Multiple-Choice Quiz on Modular Arithmetic

Which of the following correctly defines modular congruence?

• a≡b means a is always equal to b

• a≡b (mod n) means a - b is divisible by n

• a≡b (mod n) means n divides both a and b

• a≡b (mod n) means a + b is a multiple of n

What is the remainder when 29 is divided by 7?

• 2

• 3

• 4

• 5

If 17 ≡ x (mod 6), what is the value of x?

• 2

• 3

• 4

• 5

Which of the following properties of modular arithmetic states that a ≡ a (mod n)?

• Reflexivity

• Symmetry

• Transitivity

• Distributivity

If a ≡ b (mod n) and c ≡ d (mod n), which of the following is true?

What is 14×9 mod 5?

• 1

• 2

• 3

• 4

Which of the following is an example of modular arithmetic in real life?

• Calculating time on a 12-hour clock

• Finding the area of a rectangle

• Measuring temperature

• Calculating the speed of a car

What is the congruence class of -23 modulo 6?

• 1

• 2

• 3

• 4

If x ≡ 7 (mod 20), which of the following is also congruent to x modulo 20?

• 27

• 47

• 67

• All of the above

If x ≡ 4 (mod 9), which of the following values of x satisfies this congruence?

• 13

• 22

• 31

• All of the above