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If the sum of two numbers is 25 and both leave a remainder of 4 when divided by

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Question: If the sum of two numbers is 25 and both leave a remainder of 4 when divided by 7, what is the remainder when their sum is divided by 7? (2023)

Options:

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Correct Answer: 0

Exam Year: 2023

Solution: 

The sum of the remainders is 4 + 4 = 8, and 8 divided by 7 gives a remainder of 1.

If the sum of two numbers is 25 and both leave a remainder of 4 when divided by

Practice Questions

Q1
If the sum of two numbers is 25 and both leave a remainder of 4 when divided by 7, what is the remainder when their sum is divided by 7? (2023)
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Questions & Step-by-Step Solutions

If the sum of two numbers is 25 and both leave a remainder of 4 when divided by 7, what is the remainder when their sum is divided by 7? (2023)
  • Step 1: Identify the two numbers. Let's call them A and B.
  • Step 2: We know that A + B = 25.
  • Step 3: Both A and B leave a remainder of 4 when divided by 7. This means A can be expressed as 7k + 4 and B as 7m + 4, where k and m are whole numbers.
  • Step 4: Add the two expressions for A and B: (7k + 4) + (7m + 4) = 25.
  • Step 5: Simplify the equation: 7k + 7m + 8 = 25.
  • Step 6: Rearrange the equation to find 7(k + m) = 25 - 8, which simplifies to 7(k + m) = 17.
  • Step 7: Since 17 is not divisible by 7, we focus on the remainders instead.
  • Step 8: Calculate the sum of the remainders: 4 (from A) + 4 (from B) = 8.
  • Step 9: Now, find the remainder when 8 is divided by 7. 8 divided by 7 equals 1 with a remainder of 1.
  • Step 10: Therefore, the remainder when the sum of A and B is divided by 7 is 1.
  • Modular Arithmetic – Understanding how remainders work when numbers are divided by a specific divisor.
  • Properties of Addition – Using the properties of addition to combine remainders and find the overall remainder.
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