- Courses
- Tutorials
- Interview Prep
Maths and Combinatronics
Question 1
Which of the following statements is always true for an even number n?
n % 2 == 1
Last bit of n in binary is 1
n & 1 == 0
n / 2 is odd
Question 2
What is the purpose of modulo in modular exponentiation?
To speed up multiplication
To limit numbers to avoid overflow
To convert binary to decimal
To find the maximum value
Question 3
If n is divisible by m, then which of the following is true?
n % m == 1
n // m will always be 0
n % m == 0
m % n == 0
Question 4
What is the most efficient method to check if a single number (≤ 106) is prime?
Trial division up to n
Trial division up to √n
Using the Sieve of Eratosthenes
Check divisibility by 2 and 3
Question 5
Why do we use GCD in problems involving LCM?
To reduce a number
Because LCM(a, b) = (a * b) / GCD(a, b)
It helps check divisibility
To compute square root
Question 6
Why is it incorrect to directly divide in modular arithmetic like (a / b) % m?
It’s computationally slow
Division is not allowed in math
Modular division needs multiplicative inverse
All modulo operations must be done after division
Question 7
Which statement about the Euler Totient Function φ(n) is correct?
φ(n) is always even
φ(n) is the number of integers from 1 to n divisible by n
φ(n) = n - 1 if n is prime
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?
Always
When n is divisible by m
When n is not divisible by m
Never
Question 9
You are to find the closest number ≤ n that is divisible by m. Which formula works?
n // m
(n - 1) % m
(n // m) * m
n % m
Question 10
In the Sieve of Eratosthenes, why do we start striking off from i*i?
To skip checking small primes
Because smaller multiples already struck by smaller primes
To reduce space
Because i*i is always prime
There are 10 questions to complete.