Question

consider all 6 digit numbers comprising only 3's and 4's .how many of this number are multiples of 12​

Answer 1

Given :   all 6 digit numbers comprising only 3's and 4's .

To find : how many of these number are multiples of 12​

Solution:

all 6 digit numbers comprising only 3's and 4's

number are multiples of 12​

=> numbers are divisible by 12

Mean numbers are divisible by 3  & 4

If the last two digits of a whole number are divisible by 4, then the entire number is divisible by 4

Hence last two Digits  has to be  44   as 33 , 34  & 43 is not divisible by 4

Divisibility rule of  3  Sum of Digits should be  Divisible by   3

Case 1 : 3 + 3 + 3 + 4 + 4 + 4   = 21  Divisible be  3

first 4 Digits by 3 , 3 , 3 , 4   ( as last two Digits are fixed)

these can be 4 numbers -

333444  , 334344 , 343344 , 433344

Case 2 :  4 + 4 + 4 + 4 + 4 + 4  = 24  Divisible by 3

Hence 444444  is only number

so total possible numbers = 5

5 numbers out of  all 6 digit numbers comprising only 3's and 4's  are multiples of 12

333444  , 334344 , 343344 , 433344 , 444444

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