What three numbers, none of which is zero, give the same result whether they’re added or multiplied?

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

A 3 digit number is such that it's unit digit is equal to the product of the other two digits which are prime. Also, the difference between it's reverse and itself is 396.

What is the sum of the three digits?

Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.

You are given a cube that is made with the help of 10x10x10 smaller cubes summing up to a total of 1000 smaller cubes. You are asked to take off one layer of the cubes.
How many remain now?

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)

The square root of number 121 is "11". What is the square root of the number "12345678987654321."?

Double it and multiply it by 4. Then divide it by 8 and you’ll have it once more. What number is it?

If "P" means "-", "Q" means "/", "R" means "+", and "S" means "*" then find the value of the following:

21 Q 7 R 9 S 10 P 13

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209