Question

if the number 2315Y7 is divisible by 9 find the digit Y
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Answer 1

$\LARGE{\underline{\bf{Required\: Answer :}}}$

GiveN:

• 2315Y7 is a multiple of 9.

To FinD:

• Value of Y?

Step-by-Step Explanation:

To find y, we should know the condition for divisibility of 9. The condition for divisibility of 9 is:

A no. is divisible by 9 if the sum of digits of the number is divisible by 9 or is a multiple of 9.

According to the above condition,

Sum of the digits in 2315Y7 should be divisible by 9.

⇒ 18 + y is divisible by 9.

Here y is a single digit, Then there are two chances of the number divisible by 9 is when:

⇒ 18 + y = 9

18 itself is a multiple of 9 and y will be 0 or 9 such that the sum of the digits will be 18 or 27. Hence,

$\huge{ \boxed{ \pink{ \sf{y = 0\: or\: 9}}}}$

Explore more!!!

Sometimes there can be multiple values of the unknown variable to be divisible by another number. In that case, we consider the least value of unknown variable if it is a multiple choice question.

Here we have two possibilities of Y. Hence, I have mentioned both the digits possible. In case of MCQ, we can tick the digit mentioned or the least of them.

Answer 2

Question

If the number 2315Y7 is divisible by 9. Find the digit Y.

Solution

Since the number 2315Y7 is divisible by 9.

So, the sum of its digit 2+3+1+5+y+7 = 18+y is a multiple of 9.

(18+y) is either 0 or 9 or 18 or ...

Since 9 is a digit, so (18+y) must be equal to 9.

i.e., 18+y = 9

Ans:- The value of y is 0 or 9.