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    Question 1

    Which of the following statements is always true for an even number n?

    • A

      n % 2 == 1

    • B

      Last bit of n in binary is 1

    • C

      n & 1 == 0

    • D

      n / 2 is odd

    Question 2

    What is the purpose of modulo in modular exponentiation?


    • A

      To speed up multiplication

    • B

      To limit numbers to avoid overflow

    • C

      To convert binary to decimal

    • D

      To find the maximum value

    Question 3

    If n is divisible by m, then which of the following is true?


    • A

      n % m == 1

    • B

      n // m will always be 0

    • C

      n % m == 0

    • D

      m % n == 0

    Question 4

    What is the most efficient method to check if a single number (≤ 106) is prime?

    • A

      Trial division up to n

    • B

      Trial division up to √n

    • C

      Using the Sieve of Eratosthenes

    • D

      Check divisibility by 2 and 3

    Question 5

    Why do we use GCD in problems involving LCM?


    • A

      To reduce a number

    • B

      Because LCM(a, b) = (a * b) / GCD(a, b)

    • C

      It helps check divisibility

    • D

      To compute square root

    Question 6

    Why is it incorrect to directly divide in modular arithmetic like (a / b) % m?

    • A

      It’s computationally slow

    • B

      Division is not allowed in math

    • C

      Modular division needs multiplicative inverse

    • D

      All modulo operations must be done after division

    Question 7

    Which statement about the Euler Totient Function φ(n) is correct?

    • A

      φ(n) is always even

    • B

      φ(n) is the number of integers from 1 to n divisible by n

    • C

      φ(n) = n - 1 if n is prime

    • D

      φ(n) is same as number of digits in n

    Question 8

    When would ceil(n/m) != floor(n/m) be true for positive integers?


    • A

      Always

    • B

      When n is divisible by m

    • C

      When n is not divisible by m

    • D

      Never

    Question 9

    You are to find the closest number ≤ n that is divisible by m. Which formula works?

    • A

      n // m

    • B

      (n - 1) % m

    • C

      (n // m) * m

    • D

      n % m

    Question 10

    In the Sieve of Eratosthenes, why do we start striking off from i*i?

    • A

      To skip checking small primes

    • B

      Because smaller multiples already struck by smaller primes

    • C

      To reduce space

    • D

      Because i*i is always prime

    There are 10 questions to complete.

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