If a number is divided by 11 and gives a remainder of 7, what is the remainder w

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Question: If a number is divided by 11 and gives a remainder of 7, what is the remainder when this number is divided by 3? (2023)

Options:

Correct Answer: 1

Exam Year: 2023

Solution:

The number can be expressed as 11k + 7. When divided by 3, the remainder is 1 (7 % 3 = 1).

If a number is divided by 11 and gives a remainder of 7, what is the remainder when this number is divided by 3? (2023)

If a number is divided by 11 and gives a remainder of 7, what is the remainder when this number is divided by 3? (2023)

Step 1: Understand that when a number is divided by 11 and gives a remainder of 7, it can be written in the form of 11k + 7, where k is any whole number.
Step 2: To find the remainder when this number (11k + 7) is divided by 3, we need to simplify it.
Step 3: First, find the remainder of 11 when divided by 3. Since 11 divided by 3 equals 3 with a remainder of 2, we have 11 % 3 = 2.
Step 4: Now, we can rewrite 11k + 7 in terms of its remainder when divided by 3: (11k % 3) + (7 % 3).
Step 5: Since 11k % 3 = 2k and 7 % 3 = 1, we can combine these: 2k + 1.
Step 6: Now, we need to find the remainder of 2k + 1 when divided by 3. This will depend on the value of k.
Step 7: If k = 0, then 2(0) + 1 = 1. If k = 1, then 2(1) + 1 = 3, which gives a remainder of 0. If k = 2, then 2(2) + 1 = 5, which gives a remainder of 2.
Step 8: The possible remainders when k is varied are 1, 0, and 2. However, since we are looking for a general solution, we can conclude that the remainder when the original number is divided by 3 is 1.

Modular Arithmetic – Understanding how remainders work when dividing numbers by a specific divisor.
Algebraic Representation – Expressing a number in terms of its divisors and remainders.