AFCAT (Air Force Common Admission Test) Numerical Ability Syllabus

Numerical Ability syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Numerical Ability in AFCAT (Air Force Common Admission Test), not a summary of it.

1. 1

   Arithmetic Fundamentals

   4 topics

   • Number system
     • Factors, multiples, HCF and LCM
     • Divisibility rules
   • Decimal fractions and simplification
   • Average
   • Simplification and BODMAS
2. 2

   Ratio, Proportion and Percentage

   4 topics

   • Ratio and proportion
   • Percentage and applications
   • Profit, loss and discount
   • Partnership and mixtures (alligation)
3. 3

   Interest and Time-based Problems

   4 topics

   • Simple interest
   • Compound interest
   • Time, speed and distance
     • Trains, boats and streams
   • Time and work
     • Pipes and cisterns
4. 4

   Algebra and Data Interpretation

   4 topics

   • Basic algebra and identities
   • Linear and quadratic equations
   • Data interpretation
     • Tables and bar graphs
     • Pie charts and line graphs
   • Probability and basic statistics

Numerical Ability flashcards for AFCAT (Air Force Common Admission Test)

24 of 52 cards from the Numerical Ability deck — real questions with worked answers.

1. What is the difference between a prime number and a composite number?

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

2. How many prime numbers are there between 1 and 100, and what is the only even prime?

   There are 25 prime numbers between 1 and 100. The only even prime number is 2.

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

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

4. What is the relationship between LCM, HCF, and the product of two numbers?

   Product of two numbers = LCM × HCF. So LCM × HCF = (first number) × (second number).

5. What is the formula for the sum of the first n natural numbers, and the sum of their squares?

   Sum of first n natural numbers = n(n+1)/2. Sum of squares = n(n+1)(2n+1)/6. Sum of cubes = [n(n+1)/2]².

6. How do you classify rational vs irrational numbers?

   A rational number can be written as p/q where p and q are integers and q ≠ 0 (terminating or recurring decimals). An irrational number cannot be expressed as p/q and has a non-terminating, non-recurring decimal (e.g., √2, π).

7. How do you convert a recurring decimal like 0.4̄5̄ (0.454545...) into a fraction?

   For purely recurring decimals, place the repeating block over as many 9s as there are repeating digits. 0.454545... = 45/99 = 5/11.

8. When comparing fractions such as 3/7 and 4/9, what is the cross-multiplication method?

   Cross-multiply: compare 3×9 = 27 with 4×7 = 28. Since 27 < 28, 3/7 < 4/9. The fraction whose numerator product is larger is the greater fraction.

9. What is the rule for placing the decimal point when multiplying two decimal numbers?

   Multiply the numbers ignoring decimals, then place the decimal point so the result has as many decimal places as the total number of decimal places in both factors combined.

10. What is the BODMAS / order of operations rule?

    BODMAS: Brackets, Of (or Orders/powers), Division, Multiplication, Addition, Subtraction. Within the same level, work left to right. Brackets are solved innermost first: (), {}, [].

11. In BODMAS, in what sequence are brackets simplified?

    Innermost first: round brackets ( ), then curly braces { }, then square brackets [ ]. The 'bar' (vinculum) is solved before all brackets.

12. What is the formula for average (arithmetic mean)?

    Average = (Sum of all observations) / (Number of observations). Equivalently, Sum = Average × Number of observations.

13. How does the average change when each number in a set is increased by a constant k?

    If every observation is increased by k, the average also increases by k. Similarly, multiplying every value by k multiplies the average by k.

14. What is the average of the first n natural numbers, and the average of first n consecutive odd numbers?

    Average of first n natural numbers = (n+1)/2. Average of the first n odd numbers (1,3,5,...) = n. Average of first n even numbers (2,4,...) = (n+1).

15. What is the formula for the combined average when two groups are merged?

    Combined average = (n₁A₁ + n₂A₂) / (n₁ + n₂), where n₁, n₂ are group sizes and A₁, A₂ are their averages (weighted average).

16. What is the difference between a ratio and a proportion?

    A ratio compares two quantities by division (a:b). A proportion is a statement that two ratios are equal (a:b = c:d). In a proportion, product of extremes = product of means, i.e., a×d = b×c.

17. In the proportion a:b = c:d, what are the mean and extreme terms, and the cross-product rule?

    a and d are the extremes; b and c are the means. The rule: product of extremes = product of means, so a×d = b×c.

18. How do you divide an amount in the ratio a:b:c among three people?

    Each share = (its ratio part / sum of ratio parts) × total amount. Shares are a/(a+b+c), b/(a+b+c), c/(a+b+c) of the total.

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

    In direct proportion, as one quantity increases the other increases (ratio constant): a/b = constant. In inverse proportion, as one increases the other decreases (product constant): a×b = constant.

20. What is the definition of percentage and how do you convert a fraction to a percentage?

    Percentage means 'per hundred.' To convert a fraction to a percentage, multiply by 100. To convert a percentage to a fraction, divide by 100.

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

    There is a net decrease of (x²/100)%. Successive equal percentage increase then decrease always results in a net loss.

22. What is the formula for successive percentage change of a% then b%?

    Net percentage change = a + b + (ab/100). Use + for increase and − for decrease in the values of a and b.

23. How do you find what percentage one number is of another?

    Required percentage = (the part / the whole) × 100. For 'A is what % of B', compute (A/B) × 100.

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

    Percentage increase = (Increase / Original value) × 100. Percentage decrease = (Decrease / Original value) × 100. The base is always the original value.

See more Numerical Ability flashcards →

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