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

1. 1

   Arithmetic

   6 topics

   • Number Systems and Properties
   • Fractions, Decimals and Percentages
   • Ratio and Proportion
   • Average, Mixtures and Alligation
   • Profit, Loss and Discount
   • Simple and Compound Interest
2. 2

   Algebra

   5 topics

   • Algebraic Expressions and Simplification
   • Linear Equations
   • Quadratic Equations
   • Exponents and Radicals
   • Inequalities
3. 3

   Geometry

   5 topics

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

   Data Interpretation

   3 topics

   • Tables and Charts
   • Bar Graphs and Pie Charts
   • Basic Statistics
5. 5

   Word Problems

   3 topics

   • Time, Speed and Distance
   • Time and Work
   • Age and Number Problems

Quantitative Reasoning flashcards for NTS NAT-IM

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

1. What is the difference between rational and irrational numbers?

   A rational number can be expressed as p/q where p and q are integers and q≠0 (e.g., 1/2, 0.75, 4). An irrational number cannot be written as a ratio of integers and has a non-terminating, non-repeating decimal (e.g., √2, π).

2. What is a prime number, and what is the only even prime?

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

3. State the divisibility rules for 3, 9, and 11.

   Divisible by 3: sum of digits is divisible by 3. Divisible by 9: sum of digits is divisible by 9. Divisible by 11: the difference between the sum of digits in odd positions and even positions is 0 or divisible by 11.

4. How are LCM and HCF (GCD) of two numbers related to the numbers themselves?

   For any two numbers, LCM × HCF = product of the two numbers. So LCM(a,b) × HCF(a,b) = a × b.

5. What are the results of: (any number)⁰, division by zero, and multiplication by zero?

   Any nonzero number raised to power 0 = 1. Division by zero is undefined. Any number multiplied by 0 = 0.

6. Classify numbers: what are whole numbers, natural numbers, and integers?

   Natural numbers: counting numbers 1, 2, 3, … . Whole numbers: natural numbers including 0 (0, 1, 2, …). Integers: whole numbers plus their negatives (…, -2, -1, 0, 1, 2, …).

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

   Fraction to percent: multiply the fraction by 100 (e.g., 3/4 × 100 = 75%). Percent to decimal: divide by 100 (e.g., 75% = 0.75).

8. How do you convert a recurring decimal like 0.333... into a fraction?

   Let x = 0.333..., multiply to align repeating part (10x = 3.333...), subtract (10x - x = 3), so 9x = 3 and x = 1/3.

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) over the original value.

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

    There is a net decrease of (x²/100)%. For example, +10% then −10% gives a net change of −1%.

11. What does the fraction bar represent, and how do you add fractions with different denominators?

    The fraction bar represents division. To add fractions with different denominators, find a common denominator (the LCM), convert each fraction, then add the numerators and keep the common denominator.

12. What is a ratio, and how does it differ from a proportion?

    A ratio compares two quantities of the same kind (a:b = a/b). A proportion is a statement that two ratios are equal (a:b = c:d, i.e., a/b = c/d).

13. In the proportion a:b = c:d, what is the cross-multiplication property?

    In a/b = c/d, the cross products are equal: a × d = b × c. The terms a and d are the extremes; b and c are the means.

14. What is the difference between direct and inverse proportion?

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

15. How do you divide a quantity in a given ratio a:b:c?

    Add the ratio parts to get the total (a+b+c), then each share = (its part ÷ total) × whole quantity. E.g., share of 'a' = a/(a+b+c) × total.

16. What is the formula for the average (arithmetic mean) of n numbers?

    Average = (Sum of all values) ÷ (Number of values). Conversely, Sum = Average × Number of values.

17. What is the average of the first n consecutive natural numbers?

    The average of the first n natural numbers is (n+1)/2. (Sum = n(n+1)/2, divided by n.)

18. State the alligation rule for mixing two ingredients.

    Alligation: (Quantity of cheaper) ÷ (Quantity of dearer) = (Price of dearer − Mean price) ÷ (Mean price − Price of cheaper). The cheaper and dearer quantities are in inverse ratio to their distances from the mean.

19. If two quantities are mixed, how do you find the mean value of the mixture?

    Mean value = (Total value of all components) ÷ (Total quantity). For two parts: (q₁v₁ + q₂v₂) ÷ (q₁ + q₂).

20. How does the average change when a new value is added that is above the current average?

    The average increases. The amount of increase equals the excess of the new value over the old average, distributed across the new total count of values.

21. Define cost price (CP), selling price (SP), profit, and loss.

    Cost price (CP): price at which an item is bought. Selling price (SP): 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 percent and loss percent?

    Profit% = (Profit ÷ CP) × 100. Loss% = (Loss ÷ CP) × 100. Both percentages are always calculated on the cost price.

23. How do you find selling price from cost price and profit percent?

    SP = CP × (100 + Profit%)/100. For a loss, SP = CP × (100 − Loss%)/100.

24. What is discount, and on what amount is it calculated?

    Discount is a reduction from the marked price (list price). It is calculated as a percentage of the marked price: Discount = Marked Price × Discount%/100, and SP = Marked Price − Discount.

25. How do you calculate marked price when an item is sold at a discount with a desired profit?

    First find SP = CP × (100 + Profit%)/100, then Marked Price = SP ÷ (100 − Discount%)/100, i.e., MP = SP × 100/(100 − Discount%).

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