If a number leaves a remainder of 3 when divided by 7, which of the following co

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Question: If a number leaves a remainder of 3 when divided by 7, which of the following could be the number? (2023)

Options:

Correct Answer: 10

Exam Year: 2023

Solution:

10 divided by 7 gives a remainder of 3 (10-7=3).

If a number leaves a remainder of 3 when divided by 7, which of the following could be the number? (2023)

If a number leaves a remainder of 3 when divided by 7, which of the following could be the number? (2023)

Step 1: Understand the problem. We need to find a number that, when divided by 7, leaves a remainder of 3.
Step 2: Write the mathematical expression. If a number is 'x', then we can say x = 7k + 3, where k is any whole number (0, 1, 2, ...).
Step 3: Start with k = 0. Calculate x: x = 7*0 + 3 = 3.
Step 4: Next, try k = 1. Calculate x: x = 7*1 + 3 = 10.
Step 5: Now try k = 2. Calculate x: x = 7*2 + 3 = 17.
Step 6: Continue this process to find more numbers: k = 3 gives x = 24, k = 4 gives x = 31, etc.
Step 7: Check if 2023 fits the pattern. Calculate 2023 divided by 7 and find the remainder.
Step 8: If the remainder is 3, then 2023 is a valid number. If not, it is not.

Modular Arithmetic – Understanding how remainders work when dividing numbers, specifically focusing on the concept of congruences.