## 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

**[No calc]**** ****Question*** *** Hard**

Alice took 60 minutes to complete a task on her first trial. The time it took Alice to complete the task decreased by \(10 \%\) of the previous time for each additional trial. Approximately how many minutes will it take Alice to complete the task on her fifth trial?

A. 50

B. 42

C. 39

D. 35

**▶️Answer/Explanation**

Ans:C

To find out how much time Alice takes on her fifth trial, we’ll first calculate the time taken on each subsequent trial, considering that it decreases by \(10\%\) of the previous time.

On the first trial, Alice took 60 minutes.

On the second trial, she’ll take \(60 – (10\% \times 60) = 60 – 6 = 54\) minutes.

On the third trial, she’ll take \(54 – (10\% \times 54) = 54 – 5.4 = 48.6\) minutes.

On the fourth trial, she’ll take \(48.6 – (10\% \times 48.6) = 48.6 – 4.86 = 43.74\) minutes.

On the fifth trial, she’ll take \(43.74 – (10\% \times 43.74) = 43.74 – 4.374 = 39.366\) minutes.

Rounding to the nearest whole number, approximately \(39\) minutes.

So, the answer is option C: \(39\) minutes.

**[Calc]**** ****Question**** Hard**

If x>0 and p% of x is 13, which expression represents x in terms of p ?

A. 13P

B. 13P/100

C. 100P/13

D. (100)(13)/P

**▶️Answer/Explanation**

Ans: D

Given that \( p\% \) of \( x \) is 13, we can express this mathematically as:

\[ \frac{p}{100} \cdot x = 13 \]

We need to solve for \( x \) in terms of \( p \). To do this, isolate \( x \) on one side of the equation:

\[ \frac{p}{100} \cdot x = 13 \]

Multiply both sides of the equation by \( \frac{100}{p} \) to get \( x \):

\[ x = \frac{13 \cdot 100}{p} \]

So, the expression that represents \( x \) in terms of \( p \) is:

\[ x = \frac{1300}{p} \]

Therefore, the correct answer is:

\[ \boxed{(100)(13)/P} \]

**[Calc]**** ****Question** **Hard**

The value of \(r\) is \(\frac{20}{21}\) times the value of \(t\), where \(t>0\). The value of \(t\) is what percent greater than the value of \(r\) ? (Disregard the \(\%\) sign when entering your answer. For example, if your answer is \(39 \%\), enter 39)

**▶️Answer/Explanation**

5

To find the percent by which \(t\) is greater than \(r\), we need to compare their values and express the difference as a percentage of \(r\).

Let’s start by finding the difference between \(t\) and \(r\):

\[ t – r = t – \frac{20}{21} t \]

\[ t – r = \frac{21}{21} t – \frac{20}{21} t \]

\[ t – r = \frac{1}{21} t \]

Now, let’s express this difference as a percentage of \(r\):

\[ \text{Percent difference} = \frac{\text{Difference}}{r} \times 100 \]

\[ \text{Percent difference} = \frac{\frac{1}{21} t}{r} \times 100 \]

Given that \(r = \frac{20}{21} t\), we substitute it in:

\[ \text{Percent difference} = \frac{\frac{1}{21} t}{\frac{20}{21} t} \times 100 \]

\[ \text{Percent difference} = \frac{1}{20} \times 100 \]

\[ \text{Percent difference} = 5 \]

Therefore, \(t\) is \( \boxed{5\%} \) greater than \(r\).

**[Calc]**** ****Question** **Hard**

The expression \(0.6 y\) represents the result of decreasing the quantity \(y\) by \(p \%\). What is the value of \(p\) ?

**▶️Answer/Explanation**

Ans: 40

To decrease the quantity \(y\) by \(p\%\), we multiply \(y\) by \(1 – \frac{p}{100}\).

Given that \(0.6y\) represents the result of decreasing \(y\) by \(p\%\), we set up the equation:

\[0.6y = y \times \left(1 – \frac{p}{100}\right)\]

To solve for \(p\):

\[0.6 = 1 – \frac{p}{100}\]

\[\frac{p}{100} = 1 – 0.6\]

\[\frac{p}{100} = 0.4\]

Multiply both sides by \(100\):

\[p = 0.4 \times 100\]

\[p = 40\]

So, the value of \(p\) is \(\boxed{40}\).

**[Calc]**** ****Question*** *** Hard**

*p*% of *x* is 3. Which expression represents *x* in terms of *p* ?

A) \(\frac{3}{p}\)

B) \(\frac{3p}{100}\)

C) \(\frac{(3)(100)}{100}\)

D) \(\frac{p}{(100)(3)}\)

**▶️Answer/Explanation**

**C) \(\frac{(3)(100)}{100}\)**

To find \(x\) in terms of \(p\), we need to remember that “p% of x is 3.” This means that \(p\%\) of \(x\) equals \(3\). Mathematically, we can represent this as:

\[ \frac{p}{100} \times x = 3 \]

To solve for \(x\), we divide both sides by \(\frac{p}{100}\), which is the same as multiplying by \(\frac{100}{p}\). This gives us:

\[ x = \frac{3 \times 100}{p} = \frac{300}{p} \]

So, the correct answer is C) \(\frac{(3)(100)}{p}\).

**[Calc]**** ****Question**** ****Hard**

What is 19% of 200 ?

**▶️Answer/Explanation**

38

To find \( 19\% \) of 200, we multiply 200 by \( \frac{19}{100} \):

\[ 19\% \text{ of } 200 = \frac{19}{100} \times 200 = 38 \]

So, \( 19\% \) of 200 is \( \boxed{38} \).

