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

1. 1

   Arithmetic

   6 topics

   • Number Systems and Operations
   • 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 Identities
   • Linear Equations
   • Quadratic Equations
   • Inequalities
   • Exponents and Radicals
3. 3

   Geometry

   5 topics

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

   Word Problems and Data Interpretation

   4 topics

   • Time, Speed and Distance
   • Time and Work
   • Age and Number Problems
   • Tables, Bar Charts and Pie Charts

Quantitative Reasoning flashcards for NTS NAT-IGS

25 of 53 cards from the Quantitative Reasoning deck — real questions with worked answers.

1. Classify real numbers into their two main subsets.

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

2. State the rules for divisibility by 3 and by 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.

3. State the divisibility rules for 4, 8, and 11.

   By 4: last two digits form a number divisible by 4. By 8: last three digits divisible by 8. By 11: the alternating sum of digits (odd-position sum minus even-position sum) is 0 or a multiple of 11.

4. What is the relationship between the HCF and LCM of two numbers a and b?

   HCF(a,b) × LCM(a,b) = a × b.

5. State the order of operations (BODMAS/PEMDAS).

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

6. Define prime and composite numbers, and state the status of 1.

   A prime has exactly two distinct factors (1 and itself); a composite has more than two factors. The number 1 is neither prime nor composite.

7. What is the prime factorization (Fundamental Theorem of Arithmetic)?

   Every integer greater than 1 can be expressed uniquely as a product of prime numbers, apart from the order of the factors.

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

   Fraction to percent: multiply by 100. Percent to decimal: divide by 100 (move the decimal point two places left).

9. How do you convert a recurring decimal like 0.\overline{36} to a fraction?

   Place the repeating block over as many 9s as there are repeating digits: 0.\overline{36} = 36/99 = 4/11.

10. What is the formula for percentage change (increase or decrease)?

    Percentage change = (New value − Old value)/Old value × 100. A positive result is an increase, a negative result a decrease.

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

    A net decrease of (x²/100)%; the original value is never fully restored.

12. How do you compare fractions with different denominators?

    Cross-multiply (a/b vs c/d: compare a×d with b×c) or convert both to a common denominator, or convert to decimals.

13. What is the percentage equivalent of the fractions 1/8, 3/8 and 5/8?

    1/8 = 12.5%, 3/8 = 37.5%, 5/8 = 62.5%.

14. Define a ratio and how it differs from a fraction.

    A ratio a:b compares two quantities of the same kind by division; it is unitless. Unlike a fraction it expresses relative size and can be extended to more than two terms (a:b:c).

15. In a proportion a:b = c:d, what is the rule of the means and extremes?

    The product of the means equals the product of the extremes: b×c = a×d (cross-multiplication).

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

    First part = T × a/(a+b); second part = T × b/(a+b).

17. Distinguish direct proportion from inverse proportion.

    Direct: as one quantity increases the other increases, so x/y is constant (y = kx). Inverse: as one increases the other decreases, so the product xy is constant (y = k/x).

18. What is the mean proportional (geometric mean) between a and b?

    The mean proportional is √(ab); it satisfies a:x = x:b.

19. State the formula for the arithmetic mean (average) of n values.

    Average = (Sum of all observations) / (Number of observations).

20. How does the average change when each item in a data set is increased by a constant k?

    The average also increases by k (likewise it scales by a factor if every item is multiplied by that factor).

21. State the alligation rule for mixing two ingredients.

    (Quantity of cheaper)/(Quantity of dearer) = (Price of dearer − Mean price)/(Mean price − Price of cheaper).

22. A vessel has milk and water in ratio a:b. What does alligation/replacement help find?

    It finds the proportion to mix two solutions to reach a target concentration, or the amount of pure liquid left after repeated replacement using milk_left = initial × (1 − replaced/total)^n.

23. What is the average speed for a journey covering equal distances at speeds x and y?

    Average speed = 2xy/(x+y) (the harmonic mean), not the simple arithmetic average.

24. Define cost price, selling price, profit and loss.

    Cost Price (CP) is the buying price; Selling Price (SP) is the selling price. If SP > CP, Profit = SP − CP; if SP < CP, Loss = CP − SP.

25. State the formulas for profit percent and loss percent.

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

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