Question

If the number of 98y3 is divisible by 9, then the digit of y is

Answer 1

SOLUTION

GIVEN

The number of 98y3 is divisible by 9

TO DETERMINE

The value of y

CONCEPT TO BE IMPLEMENTED

Divisibility Rule of 9 :

A number is divisible by 9 if the sum of digits of the number is divisible by 9

EVALUATION

Here the given number = 98y3

Sum of the digits

= 9 + 8 + y + 3

= 20 + y

Now 98y3 is divisible by 9

⇒ Sum of digits is divisible by 9

⇒ ( 20 + y ) is divisible by 9

⇒ y = 7 [ Since y must be single digit ]

FINAL ANSWER

Hence the required value of y = 7

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Answer 2

If the number of 98y3 is divisible by 9, then the digit of y is 7.

Explanation:

• We know, the divisibility rule of 9 is,

⇒ If a number is divisible by 9 then the sum of all digits in the number should be a multiple of 9. For example: the number 8766 is divisible by 9 because $8+7+6+6 = 27$ which is a multiple of 9.

• Here, $98y3$ is divisible by 9. So,

      ⇒ $9+8+y+3$ should be multiple of 9.

      ⇒ $20+y$ should be a multiple of 9.

• For  $20+y$ to be a multiple of 9 , the sum should be equal to 27 as it is the nearest multiple which ca be obtained by adding this expression.

      ⇒ $20+y=27$

      ⇒ $y=7$

Hence, If the number of $98y3$ is divisible by 9, then the digit of y is 7.