A number is divided by 12 and gives a remainder of 7. If this number is multipli
Practice Questions
Q1
A number is divided by 12 and gives a remainder of 7. If this number is multiplied by 2, what will be the remainder when the new number is divided by 12? (2023)
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Questions & Step-by-Step Solutions
A number is divided by 12 and gives a remainder of 7. If this number is multiplied by 2, what will be the remainder when the new number is divided by 12? (2023)
Step 1: Understand that when a number is divided by 12 and gives a remainder of 7, it can be expressed as 'original number = 12k + 7', where k is some integer.
Step 2: Multiply the original number by 2. This gives us 'new number = 2 * (12k + 7)'.
Step 3: Distribute the 2 in the equation: 'new number = 2 * 12k + 2 * 7'.
Step 4: Simplify the equation: 'new number = 24k + 14'.
Step 5: Now, we need to find the remainder when 'new number' is divided by 12. We can rewrite 14 as '12 + 2'.
Step 6: When we divide '24k + 14' by 12, the '24k' part is divisible by 12, leaving us with the remainder from '14'.
Step 7: Since '14' can be expressed as '12 + 2', the remainder when dividing by 12 is simply 2.
Modular Arithmetic – Understanding how remainders work when dividing numbers.
Multiplication and Remainders – Applying multiplication to a number and determining the new remainder.
