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

Quantitative Aptitude (QA) - Arithmetic syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Aptitude (QA) - Arithmetic in CAT (Common Admission Test), not a summary of it.

1. 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. 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. 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. 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. 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

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

21 of 50 cards from the Quantitative Aptitude (QA) - Arithmetic deck — real questions with worked 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.

21. 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.

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