Let's assume the original number consists of the digits 'a' and 'b'. According to the given condition, if we interchange the digits, the new number formed would be 'ba'.

To find the sum of the original number and the new number, we can add 'ab' and 'ba' together. This gives us 'ab + ba'.

Now, let's simplify the expression. 'ab + ba' can be written as '10a + b + 10b + a'.

Combining like terms, we get '11a + 11b'.

Since we want the resulting number to be divisible by 11, we need '11a + 11b' to be a multiple of 11.

Factoring out 11, we have '11(a + b)'.

For '11(a + b)' to be divisible by 11, 'a + b' must also be divisible by 11.

Therefore, the original number will satisfy the given condition if the sum of its digits is divisible by 11.

Question

Let's assume the original number consists of the digits 'a' and 'b'. According to the given condition, if we interchange the digits, the new number formed would be 'ba'.

To find the sum of the original number and the new number, we can add 'ab' and 'ba' together. This gives us 'ab + ba'.

Now, let's simplify the expression. 'ab + ba' can be written as '10a + b + 10b + a'.

Combining like terms, we get '11a + 11b'.

Since we want the resulting number to be divisible by 11, we need '11a + 11b' to be a multiple of 11.

Factoring out 11, we have '11(a + b)'.

For '11(a + b)' to be divisible by 11, 'a + b' must also be divisible by 11.

Therefore, the original number will satisfy the given condition if the sum of its digits is divisible by 11.

Knowee AI · Accepted Answer

Let's assume the original number consists of the digits 'a' and 'b'. According to the given condition, if we interchange the digits, the new number formed would be 'ba'.

To find the sum of the original number and the new number, we can add 'ab' and 'ba' together. This gives us 'ab + ba'.

Now, let's simplify the expression. 'ab + ba' can be written as '10a + b + 10b + a'.

Combining like terms, we get '11a + 11b'.

Since we want the resulting number to be divisible by 11, we need '11a + 11b' to be a multiple of 11.

Factoring out 11, we have '11(a + b)'.

For '11(a + b)' to be divisible by 11, 'a + b' must also be divisible by 11.

Therefore, the original number will satisfy the given condition if the sum of its digits is divisible by 11.

A number consists of two digits. If the number formed by interchanging the digits is added to the original number, the resulting number (i.e. the sum) must be divisible byOptions11539

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