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
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.
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:
\[ \boxed{(100)(13)/P} \]
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 \(r\).
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 \(\boxed{40}\).
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) \(\frac{(3)(100)}{p}\).