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If x ≡ 2 (mod 3) and y ≡ 1 (mod 3), what is the value of (x + y) mod 3?

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Question: If x ≡ 2 (mod 3) and y ≡ 1 (mod 3), what is the value of (x + y) mod 3?

Options:

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Correct Answer: 1

Solution: 

x + y ≡ 2 + 1 ≡ 3 (mod 3), which is equivalent to 0, but since we are looking for the value, it is 0 mod 3.

If x ≡ 2 (mod 3) and y ≡ 1 (mod 3), what is the value of (x + y) mod 3?

Practice Questions

Q1
If x ≡ 2 (mod 3) and y ≡ 1 (mod 3), what is the value of (x + y) mod 3?
  1. 0
  2. 1
  3. 2
  4. 3

Questions & Step-by-Step Solutions

If x ≡ 2 (mod 3) and y ≡ 1 (mod 3), what is the value of (x + y) mod 3?
  • Step 1: Understand what 'x ≡ 2 (mod 3)' means. This means when you divide x by 3, the remainder is 2.
  • Step 2: Understand what 'y ≡ 1 (mod 3)' means. This means when you divide y by 3, the remainder is 1.
  • Step 3: Add the two congruences together: (x + y) ≡ (2 + 1) (mod 3).
  • Step 4: Calculate 2 + 1, which equals 3.
  • Step 5: Now find 3 mod 3. When you divide 3 by 3, the remainder is 0.
  • Step 6: Therefore, (x + y) mod 3 is equal to 0.
  • Modular Arithmetic – Understanding how to perform addition and find remainders in modular systems.
  • Congruences – Applying the properties of congruences to combine values and simplify results.
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