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HEC USAT Quantitative Reasoning Syllabus
The Quantitative Reasoning syllabus for HEC USAT in full: 6 chapters and 24 topics, every one listed below, plus 50 Quantitative Reasoning flashcards with answers.
Quantitative Reasoning syllabus: all 6 chapters
Expand any chapter to see its topics and sub-topics.
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Arithmetic
5 topics- Number Systems and Operations
- Fractions, Decimals and Percentages
- Ratio and Proportion
- Profit, Loss and Markup
- HCF and LCM
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Algebra and Functions
4 topics- Algebraic Expressions and Identities
- Exponents and Radicals
- Functions and Mapping
- Sequences and Series
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Equations
4 topics- Linear Equations
- Quadratic Equations
- Simultaneous Equations
- Inequalities
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Geometry
4 topics- Lines, Angles and Triangles
- Polygons and Circles
- Perimeter, Area and Volume
- Coordinate Geometry
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Statistics and Probability
3 topics- Measures of Central Tendency
- Data Interpretation
- Basic Probability
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Scenario-Based and Mental Mathematics
4 topics- Word Problems
- Speed, Distance and Time
- Work and Rate Problems
- Estimation and Quick Calculation
HEC USAT Quantitative Reasoning flashcards — 50 questions with answers
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.
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).
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).
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.
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.
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).
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).
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.
To find x% of a quantity N, what is the formula?
x% of N = (x/100) × N.
What is the percentage change formula?
Percentage change = [(New value − Old value) / Old value] × 100. Positive means increase, negative means decrease.
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).
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).
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).
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.
How do you divide a quantity Q in the ratio a:b?
First part = Q × a/(a+b); second part = Q × b/(a+b).
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).
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).
How is profit percentage (and loss percentage) calculated?
Profit % = (Profit / CP) × 100; Loss % = (Loss / CP) × 100. Both are always calculated on the cost price.
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.
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.
Show the other 30 Quantitative Reasoning flashcards
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.
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.
State the relationship between HCF and LCM of two numbers a and b.
HCF(a,b) × LCM(a,b) = a × b.
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.
State the identity for (a + b)² and (a − b)².
(a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b².
State the difference of squares and the identity for (a + b)(a − b).
a² − b² = (a + b)(a − b).
State the identities for (a + b)³ and a³ + b³.
(a + b)³ = a³ + 3a²b + 3ab² + b³; a³ + b³ = (a + b)(a² − ab + b²).
State the identity for a³ − b³.
a³ − b³ = (a − b)(a² + ab + b²).
What is the expansion of (a + b + c)²?
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.
State the product laws of exponents: a^m × a^n and (a^m)^n.
a^m × a^n = a^(m+n); (a^m)^n = a^(mn).
What are the rules for a^m ÷ a^n, a^0, and a^(−n)?
a^m ÷ a^n = a^(m−n); a^0 = 1 (a≠0); a^(−n) = 1/a^n.
How is a fractional exponent a^(m/n) expressed as a radical?
a^(m/n) = n-th root of a^m = (ⁿ√a)^m.
How do you rationalize a denominator of the form 1/(√a)?
Multiply numerator and denominator by √a: 1/√a = √a/a. For 1/(a+√b), multiply by the conjugate (a−√b).
Simplify √a × √b and √(a/b).
√a × √b = √(ab); √(a/b) = √a / √b (for a,b ≥ 0, b≠0).
What is a function, and what are its domain and range?
A function maps each input from the domain to exactly one output. Domain = set of allowed inputs; Range = set of actual outputs produced.
What is the vertical line test for a function?
A graph represents a function if and only if no vertical line intersects it at more than one point (each x-value has only one y-value).
Distinguish one-to-one (injective), onto (surjective), and bijective functions.
Injective: distinct inputs give distinct outputs. Surjective: every element of the codomain is an output. Bijective: both injective and surjective (a one-to-one correspondence).
What is the composition of functions (f ∘ g)(x)?
(f ∘ g)(x) = f(g(x)): apply g first, then apply f to the result.
What is the nth term formula of an arithmetic progression (AP)?
aₙ = a + (n − 1)d, where a is the first term and d is the common difference.
What is the sum of the first n terms of an arithmetic progression?
Sₙ = (n/2)[2a + (n − 1)d] = (n/2)(a + l), where l is the last term.
What is the nth term of a geometric progression (GP)?
aₙ = a·r^(n−1), where a is the first term and r is the common ratio.
What is the sum of n terms of a GP, and the sum to infinity?
Sₙ = a(rⁿ − 1)/(r − 1) for r≠1. Sum to infinity S∞ = a/(1 − r) when |r| < 1.
How do you find the arithmetic mean and geometric mean of two numbers a and b?
Arithmetic mean = (a + b)/2; Geometric mean = √(ab).
What is the general form and solution of a linear equation in one variable ax + b = 0?
It is degree-one in x. Solution: x = −b/a (a ≠ 0).
What does the slope-intercept form y = mx + c tell you about a line?
m is the slope (rate of change), and c is the y-intercept (where the line crosses the y-axis).
What is the slope of the line through points (x₁,y₁) and (x₂,y₂)?
Slope m = (y₂ − y₁)/(x₂ − x₁).
State the standard form and the quadratic formula for ax² + bx + c = 0.
Standard form: ax² + bx + c = 0 (a≠0). Quadratic formula: x = [−b ± √(b² − 4ac)] / (2a).
What does the discriminant b² − 4ac reveal about the roots of a quadratic?
If > 0: two distinct real roots; if = 0: one repeated real root; if < 0: no real roots (two complex roots).
For ax² + bx + c = 0, what are the sum and product of the roots?
Sum of roots = −b/a; Product of roots = c/a.
What are the methods to solve a pair of simultaneous linear equations, and what does the solution represent?
Substitution, elimination, and graphical methods (also matrix/Cramer's rule). The solution is the point of intersection of the two lines; parallel lines mean no solution, identical lines mean infinitely many.
HEC USAT Quantitative Reasoning FAQ
What is in the HEC USAT Quantitative Reasoning syllabus?
HEC USAT Quantitative Reasoning is split into 6 chapters: Arithmetic, Algebra and Functions, Equations, Geometry, Statistics and Probability and Scenario-Based and Mental Mathematics. Together they contain 24 topics.
How many chapters are in HEC USAT Quantitative Reasoning?
6 chapters, containing 24 topics. The largest chapter is Arithmetic, with 5 topics.
Are there flashcards for HEC USAT 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.