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

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

 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

▶️Answer/Explanation

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 \(7.956 \times 10^{27}\).

Thus, the correct answer is:
\[
\boxed{\text{A) 0.0007956}}
\]

  Question   Hard

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

▶️Answer/Explanation

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:
\[\frac{1}{10} = t\]

 Question  Hard

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

▶️Answer/Explanation

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:
\[ \boxed{27} \]

 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) \(n=-\frac{2}{p+3}\)

▶️Answer/Explanation

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:
\[ n = \frac{2}{p – 3} \]

So the answer is:
\[ \boxed{C} \]

  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?

▶️Answer/Explanation

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: \(\frac{3}{8}\)

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