Question

If x and y are the two digits of the number 115 xy such that this number is divisible by 90, then the value of x + y is:

• A. 5
• B. 6
• C. 3
• D. 2

Answer 1

Answer:

D. 2

The value of $x + y$ is 2.

• Apply divisibility rule for 10:

  • For the number $115xy$ to be divisible by 90, it must be divisible by both 10 and 9.

  • A number divisible by 10 must end in 0. Therefore, $y = 0$.

• Apply divisibility rule for 9:

  • The number now becomes $115x0$.

  • For a number to be divisible by 9, the sum of its digits must be a multiple of 9.

  • Sum of digits = $1 + 1 + 5 + x + 0 = 7 + x$.

• Find the value of $x$:

  • The nearest multiple of 9 greater than 7 is 9.

  • $7 + x = 9 \implies x = 2$.

• Calculate $x + y$:

  • $x + y = 2 + 0 = 2$.