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by shashank.ism » Tue Feb 09, 2010 12:53 pm
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?

5
6
7
11
13
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by ajith » Thu Feb 11, 2010 9:58 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?

5
6
7
11
13
Say the number was 108

if we deduct 9 it becomes 99
if we deduct 18 it becomes 81 ...

It will become 54 in no time since the sum of digits is 9 all the time

only 6 is factor of original number

Say if the number was 101
there are no factors for it
....
There is something missing in the question
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by harsh.champ » Thu Feb 18, 2010 11:34 am
ajith wrote:
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?

5
6
7
11
13
Say the number was 108

if we deduct 9 it becomes 99
if we deduct 18 it becomes 81 ...

It will become 54 in no time since the sum of digits is 9 all the time

only 6 is factor of original number

Say if the number was 101
there are no factors for it
....
There is something missing in the question
I do agree ajith.
101 is a prime no. so ultimately we will get neither of the 5 options.
I guess it should be written whether the no. should be divisible by some divisor[ex:-3 ,9 etc.]
Hey shashank,can you check if you left out any information??
Also,I tried solving the problem by the formal approach taking 100x + 10y +z
The 2 digit no. being 99x +9y(sum of digits is x+y+z)
But this way the calculation becomes very cumbersome.
I guess in this type of question it is better to plug-in numbers.
Ajith,Did you try by the above formal method??
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by money9111 » Thu Feb 18, 2010 12:07 pm
"Hey shashank,can you check if you left out any information??"

I'm sure you can check... you know where the question came from... here if you need help.. scroll to the bottom:

https://www.proprofs.com/quiz-school/sto ... at-quant-i
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