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CLT (Classic Learning Test) Quantitative Reasoning Syllabus
The Quantitative Reasoning syllabus for CLT (Classic Learning Test) in full: 5 chapters, 22 topics and 47 sub-topics, every one listed below, plus 50 Quantitative Reasoning flashcards with answers.
Quantitative Reasoning syllabus: all 5 chapters
Expand any chapter to see its topics and sub-topics.
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Section Format and Test-Taking Strategy
3 topics- Structure of the Quantitative section
- Two passages or contexts with question sets
- 40 questions in 45 minutes
- No calculator permitted
- Problem-solving approach
- Mental and paper-based computation skills
- Estimation and answer-checking
- Working backward from answer choices
- Grid and word-problem interpretation
- Translating words into expressions
- Identifying what the question asks
- Structure of the Quantitative section
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Arithmetic and Number Sense
4 topics- Operations with integers and rationals
- Order of operations
- Fractions, decimals, and conversions
- Ratios, proportions, and rates
- Setting up and solving proportions
- Unit rates and scaling
- Percentages
- Percent increase and decrease
- Percent of a quantity and reverse percent
- Number properties
- Factors, multiples, primes
- Exponents and roots
- Absolute value and signed numbers
- Operations with integers and rationals
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Algebra
5 topics- Expressions and equations
- Simplifying and evaluating expressions
- Solving linear equations
- Inequalities
- Solving and graphing inequalities
- Compound inequalities
- Systems of equations
- Substitution and elimination
- Interpreting solutions
- Functions and relations
- Function notation and evaluation
- Linear functions and slope
- Polynomials and factoring
- Multiplying and factoring expressions
- Quadratic equations
- Expressions and equations
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Geometry and Measurement
5 topics- Lines, angles, and triangles
- Angle relationships
- Triangle properties and the Pythagorean theorem
- Polygons and circles
- Perimeter and area
- Circumference and arc relationships
- Coordinate geometry
- Distance and midpoint
- Slope and line equations
- Area, surface area, and volume
- Two-dimensional area formulas
- Volume of solids
- Units and measurement
- Unit conversion
- Dimensional reasoning
- Lines, angles, and triangles
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Data Analysis and Word Problems
5 topics- Interpreting data displays
- Tables, charts, and graphs
- Reading and comparing values
- Statistics
- Mean, median, mode, and range
- Basic data interpretation
- Probability and counting
- Simple probability
- Counting outcomes
- Applied and multi-step word problems
- Distance, rate, and time
- Mixture, work, and age problems
- Logical and quantitative reasoning
- Patterns and sequences
- Deductive problem-solving
- Interpreting data displays
CLT (Classic Learning Test) Quantitative Reasoning flashcards — 50 questions with answers
On the CLT, how many questions does the Quantitative Reasoning section contain and how much time is allotted?
40 questions in 45 minutes (no calculator permitted).
What four answer-choice options appear on each CLT Quantitative Reasoning question?
Four lettered choices, A through D; exactly one is correct (no guessing penalty).
What is the recommended general problem-solving approach for a CLT Quant question?
Read the full question, identify what is asked, translate words to math, choose an efficient method (algebra, estimation, or backsolving), solve, then check the answer against the question.
What does 'backsolving' (plugging in answer choices) mean and when is it useful?
Substituting each answer choice into the problem to see which satisfies the conditions; useful when choices are numeric and direct algebra is messy.
In a word problem, what do the keywords 'of', 'is', 'per', and 'more than' typically translate to?
'of' = multiply, 'is' = equals, 'per' = divide (rate), 'more than' = add.
State the order of operations (PEMDAS).
Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).
What are the rules for the sign of a product or quotient of two integers?
Same signs give a positive result; different signs give a negative result.
How do you add two fractions with different denominators?
Find a common denominator, convert each fraction, add the numerators, keep the denominator, then simplify.
How do you divide one fraction by another?
Multiply the first fraction by the reciprocal of the second (invert and multiply).
Define a ratio and explain how it relates to a proportion.
A ratio compares two quantities (a:b or a/b); a proportion is an equation stating two ratios are equal (a/b = c/d), solved by cross-multiplication.
What is the cross-multiplication rule for a/b = c/d?
ad = bc.
What is a unit rate and how is it found?
A rate with a denominator of 1 (e.g., miles per hour); found by dividing the quantity by the number of units (divide numerator by denominator).
How do you convert a percent to a decimal and to a fraction?
Divide the percent by 100 (move decimal two places left); as a fraction, write it over 100 and simplify.
What is the formula for percent change?
Percent change = (new value − old value) / old value × 100%.
How do you find a number when a percent of it is known (e.g., 30 is 20% of what)?
Divide the part by the decimal form of the percent: 30 / 0.20 = 150.
What is the difference between a factor and a multiple of a number?
A factor divides the number evenly (e.g., 3 is a factor of 12); a multiple is the number times an integer (e.g., 24 is a multiple of 12).
Define prime number and give the smallest prime.
A whole number greater than 1 with exactly two factors, 1 and itself; the smallest prime is 2 (also the only even prime).
How do you find the greatest common factor (GCF) and least common multiple (LCM) using prime factorization?
GCF = product of common prime factors at their lowest powers; LCM = product of all prime factors at their highest powers.
