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COMSATS NTS-based Test Quantitative Reasoning Syllabus
The Quantitative Reasoning syllabus for COMSATS NTS-based Test in full: 6 chapters and 26 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 Properties
- Ratios and Proportion
- Percentages
- Order of Operations (BODMAS)
- Logarithms
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Algebra
5 topics- Linear Equations
- Quadratic Equations
- Algebraic Expressions and Factorization
- Inequalities
- Exponents and Surds
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Geometry and Mensuration
4 topics- Plane Geometry
- Coordinate Geometry Basics
- Area and Perimeter
- Volume and Surface Area
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Word Problems
4 topics- Time, Speed and Distance
- Work and Time
- Mixtures and Allegations
- Ages and Numbers
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Financial Mathematics
4 topics- Simple Interest
- Compound Interest
- Profit and Loss
- Discount and Markup
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Statistics and Probability
4 topics- Averages and Mean
- Median and Mode
- Basic Probability
- Sequences and Series
COMSATS NTS-based Test Quantitative Reasoning flashcards — 50 questions with answers
What are the prime numbers between 1 and 20?
2, 3, 5, 7, 11, 13, 17, 19. (1 is neither prime nor composite; 2 is the only even prime.)
What is the difference between rational and irrational numbers?
A rational number can be written as a fraction p/q (q ≠ 0) and has a terminating or repeating decimal. An irrational number (e.g., √2, π) cannot be written as such a fraction and has a non-terminating, non-repeating decimal.
How do you find the LCM and HCF (GCD) of two numbers using prime factorization?
HCF = product of the lowest powers of common prime factors. LCM = product of the highest powers of all prime factors appearing in either number. Also, LCM × HCF = product of the two numbers.
What is the divisibility rule for 3, 4, and 9?
Divisible by 3: sum of digits is divisible by 3. Divisible by 9: sum of digits is divisible by 9. Divisible by 4: the last two digits form a number divisible by 4.
How do you classify integers as even or odd, and what are the parity rules for addition and multiplication?
Even = divisible by 2; odd = not. even±even=even, odd±odd=even, even±odd=odd. even×anything=even; odd×odd=odd.
What is a ratio and how is it different from a proportion?
A ratio compares two quantities (a:b = a/b). A proportion is a statement that two ratios are equal (a:b = c:d, i.e., a/b = c/d).
In a proportion a/b = c/d, what does the cross-multiplication property state?
a/b = c/d implies a·d = b·c (the product of the extremes equals the product of the means).
If a quantity is divided in the ratio a:b, what fraction of the total does each part represent?
The first part is a/(a+b) of the total and the second part is b/(a+b) of the total.
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 (y = k/x, i.e., xy = constant).
How do you find the mean (third) proportional and fourth proportional?
Mean proportional between a and b is √(ab). Fourth proportional to a, b, c (a:b = c:x) is x = (b·c)/a.
How do you convert a fraction or decimal to a percentage and vice versa?
To percent: multiply by 100 (0.25 → 25%; 1/4 → 25%). From percent: divide by 100 (40% → 0.4 = 2/5).
What is the formula for percentage increase or decrease?
Percentage change = [(New value − Old value) / Old value] × 100. Positive = increase, negative = decrease.
If a price is increased by x% and then decreased by x%, what is the net effect?
There is a net decrease of (x²/100)%. (Successive % changes are not additive.)
How do you find the original value when you know the value after a percentage change?
If final = original × (1 ± p/100), then original = final ÷ (1 ± p/100). E.g., after a 20% increase to 120, original = 120/1.20 = 100.
What is the formula for successive percentage changes of a% then b%?
Overall change = a + b + (ab/100), with each percentage taken as positive for increase and negative for decrease.
What does BODMAS (BIDMAS) stand for and in what order are operations performed?
Brackets, Orders (powers/roots), Division and Multiplication (left to right), Addition and Subtraction (left to right).
In BODMAS, how are multiplication and division (or addition and subtraction) handled when both appear?
They have equal priority and are evaluated from left to right in the order they appear, not strictly multiplication before division.
Evaluate 6 + 2 × (3² − 1) using order of operations.
Brackets/order first: 3² = 9, then 9 − 1 = 8; then 2 × 8 = 16; then 6 + 16 = 22.
What is the definition of a logarithm: log_b(x) = y means what?
log_b(x) = y means b^y = x, where b is the base (b > 0, b ≠ 1) and x > 0.
State the product, quotient, and power laws of logarithms.
log(mn) = log m + log n; log(m/n) = log m − log n; log(m^k) = k·log m (all with the same base).
Show the other 30 Quantitative Reasoning flashcards
What is the change of base formula for logarithms?
log_b(x) = log_c(x) / log_c(b), for any valid base c (commonly base 10 or base e).
What are the values of log_b(1) and log_b(b)?
log_b(1) = 0 (since b^0 = 1) and log_b(b) = 1 (since b^1 = b).
