Question 2
If 31z5 is a multiple of 9, where z is a digit, what is the value of z?
You will find that there are two answers for the last problem. Why is this so?

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Solution

Since, 31z5 is a multiple of 9.
Therefore according to the divisibility rule of 9, the sum of all the digits should be a multiple of 9.

$∴ 3 + 1 + z + 5 = 9 + z \Rightarrow 9 + z = 9, 18, 27....... \Rightarrow z = 0 o r z = 9$
Hence 0 and 9 are two possible answers.
Hence 3105 and 3195 both are multiple of 9

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If 31z5 is a multiple of 9, where z is a digit, what is the value of z? [2 MARKS]

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Divisibility by 9

Standard VIII Mathematics

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Question 2 If 31z5 is a multiple of 9, where z is a digit, what is the value of z? You will find that there are two answers for the last problem. Why is this so?

Since, 31z5 is a multiple of 9. Therefore according to the divisibility rule of 9, the sum of all the digits should be a multiple of 9. ∴3+1+z+5=9+z⇒9+z=9,18,27.......⇒z=0or z=9 Hence 0 and 9 are two possible answers. Hence 3105 and 3195 both are multiple of 9

Question 2
If 31z5 is a multiple of 9, where z is a digit, what is the value of z?
You will find that there are two answers for the last problem. Why is this so?