If n is a 27-digit positive integer, all of whose digits are the same, which of the following must ...
If n is a 27-digit positive integer, all of whose digits are the same, which of the following must be true?
I. n is divisible by 3
II. n is divisible by 9
III. n is divisible by 27
Answer/Solution
I, II and III
Steps/Work
Rule for divisibility by 3: The sum of the digits of the number should be multiple of 3
Rule for divisibility by 9: The sum of the nos digits of the number should be divisible by 9 or the number should be divisible by 3 two times.
Rules for divisibility by 27: The sum of the digits should a multiple of 27
Consider no 11111111...27 times = The sum 27*1=27----> divisbible by 3,9 and 27
consider number to be 222....27 times, then sum of the no. 27*2=54 divisible by 3,9 and 27
So why so because when you sum the numbers either you can add the digits 27 times or multiply the digit *27..
Note that since 27 is divisible by 27,9 and 3 and thus the sum of the nos will be divisible by all the nos.
Answer is E
Rule for divisibility by 9: The sum of the nos digits of the number should be divisible by 9 or the number should be divisible by 3 two times.
Rules for divisibility by 27: The sum of the digits should a multiple of 27
Consider no 11111111...27 times = The sum 27*1=27----> divisbible by 3,9 and 27
consider number to be 222....27 times, then sum of the no. 27*2=54 divisible by 3,9 and 27
So why so because when you sum the numbers either you can add the digits 27 times or multiply the digit *27..
Note that since 27 is divisible by 27,9 and 3 and thus the sum of the nos will be divisible by all the nos.
Answer is E