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If x ≡ 4 (mod 7) and y ≡ 3 (mod 7), what is the value of (x + y) mod 7?

Practice Questions

Q1
If x ≡ 4 (mod 7) and y ≡ 3 (mod 7), what is the value of (x + y) mod 7?
  1. 0
  2. 1
  3. 2
  4. 3

Questions & Step-by-Step Solutions

If x ≡ 4 (mod 7) and y ≡ 3 (mod 7), what is the value of (x + y) mod 7?
  • Step 1: Understand what 'x ≡ 4 (mod 7)' means. This means when you divide x by 7, the remainder is 4.
  • Step 2: Understand what 'y ≡ 3 (mod 7)' means. This means when you divide y by 7, the remainder is 3.
  • Step 3: Add the two values: 4 (from x) + 3 (from y) = 7.
  • Step 4: Now, we need to find (x + y) mod 7. We take the result from Step 3, which is 7.
  • Step 5: Calculate 7 mod 7. When you divide 7 by 7, the remainder is 0.
  • Step 6: Therefore, (x + y) mod 7 = 0.
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