If a number leaves a remainder of 1 when divided by 4 and a remainder of 2 when
Practice Questions
Q1
If a number leaves a remainder of 1 when divided by 4 and a remainder of 2 when divided by 5, what is the maximum possible value of this number? (2023)
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Questions & Step-by-Step Solutions
If a number leaves a remainder of 1 when divided by 4 and a remainder of 2 when divided by 5, what is the maximum possible value of this number? (2023)
Step 1: Understand the problem. We need to find a number that leaves a remainder of 1 when divided by 4 and a remainder of 2 when divided by 5.
Step 2: Write down the conditions mathematically. If 'x' is our number, then: x % 4 = 1 and x % 5 = 2.
Step 3: List some numbers that satisfy the first condition (x % 4 = 1). These numbers are: 1, 5, 9, 13, 17, 21, ...
Step 4: List some numbers that satisfy the second condition (x % 5 = 2). These numbers are: 2, 7, 12, 17, 22, ...
Step 5: Find the common numbers from both lists. The common numbers are: 17.
Step 6: Check if there are any larger numbers that satisfy both conditions. The next number after 17 that satisfies x % 4 = 1 is 21, but 21 % 5 = 1, which does not satisfy the second condition.
Step 7: Conclude that the maximum number that satisfies both conditions is 17.
Modular Arithmetic – Understanding how to work with remainders when dividing numbers.
System of Congruences – Solving multiple conditions that a number must satisfy simultaneously.
