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:_____________3591116
Question
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:_____________3591116
Solution
The resulting number will be divisible by 11.
Here's why:
Let's assume the original two-digit number is 10a + b, where a and b are the tens and units digits respectively.
When the digits interchange places, the number becomes 10b + a.
Adding these two numbers together gives:
(10a + b) + (10b + a) = 11a + 11b = 11(a + b)
Since a and b are integers, the sum (a + b) is also an integer. Therefore, the resulting number is a multiple of 11, which means it is divisible by 11.
Similar Questions
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:Options :91113none
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
A six digit number is divisible by 33. If 54 is added to the number then the new number formed will also be divisible by?(1 Point)39211
The digits indicated by * in 3422213** so that this number is divisible by 99 areOptions1,93,74,65,5
A four-digit number has the sum of its digits in the odd positions equal to the sum of its digits in the even positions. If it is subtracted from the number formed by reversing it, the result will always be divisible by ______.91113Both (A) and (B)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.