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CAT (Common Admission Test) Quantitative Aptitude (QA) - Arithmetic Syllabus

The Quantitative Aptitude (QA) - Arithmetic syllabus for CAT (Common Admission Test) in full: 5 chapters, 19 topics and 41 sub-topics, every one listed below, plus 50 Quantitative Aptitude (QA) - Arithmetic flashcards with answers.

5Chapters
19Topics
41Sub-topics
50Flashcards

Quantitative Aptitude (QA) - Arithmetic syllabus: all 5 chapters

Expand any chapter to see its topics and sub-topics.

  1. Number System

     6 topics
    • Classification and Properties of Numbers
      • Natural, whole, integer, rational and irrational numbers
      • Prime, composite and co-prime numbers
      • Even, odd and perfect numbers
    • Factors and Multiples
      • Number of factors and sum of factors
      • Product of factors
      • Number of ways of expressing as product of two factors
    • HCF and LCM
      • HCF/LCM of integers and fractions
      • Application-based remainder problems
    • Divisibility Rules and Factorials
      • Divisibility tests for 7, 11, 13 and composite divisors
      • Highest power of a prime in a factorial (Legendre's formula)
      • Trailing zeroes in a factorial
    • Remainders
      • Cyclicity of unit digits
      • Fermat's, Euler's and Wilson's theorems
      • Chinese Remainder Theorem and negative remainders
    • Base Systems
      • Conversion between bases
      • Arithmetic operations in non-decimal bases

  2. Percentages, Profit and Loss

     3 topics
    • Percentage Fundamentals
      • Percentage change and successive percentage change
      • Fraction-to-percentage conversions for fast calculation
    • Profit, Loss and Discount
      • Cost price, marked price and selling price relationships
      • Successive and equivalent discounts
      • Faulty weights and dishonest dealers
    • Simple and Compound Interest
      • Difference between SI and CI
      • Compounding frequency and effective rate
      • Instalments and present value

  3. Ratio, Proportion and Variation

     4 topics
    • Ratio and Proportion
      • Componendo, dividendo and properties of ratios
      • Continued proportion and mean proportional
    • Variation
      • Direct, inverse and joint variation
    • Partnership
      • Profit sharing with varying capital and time
    • Mixtures and Alligation
      • Rule of alligation
      • Repeated replacement and removal of liquid

  4. Averages and Statistics

     3 topics
    • Averages
      • Weighted average
      • Effect of adding or removing observations
    • Measures of Central Tendency
      • Mean, median and mode
    • Dispersion
      • Range, mean deviation, variance and standard deviation

  5. Time, Speed, Distance and Work

     3 topics
    • Time, Speed and Distance
      • Average speed and relative speed
      • Trains, boats and streams
    • Races and Circular Tracks
      • Head starts and dead heats
      • Meeting points on circular tracks
    • Time and Work
      • Work equivalence and efficiency
      • Pipes and cisterns
      • Work and wages

CAT (Common Admission Test) Quantitative Aptitude (QA) - Arithmetic flashcards — 50 questions with answers

  1. What is a prime number, and which is the only even prime number?

    A prime number is a natural number greater than 1 that has exactly two distinct factors: 1 and itself. 2 is the only even prime number.

  2. How many prime numbers are there between 1 and 100?

    There are 25 prime numbers between 1 and 100.

  3. What are co-prime (relatively prime) numbers?

    Two numbers are co-prime if their HCF (highest common factor) is 1. They share no common factor other than 1 (e.g., 8 and 15). They need not be prime themselves.

  4. How do you find the number of factors of a number N = p^a x q^b x r^c (prime factorization)?

    Number of factors = (a+1)(b+1)(c+1), i.e., the product of (each exponent + 1).

  5. What is the formula for the sum of all factors of N = p^a x q^b?

    Sum of factors = [(p^(a+1) - 1)/(p-1)] x [(q^(b+1) - 1)/(q-1)].

  6. How do you find the number of ways to express N as a product of two factors?

    If N is not a perfect square: (number of factors)/2. If N is a perfect square: (number of factors + 1)/2.

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

    HCF(a,b) x LCM(a,b) = a x b. (This holds only for two numbers.)

  8. How do you find the HCF and LCM of fractions?

    HCF of fractions = HCF(numerators)/LCM(denominators). LCM of fractions = LCM(numerators)/HCF(denominators).

