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

1. 1

   Arithmetic

   6 topics

   • Number Systems
   • Fractions and Decimals
   • Ratio and Proportion
   • Percentages
   • Profit and Loss
   • Average
2. 2

   Algebra

   4 topics

   • Linear Equations
   • Algebraic Expressions
   • Exponents and Roots
   • Sequences and Series
3. 3

   Geometry

   5 topics

   • Lines and Angles
   • Triangles and Polygons
   • Circles
   • Area and Perimeter
   • Coordinate Geometry
4. 4

   Word Problems

   4 topics

   • Time, Speed and Distance
   • Time and Work
   • Ages
   • Mixtures and Alligation
5. 5

   Data Interpretation

   3 topics

   • Tables
   • Bar and Line Graphs
   • Pie Charts
6. 6

   Basic Statistics

   3 topics

   • Mean, Median and Mode
   • Probability
   • Permutations and Combinations

Quantitative Reasoning flashcards for NTS NAT-IA

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

1. What is a rational number?

   A number that can be expressed as a fraction p/q where p and q are integers and q is not zero (e.g., 1/2, -3, 0.75).

2. What is an irrational number? Give an example.

   A number that cannot be written as a ratio of two integers; its decimal is non-terminating and non-repeating. Examples: pi, square root of 2, e.

3. Define a prime number and give the only even prime.

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

4. What are composite numbers?

   Natural numbers greater than 1 that have more than two factors (i.e., divisible by a number other than 1 and itself), e.g., 4, 6, 9.

5. State 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.

6. State the divisibility rule for 4 and for 8.

   Divisible by 4 if the last two digits form a number divisible by 4; divisible by 8 if the last three digits form a number divisible by 8.

7. How are HCF (GCD) and LCM of two numbers related?

   For two numbers a and b: HCF x LCM = a x b.

8. What is the difference between a terminating and a recurring (repeating) decimal?

   A terminating decimal ends after a finite number of digits (e.g., 0.25); a recurring decimal has one or more digits repeating infinitely (e.g., 0.333...).

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

   Divide the numerator by the denominator using long division.

10. How do you add or subtract two fractions with different denominators?

    Find the LCM of the denominators, convert each fraction to an equivalent fraction with that common denominator, then add or subtract the numerators.

11. How do you divide one fraction by another?

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

12. What is a proper fraction versus an improper fraction?

    A proper fraction has numerator less than denominator (value < 1); an improper fraction has numerator greater than or equal to denominator (value >= 1).

13. How do you compare two fractions a/b and c/d?

    Cross-multiply: compare a x d with b x c. If a x d > b x c then a/b > c/d (for positive denominators).

14. What is a ratio and how is it written?

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

15. What is a proportion?

    A statement that two ratios are equal, written a:b = c:d (or a/b = c/d).

16. State the rule of cross-multiplication in a proportion a:b = c:d.

    The product of the means equals the product of the extremes: b x c = a x d (i.e., a x d = b x c).

17. What is direct proportion?

    A relationship where two quantities increase or decrease together so their ratio stays constant: y = kx (y/x is constant).

18. What is inverse proportion?

    A relationship where one quantity increases as the other decreases, keeping their product constant: xy = k.

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

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

20. How do you convert a fraction or decimal to a percentage?

    Multiply by 100 and add the percent sign (e.g., 0.25 = 0.25 x 100 = 25%).

21. How do you find x% of a number N?

    Compute (x/100) x N.

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

    Percentage change = (change in value / original value) x 100, where change = new value minus original value.

23. If a value increases by p% then decreases by p%, what is the net effect?

    There is a net decrease of (p^2/100)% from the original value.

24. Define Cost Price (CP) and Selling Price (SP).

    Cost Price is the price at which an item is bought; Selling Price is the price at which it is sold.

25. State the formulas for profit and loss.

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

See more Quantitative Reasoning flashcards →

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