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In the "Addition Trick," the sum of a two-digit number and its reverse is always divisible by?
- a)7
- b)11
- c)9
- d)3
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In the "Addition Trick," the sum of a two-digit number and its reverse...
Let the two-digit number be 10a + b, where a and b are its digits.
The reverse is 10b + a.
Sum = (10a + b) + (10b + a) = 11(a + b).
Therefore the sum is always divisible by 11; so option B is correct.
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In the "Addition Trick," the sum of a two-digit number and its reverse...
Understanding the Addition Trick
The Addition Trick involves a two-digit number and its reverse. Let's break down why the sum of these numbers is always divisible by 11.
Two-Digit Number Representation
- Let the two-digit number be represented as AB, where A is the tens digit and B is the units digit.
- Mathematically, this can be expressed as: 10A + B.
Reversed Number
- The reverse of the number AB is BA, which can be represented as: 10B + A.
Calculating the Sum
- Now, let's find the sum of the original number and its reversed form:
Sum = (10A + B) + (10B + A)
= 10A + B + 10B + A
= 11A + 11B
= 11(A + B).
Divisibility by 11
- The expression 11(A + B) clearly shows that the sum is a multiple of 11 because it is 11 times the sum of the digits (A + B).
- Since A and B are digits (0-9), A + B can range from 0 to 18, but regardless of its value, 11(A + B) itself is always divisible by 11.
Conclusion
- Therefore, the sum of a two-digit number and its reverse is always divisible by 11.
- The correct answer to the Addition Trick is option 'B' (11).
This fascinating property highlights the unique characteristics of two-digit numbers and their reversals!
The Addition Trick involves a two-digit number and its reverse. Let's break down why the sum of these numbers is always divisible by 11.
Two-Digit Number Representation
- Let the two-digit number be represented as AB, where A is the tens digit and B is the units digit.
- Mathematically, this can be expressed as: 10A + B.
Reversed Number
- The reverse of the number AB is BA, which can be represented as: 10B + A.
Calculating the Sum
- Now, let's find the sum of the original number and its reversed form:
Sum = (10A + B) + (10B + A)
= 10A + B + 10B + A
= 11A + 11B
= 11(A + B).
Divisibility by 11
- The expression 11(A + B) clearly shows that the sum is a multiple of 11 because it is 11 times the sum of the digits (A + B).
- Since A and B are digits (0-9), A + B can range from 0 to 18, but regardless of its value, 11(A + B) itself is always divisible by 11.
Conclusion
- Therefore, the sum of a two-digit number and its reverse is always divisible by 11.
- The correct answer to the Addition Trick is option 'B' (11).
This fascinating property highlights the unique characteristics of two-digit numbers and their reversals!
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In the "Addition Trick," the sum of a two-digit number and its reverse is always divisible by?a)7b)11c)9d)3Correct answer is option 'B'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about In the "Addition Trick," the sum of a two-digit number and its reverse is always divisible by?a)7b)11c)9d)3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the "Addition Trick," the sum of a two-digit number and its reverse is always divisible by?a)7b)11c)9d)3Correct answer is option 'B'. Can you explain this answer?.
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