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

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

DSAT 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

DSAT MAth and English  – full syllabus practice tests

Question Hard

\[ p = \frac{2}{n} + 3 \]

The given equation relates the numbers \( p \) and \( n \), where \( n \neq 0 \) 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
Solution

Ans: C

Given: \( p = \frac{2}{n} + 3 \)

Subtract 3: \( p – 3 = \frac{2}{n} \)

Take reciprocal: \( \frac{1}{p – 3} = \frac{n}{2} \)

Multiply by 2: \( n = \frac{2}{p – 3} \)

 Question  Hard

One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees. If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be
closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)
A.1.0
B.1.2
C.1.3
D.1.4

▶️Answer/Explanation

Ans: C
Convert 1 foot to inches: 1 foot = 12 inches
Calculate the increase in diameter for 10 years:
White birch: 10 ÷ 5.0 = 2 inches
Pin oak: 10 ÷ 3.0 = 3.33 inches
Find the new diameters:
White birch: 12 + 2 = 14 inches
Pin oak: 12 + 3.33 = 15.33 inches
Difference in diameters:
15.33 – 14 = 1.3 inches

Question Hard

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

Population of Alaska over Time

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 \( a \)?

A) \( a = 1.2 \)

B) \( a = 1.4 \)

C) \( a = 1.5 \)

D) \( a = 2.0 \)

▶️ Answer/Explanation
Solution

Ans: B

From the graph and correction:

Population in 1970 = 300 thousand

Population in 1980 = 420 thousand

Ratio = \( \frac{420}{300} = 1.4 \)

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