Question

54Z leaves remainder 2 when divided by 5 , and leaves remainder 1 when divided by 3, what is the value of Z?
[3 marks]

Answer 1

Case: 1
We know, if the unit digit of a number is 0 or 5, then it is divisible by 5.
According to the question, 54Z leaves remainder 2 when divided by 5.
Therefore, Z can either be 0 + 2 = 2 or 5 + 2 = 7.
[1 mark]

Case: 2
We know, if sum of the digits of a number is divisible by 3, then the number itself is divisible by 3.
According to the question, 54Z leaves remainder 1 when divided by 3.

For Z = 2, 54Z = 542
And 5 + 4 + 2 = 11
11 leaves a remainder of 2 when divided by 3 because 3$\times$3 = 9
[1 mark]
.
For Z = 7, 54Z = 547
5 + 4 + 7 = 16
16 leaves a remainder of 1 when divided by 3, because 3$\times$5 = 15.
[1 mark]

So, the value of Z is 7.