Question

sum of the digits of a three digit number is subtracted from the number.the resulting number is divisible by
a 9
b 6
c both 9 n 6
d all 3, 6 and 9

Answer 1

what have you tried

Answer 2

i am not getting how to translate those words into numbers

Answer 3

say the 3 digit number is \((abc)_{10}\) and consider below expression :
\[\large 100a+10b+c - (a+b+c)\]

Answer 4

i wonder if any work is required?
if it is divisible by 9 then it best be divisible by 3!

Answer 5

yes but divisibility by 6 is tricky..

Answer 6

ooho forgot about that one

Answer 7

i will be quiet now, @ganeshie8 has the answer, but if it is unclear, try and example:
\[243-2-4-3\]

Answer 8

nothing like a bit of experimenting before you get in to the algebra
number therapy is a good way to see what is going on
`

Answer 9

d

Answer 10

\((abc)_{10}\) is just a short form for \(100a+10b+c\)

Answer 11

suppose a number, take 111. sum of its digits = 3 and subtracting it from 111 will yield us with 108 which is divisible by 3,6,9. as

Answer 12

to check whether a number is divisible by 3,6 or 9 the rule is simple. add all the digits of a number and if that sum is divisible by 9, 6 or 3 you know that, that number is divisible too.

Answer 13

really?

Answer 14

take for example 11
add the digits get 2, but 11 is not divisible by 2

Answer 15

my dear friend rule is for 3,6,9 :D

Answer 16

that rule works only for 3 and 9

Answer 17

take for example 99
sum is 18 but 99 is not even

Answer 18

in fact, it is not clear to me at the moment why it is even...

Answer 19

in case of a 3 digit number it should work

Answer 20

for 6 divisiblity rule is if the number is divisible by 2 and 3 then the number is divisble by 6
for 3 and 9 add all the digits of a number and if the sum is divisble by 3 or 9 then the number is divisible by 3 n 9

Answer 21

not that easy for a final year engineering student to remember school concepts but my advise for you is that use real numbers concepts rather than going in xyz algebra to solve the questions! Best of Luck!

Answer 22

\[99a+9b\] is pretty clearly divisible by 9
not so clear as to why it is even

Answer 23

please tell me you don't have to work in cases

Answer 24

clearly it is not even when a,b have opposite parity
odd-even or even-odd

Answer 25

yeah cases are required haha

Answer 26

lol i am an idiot!

Answer 27

i made the assumption that it was true, based on the answer choices, and even suggested trying ti with numbers but didn't actually try it myself!

Answer 28

example \(234-(2+3+4)=225\)

Answer 29

options are somewhat misleading as there is no option with "3"
guess i would simply tick option a..

Answer 30

nothing like following your own advice

Answer 31

You learn something new every day :)

Answer 32

\(129-(1+2+9)=117\\
117\pmod 6=3\)