**[Calc]**** ****Question*** *** Hard**

Two different store owners in a shopping center estimated the percentage of all visitors who wear eyeglasses. They each selected a random sample of the shopping center visitors and recorded whether the visitors were wearing eyeglasses. The results from each sample are shown in the table below.

If the associated margin of error was calculated the same way for both samples, which of the following is the most likely reason that the result for Sample A has a larger margin of error?

A)Sample A included more visitors than Sample B.

B)Sample B included more visitors than Sample A.

C)Sample A included a greater percentage of visitors who were wearing eyeglasses than Sample B.

D)Sample B included a greater percentage of visitors who were wearing eyeglasses than Sample A.

**▶️Answer/Explanation**

**B)Sample B included more visitors than Sample A.**

The margin of error in a survey result is influenced by several factors, including the sample size. When the margin of error is calculated the same way for different samples, a larger margin of error typically indicates a smaller sample size. This is because the margin of error decreases as the sample size increases, due to the reduced variability in the estimate.

Given that the percentages of visitors wearing eyeglasses are the same (21%) in both samples but the margin of error differs (3% for Sample A and 2% for Sample B), the most likely reason for the larger margin of error in Sample A is that it included fewer visitors than Sample B.

Therefore, the correct answer is:

B) Sample B included more visitors than Sample A.

**[Calc]**** ***Question ***Hard**

The table gives the typical adult weight ranges and life spans for African and Asian elephants in the wild.

Based on the table, the typical life span of the African elephant in the wild is p% greater than the typical life span of the Asian elephant in the wild. What is the value of p ? (Disregard the % sign when entering your answer. For example, if your answer is 39%, enter 39)

**▶️Answer/Explanation**

Ans: 50/3, 16.6, 16.7

To find the percentage by which the typical life span of the African elephant in the wild exceeds that of the Asian elephant, we’ll compare their life spans.

The typical life span of the African elephant is 70 years, and the typical life span of the Asian elephant is 60 years.

The difference in life spans is \(70 – 60 = 10\) years.

To find the percentage increase, we’ll divide this difference by the typical life span of the Asian elephant and then multiply by 100:

\[\frac{10}{60} \times 100 = \frac{1}{6} \times 100 = \frac{100}{6}\]

\[= 16.67\% \]

Therefore, the value of \(p\) is \(\mathbf{16.67}\).

*Question *

The table gives the age groups of the total population of women and the number of registered women voters in the United States in 2012, rounded to the nearest million.

In 2012, the number of registered women voters was \(p\)% of the total population of women. What is the value of \(p\), to the nearest whole number?

**▶️Answer/Explanation**

66

*Question *

The table gives the age groups of the total population of women and the number of registered women voters in the United States in 2012, rounded to the nearest million.

If a woman is selected at random from the total population of women ages 45 to 64 years old, what is the probability of selecting a registered woman voter, rounded to the nearest hundredth? (Express your answer as a decimal, not as a percent.)

**▶️Answer/Explanation**

.71, 71/100

*Question*

$c(x)=m x+500$

A company’s total cost $c(x)$, in dollars, to produce $x$ shirts is given by the function above, where $m$ is a constant and $x>0$. The total cost to produce 100 shirts is $\$ 800$. What is the total cost, in dollars, to produce 1000 shirts? (Disregard the $\$$ sign when gridding your answer.)

**▶️Answer/Explanation**

Ans: 3500

*Questions *

The number $y$ is $20 \%$ greater than the number $x$. The number $z$ is $20 \%$ less than $y$. The number $z$ is how many times $x$ ?

**▶️Answer/Explanation**

Ans: .96, 24/25

*Questions *

The wholesale price of a kilogram of lentils decreased by $1 \%$ from the previous month for six consecutive months. If $x$ is the number of months since the price began to drop and $y$ is the cost of a kilogram of lentils, which of the following equations could model the cost of lentils over this time period?

A. $y=0.99 x+1.65$

B. $y=1.01 x+1.65$

C. $y=1.65(0.99)^x$

D. $y=1.65(1.01)^x$

**▶️Answer/Explanation**

Ans: C

*Questions *

The table above shows the distribution of color for the 4000 cars registered in Town X. Based on the table, how many more white cars than black cars are registered in Town X?

**▶️Answer/Explanation**

Ans: 760

*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.

By the end of the season, the coach wants the team to reduce its mean split time by 10% as compared to this race. At the end of the season, what should the team’s mean split time be, in seconds?

**▶️Answer/Explanation**

Ans: 99

*Questions *

Tamika is ordering desktop computers for her company. The desktop computers cost $\$ 375$ each, and tax is an additional $6 \%$ of the total cost of the computers. If she can spend no more than $\$ 40,000$ on the desktop computers, including tax, what is the maximum number of computers that Tamika can purchase?

**▶️Answer/Explanation**

Ans: 100

*Question*

When 9 is increased by $3 x$, the result is greater than 36 . What is the least possible integer value for $x$ ?

**▶️Answer/Explanation**

Ans: 10

*Question*

Last year, Gary’s tomato plants produced 24 kilograms of tomatoes. This year, Gary increased the number of tomato plants in his garden by $25 \%$. If his plants produce tomatoes this year at the same rate per plant as last year, how many kilograms of tomatoes can Gary expect the plants to produce this year?

**▶️Answer/Explanation**

Ans: 30