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A number leaves a remainder of 4 when divided by 10 and a remainder of 2 when di

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Question: A number leaves a remainder of 4 when divided by 10 and a remainder of 2 when divided by 3. What is the smallest positive integer that satisfies these conditions? (2023)

Options:

  1. 4
  2. 14
  3. 24
  4. 34

Correct Answer: 14

Exam Year: 2023

Solution: 

The smallest number that satisfies both conditions is 14 (14 % 10 = 4 and 14 % 3 = 2).

A number leaves a remainder of 4 when divided by 10 and a remainder of 2 when di

Practice Questions

Q1
A number leaves a remainder of 4 when divided by 10 and a remainder of 2 when divided by 3. What is the smallest positive integer that satisfies these conditions? (2023)
  1. 4
  2. 14
  3. 24
  4. 34

Questions & Step-by-Step Solutions

A number leaves a remainder of 4 when divided by 10 and a remainder of 2 when divided by 3. What is the smallest positive integer that satisfies these conditions? (2023)
  • Step 1: Understand the problem. We need to find a number that gives a remainder of 4 when divided by 10 and a remainder of 2 when divided by 3.
  • Step 2: Write down the first condition. A number 'x' leaves a remainder of 4 when divided by 10 can be expressed as: x % 10 = 4.
  • Step 3: Write down the second condition. A number 'x' leaves a remainder of 2 when divided by 3 can be expressed as: x % 3 = 2.
  • Step 4: List numbers that satisfy the first condition. The numbers that leave a remainder of 4 when divided by 10 are: 4, 14, 24, 34, 44, ...
  • Step 5: Check each of these numbers against the second condition. Start with 4: 4 % 3 = 1 (not valid). Next, check 14: 14 % 3 = 2 (valid).
  • Step 6: Since 14 satisfies both conditions, we have found our answer. The smallest positive integer that meets both conditions is 14.
  • Modular Arithmetic – Understanding how to work with remainders when dividing numbers.
  • System of Congruences – Solving multiple conditions that involve remainders.
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