NTS NAT-ICOM 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 NTS NAT-ICOM, not a summary of it.

1. 1

   Arithmetic

   8 topics

   • Number System
   • Fractions and Decimals
   • Ratio and Proportion
   • Percentage
   • Average
   • Profit and Loss
   • Simple and Compound Interest
   • Time, Speed and Distance
2. 2

   Algebra

   5 topics

   • Algebraic Expressions
   • Linear Equations
   • Quadratic Equations
   • Factorization
   • Exponents and Radicals
3. 3

   Geometry

   5 topics

   • Lines and Angles
   • Triangles
   • Quadrilaterals and Polygons
   • Circles
   • Perimeter, Area and Volume
4. 4

   Data Interpretation

   4 topics

   • Tables
   • Bar and Line Graphs
   • Pie Charts
   • Basic Statistics

Quantitative Reasoning flashcards for NTS NAT-ICOM

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

1. What are natural numbers?

   Counting numbers starting from 1: 1, 2, 3, 4, ... (excludes 0).

2. What is the difference between whole numbers and natural numbers?

   Whole numbers include 0 (0, 1, 2, 3, ...), while natural numbers start at 1.

3. Define a rational number.

   A number expressible as p/q where p and q are integers and q is not 0 (e.g. 3/4, -2, 0.5).

4. Define an irrational number and give an example.

   A number that cannot be written as a fraction of two integers; its decimal is non-terminating and non-repeating. Examples: pi, sqrt(2).

5. What is a prime number? Give the smallest one.

   A natural number greater than 1 with exactly two factors: 1 and itself. The smallest prime is 2 (and it is the only even prime).

6. What is a composite number?

   A natural number greater than 1 that has more than two factors (e.g. 4, 6, 9). Note: 1 is neither prime nor composite.

7. State the divisibility rule for 3.

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

8. State the divisibility rule for 9 and for 11.

   Divisible by 9 if the digit sum is divisible by 9. Divisible by 11 if the difference between the sum of digits in odd and even positions is 0 or a multiple of 11.

9. What is the relationship between LCM, HCF and two numbers a and b?

   LCM(a,b) x HCF(a,b) = a x b.

10. How do you convert a fraction to a decimal?

    Divide the numerator by the denominator (e.g. 3/4 = 3 divided by 4 = 0.75).

11. How do you add fractions with different denominators?

    Find the LCM of the denominators, convert each fraction to that common denominator, then add the numerators.

12. How do you divide one fraction by another?

    Multiply the first fraction by the reciprocal of the second: (a/b) / (c/d) = (a/b) x (d/c).

13. What does it mean for a fraction to be in its lowest terms?

    Numerator and denominator have no common factor other than 1 (HCF = 1), e.g. 6/8 reduces to 3/4.

14. Convert 0.25 to a fraction in lowest terms.

    0.25 = 25/100 = 1/4.

15. What is a ratio?

    A comparison of two quantities of the same kind by division, written a:b or a/b.

16. What is a proportion?

    A statement that two ratios are equal: a:b = c:d (i.e. a/b = c/d).

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

    The product of the means equals the product of the extremes: a x d = b x c.

18. In a:b = c:d, which terms are the means and which are the extremes?

    The means are b and c (inner terms); the extremes are a and d (outer terms).

19. How do you divide an amount in the ratio a:b?

    Total parts = a + b. Each share = (its part / total parts) x amount, e.g. first share = a/(a+b) x amount.

20. What is direct proportion versus 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).

21. What is the formula to convert a fraction to a percentage?

    Percentage = (fraction) x 100% (e.g. 3/5 = 3/5 x 100 = 60%).

22. How do you express x% as a fraction or decimal?

    x% = x/100 (e.g. 25% = 25/100 = 0.25).

23. What is the formula for percentage increase?

    Percentage increase = (increase / original value) x 100%.

24. What is the formula for percentage decrease?

    Percentage decrease = (decrease / original value) x 100%.

25. If a price increases by 20% then decreases by 20%, is it back to the original? Why?

    No. Successive percentage changes are not additive; net change = +20% then -20% gives a 4% overall decrease (e.g. 100 -> 120 -> 96).

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