If x is a digit such that the number 18x71 is divisible by 3, find possible values of x.
[3 marks]
[3 marks]
We know that the given number 18x71 is divisible by 3.
And, if a number is divisible by 3 then sum of digits must be a multiple of 3.
[0.5 mark]
i.e., 1 + 8+ x + 7 + 1 = multiple of 3
x + 17 = 0, 3, 6, 9, 12, 15, 18, 21, 24, 27,…..
[0.5 mark]
Now, first we will take x + 17 = 18 , because other multiples are less than x + 17
So, x + 17 = 18 , which gives x = 1.
x + 17 = 21, which gives x = 4.
x + 17 = 24, which gives x = 7.
∴ x = 1, 4, 7
[0.5 × 3 = 1.5 marks]
We can not take next multiple of 3 because in that case x will be a two digit number which is not possible.
[0.5 mark]
We know that the given number 18x71 is divisible by 3.
And, if a number is divisible by 3 then sum of digits must be a multiple of 3.
[0.5 mark]
i.e., 1 + 8+ x + 7 + 1 = multiple of 3
x + 17 = 0, 3, 6, 9, 12, 15, 18, 21, 24, 27,…..
[0.5 mark]
Now, first we will take x + 17 = 18 , because other multiples are less than x + 17
So, x + 17 = 18 , which gives x = 1.
x + 17 = 21, which gives x = 4.
x + 17 = 24, which gives x = 7.
∴ x = 1, 4, 7
[0.5 × 3 = 1.5 marks]
We can not take next multiple of 3 because in that case x will be a two digit number which is not possible.
[0.5 mark]
