The difference between a three digit number and a number formed by reversing its digits is 198. Determine the number, if the sum of the digits is 10
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Answer:
Any 3-digit number can be written in the form 100x + 10y + z, where x, y, and z are the hundreds, tens, and ones digits, respectively. For example, the number 325 can be written as
100(3) + 10(2) + 5.
Now, the number formed by reversing the digits will be 100z + 10y + x. For example, in the case of 325, the number with the reversed digits becomes
100(5) + 10(2) + 3.
Now, subtracting we have
100x + 10y + z – (100z + 10y + x) = 100x + 10y + z –100z – 10y – x = 99x – 99z.
Factoring, we have 99(x – z). Since x and z are 1-digitnumbers, x – z is an integer. Since 99 is a factor of 99(x – z), 99(x – z) is divisible by 99. Therefore, the difference of a 3-digit number and the number formed by reversing the order of its digits is divisible by 99
Explanation-The difference of a 3-digit number and the number formed by reversing the order of its digits is divisible by 99.
Answer:
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