What does it mean for an integer to be divisible by 3, and by 9?
Divisible by 3 if the sum of its digits is divisible by 3; divisible by 9 if the digit sum is divisible by 9.
What are the rules of exponents for multiplying and dividing like bases?
x^a · x^b = x^(a+b); x^a / x^b = x^(a−b); (x^a)^b = x^(ab).
Show the other 30 Quantitative Reasoning flashcards
What does a negative exponent and a zero exponent mean?
x^(−n) = 1/x^n; x^0 = 1 (for x ≠ 0).
How do you combine like terms in an algebraic expression?
Add or subtract the coefficients of terms that have identical variable parts (same variables raised to the same powers).
What is the distributive property?
a(b + c) = ab + ac.
How do you solve a two-step linear equation such as 3x + 5 = 20?
Undo addition/subtraction first (subtract 5 → 3x = 15), then undo multiplication/division (divide by 3 → x = 5).
What key rule applies when multiplying or dividing both sides of an inequality by a negative number?
Reverse the direction of the inequality sign.
How is a compound inequality like −2 < x ≤ 5 interpreted?
x is greater than −2 and at the same time less than or equal to 5 (x lies between the two bounds).
What are the three methods for solving a system of two linear equations?
Graphing (intersection point), substitution, and elimination (adding/subtracting equations).
How many solutions does a linear system have based on its lines?
One solution if lines intersect, no solution if parallel (same slope, different intercepts), infinitely many if the lines are identical.
Define a function and the vertical line test.
A function assigns each input exactly one output; a graph represents a function if no vertical line crosses it more than once.
For f(x), what is the difference between domain and range?
Domain is the set of all allowable input (x) values; range is the set of all resulting output (y) values.
How do you evaluate a function such as f(x) = 2x + 1 at x = 3?
Substitute 3 for x: f(3) = 2(3) + 1 = 7.
What is the FOIL method for multiplying two binomials (a+b)(c+d)?
Multiply First, Outer, Inner, Last: ac + ad + bc + bd.
Factor the difference of squares a² − b².
(a + b)(a − b).
How do you factor a quadratic x² + bx + c?
Find two numbers that multiply to c and add to b; write as (x + m)(x + n).
State the relationships among complementary, supplementary, and vertical angles.
Complementary angles sum to 90°, supplementary angles sum to 180°, and vertical angles (opposite at an intersection) are equal.
What is the sum of the interior angles of any triangle, and the Triangle Inequality?
Interior angles sum to 180°; the sum of any two side lengths must exceed the third side.
State the Pythagorean theorem and what kind of triangle it applies to.
a² + b² = c², for a right triangle where c is the hypotenuse (side opposite the right angle).
What is the sum of interior angles of a polygon with n sides?
(n − 2) × 180°.
Give the formulas for the circumference and area of a circle of radius r.
Circumference = 2πr (or πd); Area = πr².
What is the slope formula given two points (x₁,y₁) and (x₂,y₂)?
slope m = (y₂ − y₁) / (x₂ − x₁) (rise over run).
What is slope-intercept form and what do its parts mean?
y = mx + b, where m is the slope and b is the y-intercept.
What are the slope relationships for parallel and perpendicular lines?
Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals (product = −1).
Give the area formulas for a rectangle, a triangle, and a parallelogram.
Rectangle = length × width; Triangle = ½ × base × height; Parallelogram = base × height.
What are the volume formulas for a rectangular prism and a cylinder?
Prism = length × width × height; Cylinder = πr²h (base area times height).
How do you convert between units using a conversion factor (e.g., feet to inches)?
Multiply by a fraction equal to 1 whose units cancel the unwanted unit and leave the desired one (e.g., ×12 in/1 ft).
What does each part of a bar graph versus a circle (pie) graph best display?
A bar graph compares amounts across categories; a pie graph shows parts of a whole as percentages of 360°.
Define mean, median, and mode.
Mean = sum of values ÷ count; median = middle value when ordered; mode = most frequently occurring value.
What is the range of a data set and how does an outlier affect the mean versus the median?
Range = greatest value − least value; an outlier strongly shifts the mean but has little effect on the median.
What is the basic probability formula for a single event?
P(event) = (number of favorable outcomes) / (total number of equally likely outcomes).
How do you find the probability of two independent events both occurring (the counting/multiplication principle)?
Multiply their individual probabilities: P(A and B) = P(A) × P(B); for counting total outcomes, multiply the number of options at each stage.
CLT (Classic Learning Test) Quantitative Reasoning FAQ
What is in the CLT (Classic Learning Test) Quantitative Reasoning syllabus?
CLT (Classic Learning Test) Quantitative Reasoning is split into 5 chapters: Section Format and Test-Taking Strategy, Arithmetic and Number Sense, Algebra, Geometry and Measurement and Data Analysis and Word Problems. Together they contain 22 topics and 47 sub-topics.
How many chapters are in CLT (Classic Learning Test) Quantitative Reasoning?
5 chapters, containing 22 topics and 47 sub-topics. The largest chapter is Algebra, with 5 topics.
Are there flashcards for CLT (Classic Learning Test) Quantitative Reasoning?
Yes — a 50-card Quantitative Reasoning deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.