CLT (Classic Learning Test) Quantitative Reasoning Syllabus

Quantitative Reasoning syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Reasoning in CLT (Classic Learning Test), not a summary of it.

1. 1

   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
2. 2

   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
3. 3

   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
4. 4

   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
5. 5

   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

Quantitative Reasoning flashcards for CLT (Classic Learning Test)

25 of 50 cards from the Quantitative Reasoning deck — real questions with worked answers.

1. 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).

2. 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).

3. 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.

4. 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.

5. 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.

6. State the order of operations (PEMDAS).

   Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

7. 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.

8. How do you add two fractions with different denominators?

   Find a common denominator, convert each fraction, add the numerators, keep the denominator, then simplify.

9. How do you divide one fraction by another?

   Multiply the first fraction by the reciprocal of the second (invert and multiply).

10. 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.

11. What is the cross-multiplication rule for a/b = c/d?

    ad = bc.

12. 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).

13. 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.

14. What is the formula for percent change?

    Percent change = (new value − old value) / old value × 100%.

15. 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.

16. 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).

17. 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).

18. 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.

19. 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.

20. 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).

21. What does a negative exponent and a zero exponent mean?

    x^(−n) = 1/x^n; x^0 = 1 (for x ≠ 0).

22. 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).

23. What is the distributive property?

    a(b + c) = ab + ac.

24. 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).

25. What key rule applies when multiplying or dividing both sides of an inequality by a negative number?

    Reverse the direction of the inequality sign.

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