The 10-digit number 90457416xy is divisible by 9, and x - y = 3. What is the value of (5x + 3y)?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 39.
Divisibility rule of 9: if the sum of the digits of the number is divisible by 9, then the number itself is divisible by 9
Sum of digits: 9 + 0 + 4 + 5 + 7 + 4 + 1 + 6 + x + y
⇒ 36 + x + y .....(1)
⇒ x - y = 3
⇒ x = y + 3
Put in equation 1
⇒ 36 + x + y = 36 + y + 3 + y = 39 + 2y
⇒ 39 + 2y = 0
Try the value of y to make it divisible by 9;
For y = 3
⇒ 39 + 2 × 3 = 39 + 6 = 45 [divisible by 9]
⇒ x = y + 3
⇒ x = 3 + 3 = 6
The value of (5x + 3y) = (5 × 6 + 3 × 3) = 30 + 9 = 39