Review Test of Remainder Theorem

The sum of the digits of a number N is 23. The remainder when N is divided by 11 is 7. What is the remainder when N is divided by 33?

What is the remainder when (13¹⁰⁰+ 17¹⁰⁰) is divided by 25?

A number when divided by 18 leaves a remainder 7. The same number when divided by 12 leaves a remainder n. How many values can n take?

N leaves a remainder of 4 when divided by 33, what are the possible remainders when N is divided by 55?

What is the remainder when we divide 3⁹⁰ + 5⁹⁰ by 34?

N² leaves a remainder of 1 when divided by 24. What are the possible remainders we can get if we divide N by 12

A prime number p greater than 100 leaves a remainder q on division by 28. How many values can q take?

How many positive integers are there from 0 to 1000 that leave a remainder of 3 on division by 7 and a remainder of 2 on division by 4?

Three numbers leave remainders of 43, 47 and 49 on division by N. The sum of the three numbers leaves a remainder 9 on division by N. What are the values N can take?

A number leaves a remainder 3 on division by 14, and leaves a remainder k on division by 35. How many possible values can k take?