Question 1Easier
If is an even integer and is an odd integer, which of the following must be odd?
Show answer
Answer: D —
An even integer plus an odd integer is odd, so must be odd. Each other expression contains an even factor.
Study on the flyACTMathematicsReal number system and number properties
Mathematics
Real number system and number properties — ACT practice questions
- 61 practice questions in the app
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What this topic is
Questions on Real number system and number properties test how numbers behave rather than long calculations.
Typical skills include knowing that an even number times any integer is even, that an odd number plus an odd number is even, and that numbers which are multiples of two values at once are the multiples of their least common multiple. Distance on a number line is another favorite: moving from negative two to five covers seven units, because distance is never negative.
ACT Mathematics often phrases these items as what must be true, and testing a few small numbers, including negatives and zero, quickly rules out choices that only work sometimes.
Sample questions
Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.
Question 2Mid
A museum tour offered a free map to every 16th guest and a free pin to every 24th guest. Given that 960 guests entered during the day, how many guests received both a free map and a free pin?
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Answer: B — 20
. Then .
Question 3Easier
A cart starts at on a number line, moves to 8, and then moves to . What total distance does the cart travel?
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Answer: D — 25
The two distances are and . Therefore, the total distance is .
Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.
Practice 61 Real number system and number properties questions in the app
More ACT topics
Mathematics
- Integer and rational exponents
- Radicals and roots
- Complex numbers
- Vectors and matrices
- Fractions, decimals, and operations
- Percents and percent change
- Ratios, rates, and proportional relationships
- Linear equations and expressions in one variable
- Inequalities (linear and compound)
- Systems of equations
- Polynomial expressions and factoring
- Quadratic equations
- Radical and rational equations
- Exponential relationships
- Function notation and evaluating functions
- Linear functions and graphs
- Quadratic and polynomial functions
- Radical and rational functions
- Piecewise functions
- Exponential and logarithmic functions
- Key features and transformations of graphs
- Lines, angles, and polygons
- Triangles — congruence, similarity, Pythagorean theorem
- Circles — arcs, sectors, angles, equations
- Surface area and volume of solids
- Coordinate geometry — distance, midpoint, slope, line equations
- Conic sections
- Right-triangle trigonometry and trig functions
- Measures of center and spread
- Data collection methods and study design
- Bivariate data and relationships (scatterplots, correlation)
- Probability and sample spaces
- Counting, combinations, and permutations
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