Question

3. If the sum of the digits of any in- teger between 100 and 1000 is subtracted from the same inte- ger, the resulting number is al- ways divisible by (1) 2 (2) 5 (3) 6 (4) 9
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Answer 1

Answer:

.

Step-by-step explanation:

Number = 100x + 10y + z Sum of digits = x + y + z Difference = 100x + 10y + z – x – y – z = 99x + 9y = 9 (11x+y)If the sum of digits of any integer lying between 100 and 1000 is subtracted from the number, the result will always be divisible by 9.

Answer 2

Answer:

Number = 100x + 10y + z Sum of digits = x + y + z Difference = 100x + 10y + z – x – y – z = 99x + 9y = 9 (11x+y)If the sum of digits of any integer lying between 100 and 1000 is subtracted from the number, the result will always be divisible by 9