CAT Quantitative Aptitude: Arithmetic Flashcards

24 sample cards from the Quantitative Aptitude: Arithmetic deck

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

1. How does the compound interest formula change for half-yearly and quarterly compounding?

   Half-yearly: A = P(1 + R/200)^(2T). Quarterly: A = P(1 + R/400)^(4T). Rate is divided and time multiplied by the number of compounding periods per year.

2. What is the difference between CI and SI for 2 years on principal P at rate R%?

   CI - SI (2 years) = P(R/100)². For 3 years, the difference = P(R/100)²·(3 + R/100).

3. In partnership, how are profits shared when capitals are invested for different durations?

   Profit is divided in the ratio of (Capital × Time) for each partner. Equal time means profit ratio equals capital ratio.

4. What is the difference between a working (active) partner and a sleeping partner?

   A working partner manages the business and may receive a salary/commission before profit division; a sleeping partner only invests capital and shares profit per the capital-time ratio.

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

   A ratio compares two quantities (a:b). A proportion states two ratios are equal (a:b = c:d, i.e., a/b = c/d). In a proportion, product of means = product of extremes (bc = ad).

6. What are the third, fourth, and mean proportionals?

   Fourth proportional to a, b, c is x where a:b = c:x. Third proportional to a, b is x where a:b = b:x. Mean proportional between a and b is √(ab).

7. How do you combine ratios a:b and b:c, and what is a:b:c?

   If a:b and b:c are given with a common term b, write directly as a:b:c. If b differs, scale to make the common terms equal (e.g., a:b = 2:3, b:c = 4:5 → a:b:c = 8:12:15).

8. What is the difference between direct and inverse variation?

   Direct variation: y = kx (y increases as x increases; y/x constant). Inverse variation: y = k/x (y decreases as x increases; xy constant).

9. What is joint variation? Give the general form.

   Joint variation means a quantity varies with two or more variables. E.g., z varies jointly as x and y means z = kxy. Combined direct/inverse: z = k·x/y.

10. State the rule of alligation (the alligation formula).

    (Cheaper quantity)/(Dearer quantity) = (Dearer price - Mean price)/(Mean price - Cheaper price). It gives the ratio in which two ingredients are mixed to get a desired mean value.

11. A vessel has x litres of pure liquid; y is drawn out and replaced with water, repeated n times. What fraction of pure liquid remains?

    Remaining pure liquid = x · (1 - y/x)^n = x · ((x - y)/x)^n. This is the repeated-replacement formula.

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

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

13. What is a weighted average and its formula?

    Weighted average = (w₁x₁ + w₂x₂ + ... + wₙxₙ)/(w₁ + w₂ + ... + wₙ), where each value xᵢ has weight wᵢ. Used when groups differ in size or importance.

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

    First n natural numbers: (n+1)/2. First n odd numbers: average = n (sum = n²). First n even numbers: average = n+1.

15. How does adding/removing a member change an average? (effect on average)

    If a new value equals the current average, the average is unchanged. New average shifts toward the new value; net change in sum = (new value - old average) when adding one item.

16. What is the basic relationship between speed, distance, and time, including unit conversion?

    Speed = Distance/Time. To convert km/hr to m/s, multiply by 5/18; to convert m/s to km/hr, multiply by 18/5.

17. What is the average speed for a round trip covering equal distances at speeds x and y?

    Average speed = 2xy/(x + y), the harmonic mean of the two speeds. (Not the simple average, since equal distances are covered.)

18. What is relative speed for objects moving in the same direction versus opposite directions?

    Same direction: relative speed = difference of speeds (|u - v|). Opposite directions: relative speed = sum of speeds (u + v).

19. How long does a train of length L take to cross a stationary pole versus a platform of length P?

    Crossing a pole: time = L/speed (only train length matters). Crossing a platform: time = (L + P)/speed (sum of train and platform lengths).

20. In boats and streams, what are downstream and upstream speeds?

    If boat speed in still water = b and stream speed = s: Downstream speed = b + s; Upstream speed = b - s. Then b = (down + up)/2 and s = (down - up)/2.

21. What is a 'start' and a 'dead heat' in races?

    A start (e.g., 'A gives B a 20 m start') means B begins 20 m ahead, so A runs the full distance while B runs less. A dead heat is a race that ends in a tie (both finish together).

22. On a circular track of length L, when do two runners (speeds u, v) first meet at the starting point?

    First meeting at the START point = LCM of (L/u) and (L/v), their individual lap times. (First meeting anywhere uses L/relative speed.)

23. What is the core formula relating work, rate, and time, and how do combined rates work?

    If A does a job in 'a' days, A's rate = 1/a per day. Working together, rates add: combined time = 1/(1/a + 1/b) = ab/(a+b) for two workers.

24. State the chain rule for the relationship between persons (M), days (D), hours (H), and work (W).

    (M₁ × D₁ × H₁)/W₁ = (M₂ × D₂ × H₂)/W₂. This relates two work scenarios with differing manpower, days, hours, and amount of work.

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Quantitative Aptitude: Arithmetic flashcards FAQ