If the 7-digit number 456x45y is divisible by 36, then find the value of (x + y) for the smallest value of y.
Correct Answer : c ) 3Explanation :
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
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
Hence, (c) is the correct answer.
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