Number System
Aptitude

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Q.

The sum of three digit number is subtracted from the number.

The resulting number is always:

 A.

divisible by 6

 B.

not divisible by 6

 C.

divisible by 9

 D.

not divisible by 9

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Solution:
Option(C) is correct

Let the three digit number be $439$

Sum of digits $=16$
Difference $= 439-16 = 423$ which is divisible by 9.


(9) Comment(s)


Arun
 ()

if we take no as 999 then it get divisible by both 6 and 9.


Vishal Vasnani
 ()

The question reads 'always'!


DUDE
 ()

This is the property which will be true for all. Doesn't matter how may digits you take it will be always divisible by 9.

ie.2,3,4,5,6...and so on



Riya
 ()

It holds for 153 too..

sum of digits $=9.$

subtracting 9 from 153 you get 144 which is divisible by 9 Tongue


Shreya
 ()

it holds for 6 also which is also given in the options


Shreya
 ()

what if we take the example 153?



Deepak
 ()

Let the $3$ digit number be: $XYZ$

As per the question we have to find the divisibility of number $P$ (let),

$\Rightarrow  P=(100X+10Y+Z)-(X+Y+Z)$

$\Rightarrow P=(99X+9Y)$

$\Rightarrow P=9 \times (11X+Y)$

which is divisible by 9.

So if the sum of three digit number is subtracted from the number. The resulting number is always divisible by 9.


Honey Kumar
 ()

ur answer also not divisible by 6 at all.Smile