AFCAT (Air Force Common Admission Test) Numerical Ability Flashcards

24 sample cards from the Numerical Ability deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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).

13. 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.

14. 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).

15. 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.

16. 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).

17. 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).

18. What is the identity for (a+b+c)²?

    (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca.

19. 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.

20. What is the quadratic formula for ax² + bx + c = 0?

    x = [−b ± √(b² − 4ac)] / 2a. The term b² − 4ac is the discriminant (D).

21. 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).

22. 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.

23. 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.

24. 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).

What this deck covers

Numerical Ability flashcards FAQ