  9. What is the divisibility rule for 8 and for 11?

    Divisible by 8: last three digits form a number divisible by 8. Divisible by 11: the difference between the sum of digits at odd places and even places is 0 or a multiple of 11.

  10. How do you find the highest power of a prime p that divides n! (number of trailing zeros relation)?

    Highest power of p in n! = [n/p] + [n/p^2] + [n/p^3] + ... (floor of each), summed until terms become 0. Number of trailing zeros in n! = highest power of 5 in n!.

  11. How many trailing zeros does 100! have?

    Highest power of 5 = [100/5] + [100/25] = 20 + 4 = 24. So 100! has 24 trailing zeros.

  12. State the Remainder Theorem (Chinese Remainder approach) basic idea and Fermat's Little Theorem.

    Fermat's Little Theorem: if p is prime and a is not divisible by p, then a^(p-1) ≡ 1 (mod p). Useful for finding remainders of large powers.

  13. What is Wilson's Theorem?

    Wilson's Theorem: for a prime p, (p-1)! ≡ -1 (mod p), i.e., (p-1)! + 1 is divisible by p.

  14. What is the cyclicity of the units digit of powers of 2, 3, 7, and 8?

    All have a cyclicity of 4. 2: 2,4,8,6; 3: 3,9,7,1; 7: 7,9,3,1; 8: 8,4,2,6. (Digits 0,1,5,6 have cyclicity 1; 4 and 9 have cyclicity 2.)

  15. How do you convert a number from base b to base 10?

    Multiply each digit by b raised to its positional power (rightmost = b^0) and sum them. E.g., (101)_2 = 1x4 + 0x2 + 1x1 = 5 in base 10.

  16. How do you convert a base-10 number to another base b?

    Repeatedly divide the number by b, recording remainders. Read the remainders in reverse order (last remainder first) to get the number in base b.

  17. What is the formula to convert a percentage change into a multiplying factor, and how to find percentage change from a multiplier?

    Multiplier = 1 + (percentage/100). An increase of x% means multiply by (1 + x/100); a decrease of x% means multiply by (1 - x/100).

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

    There is a net decrease of (x^2/100)%. The original value is never restored; it always decreases.

  19. What is the percentage equivalent of the fraction 1/8, 1/6, and 1/3?

    1/8 = 12.5%, 1/6 = 16.66%, 1/3 = 33.33%.

  20. What are the formulas for profit/loss percentage (based on cost price)?

    Profit% = (Profit/CP) x 100; Loss% = (Loss/CP) x 100. Profit = SP - CP; Loss = CP - SP. Percentages are calculated on cost price by default.

Show the other 30 Quantitative Aptitude (QA) - Arithmetic flashcards

  1. What is the relationship between Marked Price (MP), Selling Price (SP), and Discount?

    SP = MP x (1 - Discount%/100). Discount = MP - SP, and Discount% is calculated on the marked price.

  2. If two articles are sold at the same SP, one at x% profit and the other at x% loss, what is the net result?

    There is always a net loss of (x^2/100)%, regardless of the selling price.

  3. What is the simple interest formula?

    SI = (P x R x T)/100, where P = principal, R = rate per annum, T = time in years. Amount = P + SI.

  4. What is the compound interest formula for annual compounding?

    Amount A = P(1 + R/100)^T, and CI = A - P. For n compoundings per year: A = P(1 + R/(100n))^(nT).

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

    Difference = P x (R/100)^2 for 2 years. For 3 years, difference = P(R/100)^2 x (3 + R/100).

  6. If a sum doubles in T years at simple interest, how is the rate found, and what is the rule for compound interest doubling?

    SI: rate R = 100/T per year (since interest = principal). CI: use the Rule of 72 (approx time to double = 72/R) or solve 2 = (1 + R/100)^T.

  7. What is the difference between ratio and proportion?

    A ratio (a:b) compares two quantities. A proportion is an equality of two ratios (a:b = c:d), meaning a x d = b x c (product of extremes = product of means).

  8. In a proportion a:b = c:d, what are componendo and dividendo?

    Componendo: (a+b)/b = (c+d)/d. Dividendo: (a-b)/b = (c-d)/d. Componendo-Dividendo: (a+b)/(a-b) = (c+d)/(c-d).

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

    Mean proportional = sqrt(a x b). It is the value x such that a:x = x:b.

