Manav Goyal

Number System - Aptitude

  • Basic
    • (xn+an) is divisible by (x+a) ∀ odd values of n
    • Dividend = (Divisor x Quotient) + Remainder
  • Category of Numbers
    • Natural Number
      • 1, 2, 3, 4, 5, ...
    • Whole Number
      • 0, 1, 2, 3, 4, ...
    • Integer
      • -3, -2, -1, 0, 1, 2, 3, ...
    • Even Number
      • 0, 2, 4, 6, 8, ...
    • Odd Number
      • 1, 2, 5, 7, 9, ...
    • Prime Number
      • 2, 3, 5, 7, 11, ...
    • Composite Number
      • 4, 6, 8, 9, 10, ...
    • Perfect Number
      • 6, 28, ...
    • Co-prime Number
      • (2, 3), (8, 9), ...
    • Rational Number
      • 1/8, -7/11, ...
    • Irrational Number
      • √2, √3, π, ...
  • Divisibility Test
    • 2
      • Unit digit is one among the following 0, 2, 4, 6, 8
    • 3
      • Sum of digits is divisible by 3
    • 4
      • Last 2 digits taken together is divisible by 4
    • 5
      • Unit digit is 0 or 5
    • 6
      • Number is divisible by 2 and 3
    • 7
      • Difference between twice the unit digit and remaining part is 0 or multiple of 7
    • 8
      • Last 3 digits taken together is divisible by 8
    • 9
      • Sum of digits is divisible by 9
    • 10
      • Unit digit is 0
    • 11
      • Subtraction of (odd - even) digits is 0 or divisible by 11
    • 12
      • Number is divisible by 3 and 4
    • 16
      • Last 4 digits taken together is divisible by 16
    • 18
      • Number is divisible by 2 and 9
    • 25
      • Last 2 digits is 00 or 25
  • Question types
    • Find if the given number (P) is prime
      • Find smallest value of N using condition N2 ≥ P
      • List all the prime numbers till N
      • If P is not divisible by any of these numbers then P is also prime
    • Find value of "x" in given number if it is divisible by N
      • Use divisibility test
    • Find value of "x" & "y" in given number if it is divisible by N1 & N2
      • Use divisibility test
    • Find remainder if xy is divided by N
      • (xn-an) is divisible by (x-a) ∀ n
    • Find remainder if (xz - yz) is divided by N
      • (xn-an) is divisible by (x+a) ∀ even values of n
    • Find remainder with Factorials
      • Remainder after a certain number will become zero, calculate for the remaining
    • When a certain number is divided by "N" product consists of only "M", Find minimum number of "M" in product
      • Divide "N" by "M" till remainder is 0 by taking "M" as carry whenever required
    • Find greatest/smallest number of "N" digits which is exactly divisible by "M"
      • Take the greatest/smallest "N" digits number and divide it by "M", Substract/Add the remainder/(M-remainder) to get the result
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