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Question 4

If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?


Solution

Since  31z5 is a multiple of 3.
Therefore according to the divisibility rule of 3, the sum of all the digits should be a multiple of 3.
Since,  z is a digit.
3 + 1 + z + 5 = 9 + z
9 + z = 9 z = 0
If 3+1+z+5=12  
9+z=12z=3
If 3+1+z+5=15  
9+z=15z=6
If 3+1+z+5=18  
9+z=18z=9
Hence  0, 3, 6 and 9 are four possible answers.

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