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AFCAT (Air Force Common Admission Test) Numerical Ability Syllabus
The Numerical Ability syllabus for AFCAT (Air Force Common Admission Test) in full: 4 chapters, 16 topics and 6 sub-topics, every one listed below, plus 52 Numerical Ability flashcards with answers.
Numerical Ability syllabus: all 4 chapters
Expand any chapter to see its topics and sub-topics.
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Arithmetic Fundamentals
4 topics- Number system
- Factors, multiples, HCF and LCM
- Divisibility rules
- Decimal fractions and simplification
- Average
- Simplification and BODMAS
- Number system
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Ratio, Proportion and Percentage
4 topics- Ratio and proportion
- Percentage and applications
- Profit, loss and discount
- Partnership and mixtures (alligation)
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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
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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
AFCAT (Air Force Common Admission Test) Numerical Ability flashcards — 52 questions with answers
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.
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.
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.
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).
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.
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).
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.
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.
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.
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: (), {}, [].
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.
What is the formula for average (arithmetic mean)?
Average = (Sum of all observations) / (Number of observations). Equivalently, Sum = Average × Number of observations.
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.
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).
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).
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.
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.
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.
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.
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.
Show the other 32 Numerical Ability flashcards
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.
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.
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.
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.
What are the formulas for profit, loss, profit% and loss%?
Profit = SP − CP; Loss = CP − SP. Profit% = (Profit/CP) × 100; Loss% = (Loss/CP) × 100. Profit and loss percentages are always calculated on the cost price (CP).
How do you find Selling Price from Cost Price given a profit% or loss%?
SP = CP × (100 + Profit%)/100 for profit. SP = CP × (100 − Loss%)/100 for loss.
What is discount, and on what value is it calculated?
Discount is a reduction on the Marked Price (MP/list price). Discount = MP − SP. Discount% = (Discount/MP) × 100. SP = MP × (100 − Discount%)/100.
What is the formula for two successive discounts of d1% and d2%?
Net single equivalent discount = d1 + d2 − (d1×d2)/100. Apply discounts one after another on the reducing price.
In a partnership, how is profit shared when partners invest for different time periods?
Profit is shared in the ratio of (capital × time) for each partner. If capitals are C₁, C₂ for times t₁, t₂, profit ratio = C₁t₁ : C₂t₂. With equal time, ratio is simply of capitals.
What is the alligation (mixtures) rule for finding the ratio of two ingredients?
Quantity of cheaper / Quantity of dearer = (Price of dearer − Mean price) / (Mean price − Price of cheaper). The mean price lies between the two ingredient prices.
If a vessel contains x litres and y litres are removed and replaced with water n times, what fraction of pure liquid remains?
Remaining pure liquid = x × (1 − y/x)ⁿ. The replacement formula: final quantity of original liquid = initial × (1 − removed/total)ⁿ.
What is the formula for Simple Interest?
Simple Interest (SI) = (P × R × T) / 100, where P = principal, R = rate% per annum, T = time in years. Amount = P + SI.
In simple interest, how long does it take for a sum to double at rate R%?
Time to double = 100/R years (since SI must equal P, so P = P×R×T/100 gives T = 100/R). To triple, time = 200/R years.
What is the formula for Compound Interest (compounded annually)?
Amount A = P(1 + R/100)ᵀ. Compound Interest = A − P = P[(1 + R/100)ᵀ − 1], where P = principal, R = rate%, T = time in years.
What is the difference between CI and SI for 2 years on the same principal and rate?
Difference (CI − SI) for 2 years = P × (R/100)². This represents interest on the first year's interest.
How do you adjust the CI formula when interest is compounded half-yearly or quarterly?
Half-yearly: rate becomes R/2 and time becomes 2T, so A = P(1 + R/200)^(2T). Quarterly: A = P(1 + R/400)^(4T). Divide rate and multiply time by the compounding frequency.
What is the basic relationship between speed, distance, and time?
Speed = Distance / Time; Distance = Speed × Time; Time = Distance / Speed. Speed and time are inversely proportional for a fixed distance.
How do you convert km/hr to m/s and vice versa?
To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.
What is the formula for average speed when equal distances are covered at speeds x and y?
Average speed = 2xy/(x+y) (the harmonic mean). This is NOT the simple average (x+y)/2 unless the times are equal.
How do relative speeds work for two objects moving in the same vs opposite directions?
Opposite directions (or approaching): relative speed = sum of speeds (a + b). Same direction: relative speed = difference of speeds (a − b).
How long does a train of length L take to cross a platform of length P at speed S?
Time = (L + P)/S. To cross a pole or stationary point, time = L/S (length of train only). To cross a platform, add both lengths.
If A can do a job in x days and B in y days, how long do they take working together?
Together they take xy/(x+y) days. Reason: combined one-day work = 1/x + 1/y, so time = 1/(1/x + 1/y).
What is the relationship between the number of workers and time to complete work (with output fixed)?
Workers and time are inversely proportional: M₁D₁/W₁ = M₂D₂/W₂ (men × days / work = constant). More workers means less time.
State the three key algebraic identities for (a+b)², (a−b)², and a²−b².
(a+b)² = a² + 2ab + b²; (a−b)² = a² − 2ab + b²; a² − b² = (a+b)(a−b).
What is the identity for a³ + b³ and a³ − b³?
a³ + b³ = (a+b)(a² − ab + b²); a³ − b³ = (a−b)(a² + ab + b²). Also a³ + b³ + c³ − 3abc = (a+b+c)(a²+b²+c²−ab−bc−ca).
What is the identity for (a+b+c)²?
(a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca.
What is the standard method to solve a pair of linear equations in two variables?
Use substitution (express one variable, substitute into the other), elimination (add/subtract to cancel a variable), or cross-multiplication. A unique solution exists when a₁/a₂ ≠ b₁/b₂.
What is the quadratic formula for ax² + bx + c = 0?
x = [−b ± √(b² − 4ac)] / 2a. The term b² − 4ac is the discriminant (D).
What does the discriminant (b² − 4ac) tell you about the roots of a quadratic equation?
If D > 0: two distinct real roots. If D = 0: two equal (real) roots. If D < 0: no real roots (complex/imaginary roots).
What are the sum and product of the roots of ax² + bx + c = 0?
Sum of roots = −b/a; Product of roots = c/a. A quadratic with roots α and β is x² − (α+β)x + αβ = 0.
What are the three measures of central tendency, and how is the mode defined?
Mean (average), Median (middle value when data is ordered), and Mode (most frequently occurring value). Empirical relation: Mode = 3 × Median − 2 × Mean.
What is the basic formula for the probability of an event, and its range?
P(E) = (Number of favourable outcomes) / (Total number of possible outcomes). Probability always lies between 0 and 1 inclusive; P(certain) = 1, P(impossible) = 0. Also P(not E) = 1 − P(E).
AFCAT (Air Force Common Admission Test) Numerical Ability FAQ
What is in the AFCAT (Air Force Common Admission Test) Numerical Ability syllabus?
AFCAT (Air Force Common Admission Test) Numerical Ability is split into 4 chapters: Arithmetic Fundamentals, Ratio, Proportion and Percentage, Interest and Time-based Problems and Algebra and Data Interpretation. Together they contain 16 topics and 6 sub-topics.
How many chapters are in AFCAT (Air Force Common Admission Test) Numerical Ability?
4 chapters, containing 16 topics and 6 sub-topics. The largest chapter is Arithmetic Fundamentals, with 4 topics.
Are there flashcards for AFCAT (Air Force Common Admission Test) Numerical Ability?
Yes — a 52-card Numerical Ability deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.