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

1. 1

   Arithmetic

   7 topics

   • Number Systems and Properties
   • Fractions, Decimals and Percentages
   • Ratio and Proportion
   • Averages
   • Profit, Loss and Discount
   • Simple and Compound Interest
   • Time, Speed and Distance
2. 2

   Algebra

   4 topics

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

   Geometry

   5 topics

   • Lines and Angles
   • Triangles and Polygons
   • Circles
   • Area, Perimeter and Volume
   • Coordinate Geometry

Quantitative Reasoning flashcards for NTS NAT-IE

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

1. What are the main categories of real numbers based on whether they can be written as a fraction p/q?

   Rational numbers (expressible as p/q with integers p, q and q≠0, including terminating and repeating decimals) and irrational numbers (non-terminating, non-repeating decimals such as √2 and π).

2. Define prime numbers and composite numbers.

   A prime number has exactly two distinct positive factors: 1 and itself (e.g., 2, 3, 5, 7). A composite number has more than two factors (e.g., 4, 6, 8, 9). The number 1 is neither prime nor composite.

3. What is the only even prime number, and why?

   2 is the only even prime, because every other even number is divisible by 2 and therefore has more than two factors.

4. State the divisibility rules for 3 and 9.

   A number is divisible by 3 if the sum of its digits is divisible by 3; it is divisible by 9 if the sum of its digits is divisible by 9.

5. What is the relationship between HCF (GCD) and LCM of two numbers a and b?

   HCF(a, b) × LCM(a, b) = a × b. So the product of two numbers equals the product of their HCF and LCM.

6. List the order of operations (BODMAS/PEMDAS) for evaluating an expression.

   Brackets/Parentheses, Orders/Exponents (powers and roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

7. How do you convert a fraction to a percentage, and a percentage to a fraction?

   Fraction → percentage: multiply the fraction by 100 (e.g., 3/4 = 75%). Percentage → fraction: write over 100 and simplify (e.g., 40% = 40/100 = 2/5).

8. How do you convert a percentage to a decimal and a decimal to a percentage?

   Percentage → decimal: divide by 100 / move the decimal point two places left (25% = 0.25). Decimal → percentage: multiply by 100 / move two places right (0.6 = 60%).

9. What is the formula for percentage increase and percentage decrease?

   Percentage change = (change ÷ original value) × 100. Increase uses (new − old); decrease uses (old − new), each divided by the original value.

10. If a quantity increases by x% and then decreases by x%, what is the net percentage change?

    There is a net decrease of (x²/100)%. The final value is less than the original because the decrease is applied to a larger base.

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

    Find a common denominator (the LCM of the denominators), convert each fraction to an equivalent fraction with that denominator, then add or subtract 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) × (d/c) = ad/bc.

13. 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, or a/b = c/d).

14. State the cross-multiplication property for the proportion a/b = c/d.

    a/b = c/d implies a×d = b×c (the product of the means equals the product of the extremes).

15. In direct vs. inverse proportion, how do the quantities behave?

    Direct proportion: as one quantity increases, the other increases at the same rate (y = kx). Inverse proportion: as one increases, the other decreases (xy = k, or y = k/x).

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

    Total parts = a + b. Each share = (its ratio term ÷ total parts) × the quantity. So the shares are a/(a+b) and b/(a+b) of the total.

17. What is the formula for the arithmetic mean (average) of n values?

    Average = (sum of all values) ÷ (number of values). Equivalently, Sum = Average × number of values.

18. If the average of n numbers is A and a new number x is added, how does the average change?

    New average = (nA + x) ÷ (n + 1). The average rises if x is above the old average and falls if x is below it.

19. What is the average of the first n natural numbers?

    (n + 1) ÷ 2. This follows because their sum is n(n+1)/2, divided by n.

20. What is the formula for the weighted average of values with weights w₁, w₂, ...?

    Weighted average = (w₁x₁ + w₂x₂ + ... + wₙxₙ) ÷ (w₁ + w₂ + ... + wₙ).

21. Define Cost Price (CP), Selling Price (SP), Profit and Loss.

    CP is the price at which an item is bought; SP is the price at which it is sold. Profit = SP − CP (when SP > CP); Loss = CP − SP (when CP > SP).

22. What are the formulas for Profit% and Loss%?

    Profit% = (Profit ÷ CP) × 100; Loss% = (Loss ÷ CP) × 100. Both percentages are always calculated on the Cost Price.

23. How do you find SP from CP given a profit or loss percentage?

    SP = CP × (100 + Profit%)/100 for a profit; SP = CP × (100 − Loss%)/100 for a loss.

24. What is the formula for discount and the relationship between Marked Price, Discount and Selling Price?

    Discount = Marked Price × Discount%/100, and Selling Price = Marked Price − Discount. Discount is always calculated on the Marked (list) Price.

25. State the simple interest formula and the total amount formula.

    Simple Interest (SI) = (P × R × T) ÷ 100, where P = principal, R = rate per year, T = time in years. Amount A = P + SI.

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