COMSATS NTS-based 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 COMSATS NTS-based Test, not a summary of it.

1. 1

   Arithmetic

   5 topics

   • Number Properties
   • Ratios and Proportion
   • Percentages
   • Order of Operations (BODMAS)
   • Logarithms
2. 2

   Algebra

   5 topics

   • Linear Equations
   • Quadratic Equations
   • Algebraic Expressions and Factorization
   • Inequalities
   • Exponents and Surds
3. 3

   Geometry and Mensuration

   4 topics

   • Plane Geometry
   • Coordinate Geometry Basics
   • Area and Perimeter
   • Volume and Surface Area
4. 4

   Word Problems

   4 topics

   • Time, Speed and Distance
   • Work and Time
   • Mixtures and Allegations
   • Ages and Numbers
5. 5

   Financial Mathematics

   4 topics

   • Simple Interest
   • Compound Interest
   • Profit and Loss
   • Discount and Markup
6. 6

   Statistics and Probability

   4 topics

   • Averages and Mean
   • Median and Mode
   • Basic Probability
   • Sequences and Series

Quantitative Reasoning flashcards for COMSATS NTS-based Test

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

1. 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.)

2. 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.

3. 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.

4. 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.

5. 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.

6. 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).

7. 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).

8. 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.

9. 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).

10. 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.

11. 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).

12. What is the formula for percentage increase or decrease?

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

13. 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.)

14. 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.

15. 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.

16. 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).

17. 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.

18. 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.

19. 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.

20. 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).

21. 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).

22. 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).

23. What is the difference between common logarithm and natural logarithm?

    Common log (log) has base 10. Natural log (ln) has base e ≈ 2.718.

24. 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.

25. 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).

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