Divisibility Rule of 4 and 9

Question of The Day28-06-2021

If the 7-digit number 456x45y is divisible by 36, then find the value of (x + y) for the smallest value of y.

Answer

Correct Answer : c ) 3

Explanation :

According to the question

456x45y is divisible by 36

The prime factorization of 36 - 2² x 3³

⇒ The number should be divisible by the factors of 36

⇒ Factors of 36 = 4 and 9

⇒ 456x45y is divisible by 4 and 9

Divisibility rule of 4

If the last 2 digits are divisible by 4 then the number is divisible by 4

Last 2 digit of the number = 5y

The values of y for which 5y is divisible are 2 and 6. Let's consider the smallest value 2.

⇒52 is divisible by 4

⇒ y = 2

⇒ Number becomes 456x452

Divisibility rule for 9

If the sum of the digit is divisible by 9 then the number is divisible by 9

⇒ Sum of the digits of the number = 4 + 5 + 6 + x + 4 + 5 + 2

⇒ 26 + x

Since 26 + 1 = 27 is divisible by 9

⇒ x = 1

⇒ Value of (x + y) = 1 + 2

⇒ 3

Hence, (c) is the correct answer.

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