When a number is divided by 11, it leaves a remainder of 7. What will be the rem
Practice Questions
Q1
When a number is divided by 11, it leaves a remainder of 7. What will be the remainder when this number is divided by 3? (2023)
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Questions & Step-by-Step Solutions
When a number is divided by 11, it leaves a remainder of 7. What will be the remainder when this number is divided by 3? (2023)
Step 1: Understand that when a number is divided by 11, it leaves a remainder of 7. This means the number can be written as '11k + 7' for some integer k.
Step 2: We need to find the remainder when this number (11k + 7) is divided by 3.
Step 3: First, find the remainder of 11 when divided by 3. Since 11 divided by 3 is 3 with a remainder of 2, we have 11 ≡ 2 (mod 3).
Step 4: Now, substitute this back into our expression: 11k + 7 ≡ 2k + 7 (mod 3).
Step 5: Next, find the remainder of 7 when divided by 3. Since 7 divided by 3 is 2 with a remainder of 1, we have 7 ≡ 1 (mod 3).
Step 6: Now combine the results: 2k + 1 (mod 3).
Step 7: The value of 2k can be either 0, 1, or 2 depending on the value of k (0, 1, or 2 mod 3).
Step 8: Therefore, the possible remainders when 2k + 1 is divided by 3 can be calculated: If k ≡ 0 (mod 3), remainder is 1; if k ≡ 1 (mod 3), remainder is 0; if k ≡ 2 (mod 3), remainder is 2.
Step 9: Since we are looking for the remainder when the original number is divided by 3, we can conclude that the remainder can be 0, 1, or 2 depending on k.
