Question

if 34x is a multiple of 3 , where x is a digit, what is the value of x?

Answer 1

Divisibility Rule of 3=The sum of the digits should be divisible with 3.
There are many possible answers but here's one.
34x=7x
So 7 must be added to 2 to make 9 which is divisible by 3.
x=2
Hope This Helps.

Answer 2

If a number is a multiple of 3, then the sum of it's digits is a multiple of 3.
So you can substitute anything in the place of x to get the sum of digits a multiple of 3.
We can do trial and error
For 0:
3 + 4 + 0 = 7      No
For 1:
3 + 4 + 1 = 8      No
For 2:
3 + 4 + 2 = 9      Yes
For 3 :
3 + 4 + 3 = 10    No
For 4:
3 + 4 + 4 = 11    No
For 5:
3 + 4 + 5 = 12    Yes 
For 6:
3 + 4 + 6 = 13    No
For 7:
3 + 4 + 7 = 14    No 
For 8:
3 + 4 + 8 = 15    Yes
For 9:
3 + 4 + 9 = 16     No
We can see a definite pattern here too..
All you have to do is to check for the digits 0,1,2.
The given number will definitely satisfy any of the mentioned digits.
If it satisfies any one of the mentioned three, add three to the number the number to get the next number.
Remember, it is applicable only till 9.

∴ x = 2 (or) 5 (or) 8.


Hope my answer helps you..