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Digital SAT Math: Practice Questions-Problem solving and data analysis-Percents

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  Easy

There are 435 voting members of the US House of Representatives. If \(b\) voting members are in favor of a certain bill, which expression represents the percentage of the voting members in favor of the bill?
A. \(100\left(\frac{b}{435}\right)\)
B. \(100\left(\frac{435}{b}\right)\)
C. \(435\left(\frac{b}{100}\right)\)
D. \(435(100 b)\)

▶️Answer/Explanation

Ans:A

To represent the percentage of the voting members in favor of the bill, we need to calculate the ratio of the number of members in favor (\(b\)) to the total number of members (435), and then multiply by \(100\) to convert it to a percentage.

So, the expression representing the percentage of members in favor of the bill is:

\[100\left(\frac{b}{435}\right)\]

Therefore, the correct answer is option A: \(100\left(\frac{b}{435}\right)\).

Question   Easy

A forestry department measures tree trunk diameter, in inches, at a constant height from the ground for each tree growing in a certain area. The data for 95 of these trees are summarized in the histogram. The first bar represents trees with a trunk diameter less than 6 inches. The second bar represents trees with a trunk diameter of at least 6 inches but less than 12 inches, and so on.

Approximately what percentage of these trees have a trunk diameter less than 6 inches?
A. 2.6%
B. 5.3%
C. 10.5%
D. 15.8%

▶️Answer/Explanation

Ans: B

To determine the percentage of trees with a trunk diameter less than 6 inches, we first need to identify the number of trees in this category from the histogram.

From the histogram:

  • The first bar represents trees with trunk diameters less than 6 inches.
  • The height of the first bar is 5, indicating there are 5 trees in this category.

There are a total of 95 trees.

To find the percentage of trees with trunk diameters less than 6 inches:

\[
\frac{5}{95} \times 100=\frac{1}{19} \times 100 \approx 5.26 \%
\]

Thus, the percentage of these trees with a trunk diameter less than 6 inches is approximately:
B. \(5.3 \%\)

  Question  Easy

What is 90% of 80 ?
A. 10
B. 72
C. 88
D. 152

▶️Answer/Explanation

Ans: B

To find \(90\%\) of \(80\), we multiply \(80\) by \(0.90\) since \(90\%\) is equivalent to \(0.90\):

\[90\% \text{ of } 80 = 0.90 \times 80 = 72\]

So, \(90\%\) of \(80\) is \(72\).

Therefore, the correct answer is option B) \(72\).

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.

Which of the following is closest to the percentage of participants who gave a rating of 5 ?

A) 9%

B) 18%

C) 27%

D) 45%

▶️Answer/Explanation

B) 18%

We need to find the percentage of participants who gave a rating of 5.

Given ratings:
\[4, 5, 5, 6, 7, 8, 8, 9, 9, 9, 10\]

Count the number of 5s:
There are \(2\) ratings of \(5\) out of \(11\) total ratings.

Calculate the percentage:
\[ \text{Percentage} = \left(\frac{2}{11}\right) \times 100 \approx 18.18\%\]

So, the closest percentage is:
\[ \boxed{18\%} \]

  Question Easy

If m% of 300 is 150, what ism% of 180?
A) 45
B) 90
C) 120
D) 360

▶️Answer/Explanation

B) 90

If \( m \% \) of 300 is 150, we need to determine \( m \% \) of 180.

1. Find \( m \% \) from the given information:
\[
\frac{m}{100} \times 300 = 150
\]
\[
m \times 3 = 150
\]
\[
m = 50
\]

2. Calculate \( m \% \) of 180:
\[
\frac{50}{100} \times 180 = 0.5 \times 180 = 90
\]

Thus, \( m \% \) of 180 is:\[ \boxed{90} \]

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