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If a number is multiple of 3, the the sum of its digits will be multiple of 3. Sum of digits of 31z5 = 3 + 1 + z + 5 = 9 + z  9 + z is a multiple of 3 and since z is a single digit  9 + z  is any one of 9, 12, 15 or 18 thus value of z is 0, 3, 6 or 9 respectively. Hence possible value of z is 0,3,6 or 9.
if a number is multiple of 3 then the sum of its digits is also a multiple of 3. Summ of digits of 24x = 2 + 4 + x = 6 + x 6 + x is a multiple of 3 which means 6 + x = 0 or 3 or 9 or 12.... but since x is a single digit the possible sum is 6 or 9 or 12 or 15 and hence value of x are 0 or 3 or 6 or 9 respectively. hence possible value of x = 0, 3, 6, or 9.
If a number is a multiple of 9 , then the sum of its digit will be divisible by 9. Sum of digits of 21y5= 2 + 1 + y + 5 = 8 + y 8 + y is a multiple of 9 when y = 1 (since y can only be single digit ) hence y = 1 is correct answer.
If a number is a multiple of 9, then the sum of its digit will be divisible by 9 . Sum of digits of 31z5 = 3 + 1 + z + 5 = 9 + z  hence 9 + z have to be multiple of 9  this possible when 9 + z = 0, 9 , 18, 27 ... since z is a single digit number this sum can only be 9 or 18 . therefore, z should be 0 or 9 . hence two possible values of z = 0 or 9.
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