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Sum

by shashank.ism » Mon Feb 08, 2010 9:08 am
If the sum of the digits of a three-digit number is subtracted from that number, it results in a
two-digit number. This process of subtracting the sum of digits of a number from that number is continued further with that resulting two-digit number also, till we get a factor of the
original three-digit number. Which of the following is a factor of the original three-digit
number?

a) 5
b) 6
c) 7
d) 11
e) 13
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by ajith » Mon Feb 08, 2010 10:09 am
shashank.ism wrote:If the sum of the digits of a three-digit number is subtracted from that number, it results in a
two-digit number. This process of subtracting the sum of digits of a number from that number is continued further with that resulting two-digit number also, till we get a factor of the
original three-digit number. Which of the following is a factor of the original three-digit
number?

a) 5
b) 6
c) 7
d) 11
e) 13
let the number be 'abc'

100a+10b+c - (a+b+c) = 99a+9b

Now since this is a two digit number a=1 and b=0
Sum of digits of 99 =18
18 is a factor of 10c
=> c =8
[spoiler]
108 is the number

B is the answer[/spoiler]
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