HEC USAT 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 HEC USAT, not a summary of it.

1. 1

   Arithmetic

   5 topics

   • Number Systems and Operations
   • Fractions, Decimals and Percentages
   • Ratio and Proportion
   • Profit, Loss and Markup
   • HCF and LCM
2. 2

   Algebra and Functions

   4 topics

   • Algebraic Expressions and Identities
   • Exponents and Radicals
   • Functions and Mapping
   • Sequences and Series
3. 3

   Equations

   4 topics

   • Linear Equations
   • Quadratic Equations
   • Simultaneous Equations
   • Inequalities
4. 4

   Geometry

   4 topics

   • Lines, Angles and Triangles
   • Polygons and Circles
   • Perimeter, Area and Volume
   • Coordinate Geometry
5. 5

   Statistics and Probability

   3 topics

   • Measures of Central Tendency
   • Data Interpretation
   • Basic Probability
6. 6

   Scenario-Based and Mental Mathematics

   4 topics

   • Word Problems
   • Speed, Distance and Time
   • Work and Rate Problems
   • Estimation and Quick Calculation

Quantitative Reasoning flashcards for HEC USAT

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

1. What is a prime number, and what is the smallest/only even prime?

   A natural number greater than 1 with exactly two distinct factors: 1 and itself. The smallest prime is 2, which is also the only even prime.

2. State the order of operations (BODMAS/PEMDAS) for evaluating arithmetic expressions.

   Brackets, then Orders (exponents/roots), then Division and Multiplication (left to right), then Addition and Subtraction (left to right).

3. How do you find the place value vs. face value of a digit in a number?

   Face value is the digit itself; place value is the digit multiplied by its positional value (e.g., in 327, the 2 has face value 2 and place value 20).

4. What is the divisibility rule for 3 and for 9?

   A number is divisible by 3 if the sum of its digits is divisible by 3; divisible by 9 if the digit sum is divisible by 9.

5. What is the divisibility rule for 11?

   A number is divisible by 11 if the difference between the sum of digits in odd positions and the sum of digits in even positions is 0 or a multiple of 11.

6. Classify numbers into the main sets: natural, whole, integers, rational, irrational.

   Natural: 1,2,3...; Whole: 0,1,2...; Integers: ...-2,-1,0,1,2...; Rational: can be written as p/q (q≠0); Irrational: cannot (e.g., √2, π).

7. How do you convert a fraction to a percentage and a percentage to a fraction?

   Fraction to percent: multiply by 100 (e.g., 3/4 = 75%). Percent to fraction: divide by 100 and simplify (e.g., 40% = 40/100 = 2/5).

8. How do you convert a recurring decimal like 0.333... to a fraction?

   Set x = 0.333..., multiply to shift the repeat (10x = 3.333...), subtract (9x = 3), so x = 3/9 = 1/3.

9. To find x% of a quantity N, what is the formula?

   x% of N = (x/100) × N.

10. What is the percentage change formula?

    Percentage change = [(New value − Old value) / Old value] × 100. Positive means increase, negative means decrease.

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

    Find the LCM of the denominators, convert each fraction to that common denominator, then add the numerators (e.g., 1/3 + 1/4 = 4/12 + 3/12 = 7/12).

12. How do you divide one fraction by another?

    Multiply the first fraction by the reciprocal of the second (e.g., (2/3) ÷ (4/5) = (2/3) × (5/4) = 10/12 = 5/6).

13. What is the difference between a ratio and a proportion?

    A ratio compares two quantities (a:b). A proportion is a statement that two ratios are equal (a:b = c:d).

14. State the cross-multiplication property of a proportion a:b = c:d.

    In a proportion a/b = c/d, the product of the means equals the product of the extremes: a × d = b × c.

15. How do you divide a quantity Q in the ratio a:b?

    First part = Q × a/(a+b); second part = Q × b/(a+b).

16. What is the difference between direct and inverse proportion?

    Direct: as one quantity increases, the other increases at the same rate (y = kx). Inverse: as one increases, the other decreases (xy = k, or y = k/x).

17. What is the formula for profit and loss in terms of cost price (CP) and selling price (SP)?

    Profit = SP − CP (when SP > CP); Loss = CP − SP (when CP > SP).

18. How is profit percentage (and loss percentage) calculated?

    Profit % = (Profit / CP) × 100; Loss % = (Loss / CP) × 100. Both are always calculated on the cost price.

19. What is markup, and how does it differ from profit?

    Markup is the amount added to the cost price to set the selling/list price (Markup = List Price − CP). Profit is what remains after any discount; markup is computed before discount.

20. How do you find selling price after a discount on the marked price (MP)?

    SP = MP × (1 − discount%/100). For example, 20% off a Rs.500 item gives SP = 500 × 0.80 = Rs.400.

21. If a price is increased by x% then decreased by x%, what is the net effect?

    There is a net decrease of (x²/100)%. For example, +10% then −10% gives a net 1% loss, not 0.

22. Define HCF (GCD) and LCM.

    HCF (Highest Common Factor) is the largest number dividing all given numbers. LCM (Least Common Multiple) is the smallest number that all given numbers divide into.

23. State the relationship between HCF and LCM of two numbers a and b.

    HCF(a,b) × LCM(a,b) = a × b.

24. How do you find the HCF and LCM using prime factorization?

    HCF = product of common prime factors with their lowest powers. LCM = product of all prime factors with their highest powers.

25. State the identity for (a + b)² and (a − b)².

    (a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b².

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