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A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:
- a)3
- b)5
- c)9
- d)11
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A number consists of two digits. If the digits interchange places and ...
Interchanging the digits of a two-digit number and adding the new number to the original number:
Let's consider a two-digit number, AB, where A represents the tens digit and B represents the units digit. The value of this number can be represented as 10A + B.
If we interchange the digits, the new number will be BA, which can be represented as 10B + A.
When we add the original number (10A + B) to the new number (10B + A), the resulting number can be calculated as:
(10A + B) + (10B + A) = 11A + 11B = 11(A + B)
Divisibility by 11:
To determine if the resulting number is divisible by 11, we need to check if (A + B) is divisible by 11.
If (A + B) is divisible by 11, then 11(A + B) will also be divisible by 11.
Example:
Let's consider the number 34.
If we interchange the digits, we get the number 43.
When we add 34 and 43, we get 77, which is divisible by 11 because 7 + 7 = 14, and 14 is divisible by 11.
Conclusion:
In general, whenever we interchange the digits of a two-digit number and add the new number to the original number, the resulting number will always be divisible by 11.
Therefore, the correct answer is option D) 11.
Let's consider a two-digit number, AB, where A represents the tens digit and B represents the units digit. The value of this number can be represented as 10A + B.
If we interchange the digits, the new number will be BA, which can be represented as 10B + A.
When we add the original number (10A + B) to the new number (10B + A), the resulting number can be calculated as:
(10A + B) + (10B + A) = 11A + 11B = 11(A + B)
Divisibility by 11:
To determine if the resulting number is divisible by 11, we need to check if (A + B) is divisible by 11.
If (A + B) is divisible by 11, then 11(A + B) will also be divisible by 11.
Example:
Let's consider the number 34.
If we interchange the digits, we get the number 43.
When we add 34 and 43, we get 77, which is divisible by 11 because 7 + 7 = 14, and 14 is divisible by 11.
Conclusion:
In general, whenever we interchange the digits of a two-digit number and add the new number to the original number, the resulting number will always be divisible by 11.
Therefore, the correct answer is option D) 11.
Community Answer
A number consists of two digits. If the digits interchange places and ...
Let the ten's digit be x and unit's digit be y.
Then, number = 10x + y
Number obtained by interchanging the digits = 10y + x
∴ (10x + y) + (10y + x) = 11(x + y), which is divisible by 11
Then, number = 10x + y
Number obtained by interchanging the digits = 10y + x
∴ (10x + y) + (10y + x) = 11(x + y), which is divisible by 11
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A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:a)3b)5c)9d)11Correct answer is option 'D'. Can you explain this answer?
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