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Two different numbers are divided by the same divisor and left remainder 11 and 21 respectively and when their sum was divided by the same divisor, remainder was 4. What is the divisor?
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Two different numbers are divided by the same divisor and left remaind...
Understanding the Problem:
Given:
- Two different numbers leave remainders 11 and 21 when divided by the same divisor.
- The sum of these two numbers leaves a remainder of 4 when divided by the same divisor.
Finding the Divisor:
Let's denote the divisor as D.
- The first number can be represented as D*x + 11, where x is an integer.
- The second number can be represented as D*y + 21, where y is an integer.
Expressing the Sum:
The sum of the two numbers is (D*x + 11) + (D*y + 21) = D*(x + y) + 32.
When this sum is divided by D, the remainder is 4.
Equation:
Therefore, we have the equation D*(x + y) + 32 ≡ 4 (mod D).
This can be simplified to D*(x + y) ≡ -28 (mod D).
Finding the Divisor:
To find the divisor D, we need to find a number that when multiplied by the sum of x and y, leaves a remainder of -28 when divided by D.
Since the remainder cannot be negative, we add D to -28 to get a positive remainder.
Final Calculation:
The divisor D will be the smallest number that divides (x + y) and leaves a remainder of 4.
Hence, the divisor in this case would be 8.
Conclusion:
Therefore, the divisor in this problem is 8, which satisfies all the given conditions.
Given:
- Two different numbers leave remainders 11 and 21 when divided by the same divisor.
- The sum of these two numbers leaves a remainder of 4 when divided by the same divisor.
Finding the Divisor:
Let's denote the divisor as D.
- The first number can be represented as D*x + 11, where x is an integer.
- The second number can be represented as D*y + 21, where y is an integer.
Expressing the Sum:
The sum of the two numbers is (D*x + 11) + (D*y + 21) = D*(x + y) + 32.
When this sum is divided by D, the remainder is 4.
Equation:
Therefore, we have the equation D*(x + y) + 32 ≡ 4 (mod D).
This can be simplified to D*(x + y) ≡ -28 (mod D).
Finding the Divisor:
To find the divisor D, we need to find a number that when multiplied by the sum of x and y, leaves a remainder of -28 when divided by D.
Since the remainder cannot be negative, we add D to -28 to get a positive remainder.
Final Calculation:
The divisor D will be the smallest number that divides (x + y) and leaves a remainder of 4.
Hence, the divisor in this case would be 8.
Conclusion:
Therefore, the divisor in this problem is 8, which satisfies all the given conditions.
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Two different numbers are divided by the same divisor and left remainder 11 and 21 respectively and when their sum was divided by the same divisor, remainder was 4. What is the divisor?
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Two different numbers are divided by the same divisor and left remainder 11 and 21 respectively and when their sum was divided by the same divisor, remainder was 4. What is the divisor? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two different numbers are divided by the same divisor and left remainder 11 and 21 respectively and when their sum was divided by the same divisor, remainder was 4. What is the divisor? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two different numbers are divided by the same divisor and left remainder 11 and 21 respectively and when their sum was divided by the same divisor, remainder was 4. What is the divisor?.
Two different numbers are divided by the same divisor and left remainder 11 and 21 respectively and when their sum was divided by the same divisor, remainder was 4. What is the divisor? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two different numbers are divided by the same divisor and left remainder 11 and 21 respectively and when their sum was divided by the same divisor, remainder was 4. What is the divisor? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two different numbers are divided by the same divisor and left remainder 11 and 21 respectively and when their sum was divided by the same divisor, remainder was 4. What is the divisor?.
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