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If the sum of two numbers is 50 and both leave a remainder of 4 when divided by

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Question: If the sum of two numbers is 50 and both leave a remainder of 4 when divided by 6, what is the remainder when their sum is divided by 6? (2023)

Options:

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Correct Answer: 0

Exam Year: 2023

Solution: 

Both numbers can be expressed as 6k + 4. Their sum is 12k + 8, which gives a remainder of 2 when divided by 6.

If the sum of two numbers is 50 and both leave a remainder of 4 when divided by

Practice Questions

Q1
If the sum of two numbers is 50 and both leave a remainder of 4 when divided by 6, what is the remainder when their sum is divided by 6? (2023)
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Questions & Step-by-Step Solutions

If the sum of two numbers is 50 and both leave a remainder of 4 when divided by 6, what is the remainder when their sum is divided by 6? (2023)
  • Step 1: Understand that we have two numbers that add up to 50.
  • Step 2: Both numbers leave a remainder of 4 when divided by 6. This means we can express each number in the form of 6k + 4, where k is an integer.
  • Step 3: Let's say the first number is 6k1 + 4 and the second number is 6k2 + 4, where k1 and k2 are integers.
  • Step 4: Now, add the two numbers: (6k1 + 4) + (6k2 + 4) = 6k1 + 6k2 + 8.
  • Step 5: This can be simplified to 6(k1 + k2) + 8.
  • Step 6: Notice that 8 can be rewritten as 6 + 2, so we have 6(k1 + k2 + 1) + 2.
  • Step 7: When we divide this sum by 6, the 6(k1 + k2 + 1) part will leave no remainder, and we are left with the remainder of 2.
  • Step 8: Therefore, the remainder when the sum of the two numbers (which is 50) is divided by 6 is 2.
  • Modular Arithmetic – Understanding how remainders work when numbers are divided by a specific divisor.
  • Algebraic Expressions – Using algebraic expressions to represent numbers based on given conditions.
  • Properties of Addition – Applying properties of addition to combine numbers and analyze their remainders.
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