What is the difference between common logarithm and natural logarithm?
Common log (log) has base 10. Natural log (ln) has base e ≈ 2.718.
What is the general form of a linear equation in one variable and how do you solve it?
ax + b = 0 (a ≠ 0). Solve by isolating x: x = −b/a, using inverse operations on both sides.
What does the slope-intercept form y = mx + c represent?
A straight line where m is the slope (rate of change) and c is the y-intercept (value of y when x = 0).
How do you solve a system of two linear equations by elimination?
Multiply equations so one variable has matching coefficients, add or subtract to eliminate that variable, solve for the remaining one, then back-substitute.
What does it mean if a system of linear equations has no solution or infinitely many solutions?
No solution: lines are parallel (same slope, different intercepts). Infinitely many: lines are identical (coincident).
What is the standard form of a quadratic equation?
ax² + bx + c = 0, where a ≠ 0.
State the quadratic formula for solving ax² + bx + c = 0.
x = [−b ± √(b² − 4ac)] / (2a).
What is the discriminant and what does it tell you about the roots?
Discriminant D = b² − 4ac. D > 0: two distinct real roots; D = 0: one repeated real root; D < 0: two complex (no real) roots.
What are the sum and product of the roots of ax² + bx + c = 0?
Sum of roots = −b/a; product of roots = c/a.
What does it mean to solve a quadratic by factoring?
Write ax² + bx + c = 0 as (px + q)(rx + s) = 0, then set each factor to zero (zero-product property) and solve for x.
What is the difference between an expression and an equation?
An expression is a combination of terms with no equals sign (e.g., 3x + 2). An equation states two expressions are equal (e.g., 3x + 2 = 8) and can be solved.
State the identity for the difference of two squares.
a² − b² = (a + b)(a − b).
State the expansions of (a + b)² and (a − b)².
(a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b².
How do you factor a quadratic trinomial x² + bx + c?
Find two numbers whose product is c and whose sum is b; then x² + bx + c = (x + p)(x + q) where p + q = b and pq = c.
State the sum and difference of cubes factorization formulas.
a³ + b³ = (a + b)(a² − ab + b²); a³ − b³ = (a − b)(a² + ab + b²).
What happens to an inequality when you multiply or divide both sides by a negative number?
The inequality sign reverses (e.g., −2x > 6 becomes x < −3).
How do you express the solution set of a linear inequality on a number line?
Use an open circle for strict inequalities (< or >) and a closed/filled circle for inclusive ones (≤ or ≥), shading toward the satisfying values.
How do you solve a compound inequality such as a < x + b < c?
Perform the same operation on all three parts simultaneously to isolate x while keeping the inequalities aligned.
State the basic laws of exponents for multiplication, division, and power of a power.
a^m · a^n = a^(m+n); a^m / a^n = a^(m−n); (a^m)^n = a^(mn).
What do a⁰, a^(−n), and a^(1/n) equal?
a⁰ = 1 (a ≠ 0); a^(−n) = 1/a^n; a^(1/n) = ⁿ√a (the nth root of a).
What is a surd, and what does it mean to rationalize the denominator?
A surd is an irrational root that cannot be simplified to a rational number (e.g., √2, √5). Rationalizing means removing the surd from the denominator, e.g., multiply by the conjugate so the denominator becomes rational.
How do you simplify √(ab) and √(a/b)?
√(ab) = √a · √b and √(a/b) = √a / √b (for a, b ≥ 0, b ≠ 0).
What is the sum of interior angles of a triangle, and of a polygon with n sides?
Triangle: 180°. Polygon with n sides: (n − 2) × 180°.
State the Pythagorean theorem.
In a right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides: a² + b² = c² (c is the hypotenuse).
What are the area formulas for a triangle, rectangle, and circle?
Triangle = ½ × base × height; Rectangle = length × width; Circle = πr².
What is the circumference of a circle and the relationship between radius and diameter?
Circumference = 2πr = πd, where diameter d = 2r.
What is the distance formula between two points (x₁, y₁) and (x₂, y₂)?
Distance = √[(x₂ − x₁)² + (y₂ − y₁)²].
What are the midpoint and slope formulas for a line segment between (x₁, y₁) and (x₂, y₂)?
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2); Slope m = (y₂ − y₁)/(x₂ − x₁).
COMSATS NTS-based Test Quantitative Reasoning FAQ
What is in the COMSATS NTS-based Test Quantitative Reasoning syllabus?
COMSATS NTS-based Test Quantitative Reasoning is split into 6 chapters: Arithmetic, Algebra, Geometry and Mensuration, Word Problems, Financial Mathematics and Statistics and Probability. Together they contain 26 topics.
How many chapters are in COMSATS NTS-based Test Quantitative Reasoning?
6 chapters, containing 26 topics. The largest chapter is Arithmetic, with 5 topics.
Are there flashcards for COMSATS NTS-based 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.