centimeters tall the day she turned 4 years old. If Anna’s height increases by the same amount each year between the ages of 2 and 8 , how many centimeters tall will she be the day she turns 7 years old?

Ans: 129

Questions

A contractor purchased two slabs of granite, both in the shape of a right rectangular prism. The table below shows some information about the two slabs.

Slab2 has a ratio of length to width of 5 to 2. How many centimeters wide is Slab2?

Ans: 50

Questions

A pizza parlor sells pizza slices for $\$ 3$each and calzones for$\$4$ each. A group of friends spent $\$ 51$on pizza slices and calzones at the parlor. If they bought 6 calzones, how many pizza slices did they buy? ▶️Answer/Explanation Ans: 9 Questions A baker is gathering the ingredients required to make 15 batches of oatmeal cookies and 1 cake. The cake will require one-quarter bag of flour. The baker needs a total of more than 3 but less than 4 bags of flour. What is one possible value for the fraction of one bag of flour required for each batch of cookies? ▶️Answer/Explanation Ans:$11 / 60<\mathrm{x}<1 / 4, .183<\mathrm{X}<.25$Questions Pure beeswax has a density of 0.555 ounce per cubic inch. An online company sells pure beeswax at a price of$\$8.00$ per ounce. What is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company? (Disregard the $\$$sign when gridding your answer. For example, if your answer is$\$1.37$, grid 1.37)

Ans: $4.44,111 / 25$

Questions

Anita created a batch of green paint by mixing 2 ounces of blue paint with 3 ounces of yellow paint. ,She must mix a second batch using the same ratio of blue and yellow paint as the first batch. If she uses 5 ounces of blue paint for the second batch, how much yellow paint should Anita use?
A. Exactly 5 ounces
B. 3 ounces more than the amount of yellow paint used in the first batch
C. 1.5 times the amount of yellow paint used in the first batch
D. 1.5 times the amount of blue paint used in the second batch

Ans: D

Questions

The line graph above shows the population, in thousands, of people living in Alaska every 10 years from 1900 to 2000.

The ratio of the population of Alaska in 1980 to the population of Alaska in 1970 can be written as $$a$$: 1. What is the value of $$a$$?

Ans: 1.34, 67/50

Questions

A museum built a scale model of an Apatosaurus dinosaur skeleton, where 1 centimeter in the model is equivalent to 16 centimeters of the actual skeleton. If the length of the femur bone of the actual skeleton is 184 centimeters, what is the length, to the nearest tenth of a centimeter, of the femur bone in the model?

Ans: $23 / 2,11.5$

Questions

A rowing team entered a 2000-meter race. The team’s coach is analyzing the race based on the team’s split times, as shown in the table above. A split time is the time it takes to complete a 500-meter segment of the race.

During the fourth split of the race, the team rowed at a rate of 28 strokes per minute. To the nearest whole number, how many strokes did it take the team to complete the final 500 meters of the race?

Ans: 50

Questions

George took a nonstop flight from Dallas to Los Angeles, a total flight distance of 1,233 miles. The plane flew at a speed of 460 miles per hour for the first 75 minutes of the flight and at a speed of 439 miles per hour for the remainder of the flight. To the nearest minute, for how many minutes did the plane fly at a speed of 439 miles per hour?

Ans: 90

Questions

The front row of an auditorium has 10 seats. There are 50 rows in total. If each row has 2 more seats than the row before it, which expression gives the total number of seats in the last row?
A. $10+2(50-1)$
B. $10+2(50)$
C. $50(10+2)$
D. $10+2^{50}$

A fashion buyer for a large retail store purchased 315 items directly from the manufacturer for a total of $\$ 6000$. Some of the items were dresses purchased for$\$25$ each, and the rest were shirts purchased for $\$ 10$each. How many more dresses than shirts did the buyer purchase? ▶️Answer/Explanation Ans: 65 Question$h(t)=-\frac{1}{175} t+481$An archeologist estimates that, as a result of erosion, the height of the Great Pyramid of Giza has been decreasing at a constant rate since it was built. The function above is used by the archeologist to model the height$h(t)$, in feet, of the pyramid$t$years after it was built. According to the function, which of the following statements is true? A. Every 1,750 years the height of the pyramid decreases by 10 feet. B. Every 175 years the height of the pyramid decreases by 0.1 foot. C. Every 100 years the height of the pyramid decreases by 1.75 feet. D. Every year the height of the pyramid decreases by 175 feet. ▶️Answer/Explanation Ans: A Question Isabella sells only rings and necklaces on her website. Rings sell for$\$50$ each, and necklaces sell for $\$ 30$each. If Isabella sold 25 pieces of jewelry and her sales totaled$\$1050$, how many necklaces did Isabella sell?