Question

If 31z5+51z3 is divisible by 3, where z is a digit less than 5. Values of z are
A.0.1
B.0,3
C.1,3
D.1,4

Answer 1

Hint: Here the sum of numbers given is divisible by 3 so we will Use divisibility test of 3. Because it will help in finding which digits will fit in that place.

Complete step-by-step answer:
Given that ,
31z5+51z3 is divisible by 3.
But the values of digit z are missing.
To find the value of digit z means completing the number.
It is already given that the addition of the numbers is divisible by 3.

Thus the addition is 82_8. The underscore here represents the sum of z placed digits.
Now, using the divisibility test of 3 we have to find the values of z.
Divisibility test of 3:
If the sum of the digits of the number is exactly divisible by 3 , then the whole number is exactly divisible by 3.
Now , the sum of digits already present is 8+2+8=18.
Since sum is 18 and it is exactly divisible by 3, the sum of z digits should be either 0 or multiple of z .
This simply eliminates option A,C and D. because the sum of those digits is neither 0 nor multiple of 3.
Sum of the digits is 3 and it is multiple of 3 also.
So option B is the correct option..

Note: Using divisibility test will make our work easy.
We can also add the digits of numbers separately and then can find the required value of z.