  10. Define direct, inverse, and joint variation.

    Direct: y = kx (y increases as x increases). Inverse: y = k/x (y decreases as x increases). Joint: y varies with the product/combination of multiple variables, e.g., y = kxz.

  11. In a partnership, how is profit shared when partners invest different amounts for different time periods?

    Profit is shared in the ratio of (capital x time) for each partner. E.g., if A invests Pa for Ta and B invests Pb for Tb, ratio = Pa.Ta : Pb.Tb.

  12. What is the difference between a working partner and a sleeping partner?

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

  13. What is the rule of alligation (alligation rule)?

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

  14. In a vessel with x litres of pure liquid, after removing y litres and replacing with water n times, what remains?

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

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

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

  16. What is the weighted average formula?

    Weighted average = (w1.x1 + w2.x2 + ... + wn.xn)/(w1 + w2 + ... + wn), where wi are weights and xi are values.

  17. How does the average change when a new value is added or removed?

    If a value greater than the current average is added, the average rises; if smaller, it falls. New sum = old sum +/- the value; recompute average with the new count.

  18. Define the three measures of central tendency: mean, median, and mode.

    Mean = arithmetic average. Median = middle value when data is ordered (average of two middle values if even count). Mode = most frequently occurring value.

  19. What is the empirical relationship between mean, median, and mode?

    Mode = 3 x Median - 2 x Mean (approximately, for moderately skewed distributions).

  20. What are the main measures of dispersion?

    Range, Quartile Deviation, Mean Deviation, Variance, and Standard Deviation. They measure how spread out the data is around a central value.

  21. What is the formula for standard deviation and variance?

    Variance = (1/n) x Sum of (xi - mean)^2. Standard Deviation (SD) = sqrt(Variance). SD has the same units as the data.

  22. What is the coefficient of variation and what does it measure?

    Coefficient of Variation (CV) = (Standard Deviation / Mean) x 100%. It measures relative variability and allows comparison of dispersion between datasets with different means/units.

  23. What is the fundamental relationship between speed, distance, and time, and key unit conversions?

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

  24. What is the formula for relative speed in same-direction and opposite-direction motion?

    Opposite directions: relative speed = sum of speeds (s1 + s2). Same direction: relative speed = difference of speeds (s1 - s2).

  25. What is the average speed for a round trip covering equal distances at speeds a and b?

    Average speed = 2ab/(a+b) (the harmonic mean), NOT the arithmetic mean of the two speeds.

  26. How long does a train of length L take to cross a platform of length P at speed v?

    Time = (L + P)/v. To cross a pole/point object, time = L/v (only the train's length matters).

  27. In a race, what do 'a beats b by x metres' and 'a beats b by t seconds' mean?

    'Beats by x metres' means when A finishes, B is x metres behind. 'Beats by t seconds' means A finishes t seconds before B. A 'start of x metres' means B begins x metres ahead.

  28. On a circular track of length L, when do two runners starting together (same point) first meet, in same and opposite directions?

    Same direction: time = L/(s1 - s2). Opposite directions: time = L/(s1 + s2). Time to meet again at the starting point = LCM of (L/s1, L/s2).

  29. If A completes a work in 'a' days and B in 'b' days, how long do they take together?

    Combined time = ab/(a+b) days. (Their combined one-day work = 1/a + 1/b.)

  30. What is the formula relating men, days, hours, and work (work equivalence)?

    (M1 x D1 x H1)/W1 = (M2 x D2 x H2)/W2, where M = number of workers, D = days, H = hours/day, W = amount of work. This is the chain rule of work.

CAT (Common Admission Test) Quantitative Aptitude (QA) - Arithmetic FAQ

What is in the CAT (Common Admission Test) Quantitative Aptitude (QA) - Arithmetic syllabus?

CAT (Common Admission Test) Quantitative Aptitude (QA) - Arithmetic is split into 5 chapters: Number System, Percentages, Profit and Loss, Ratio, Proportion and Variation, Averages and Statistics and Time, Speed, Distance and Work. Together they contain 19 topics and 41 sub-topics.

How many chapters are in CAT (Common Admission Test) Quantitative Aptitude (QA) - Arithmetic?

5 chapters, containing 19 topics and 41 sub-topics. The largest chapter is Number System, with 6 topics.

Are there flashcards for CAT (Common Admission Test) Quantitative Aptitude (QA) - Arithmetic?

Yes — a 50-card Quantitative Aptitude (QA) - Arithmetic 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.