If the 9-digit number 45069x4y8 is divisible by 44, then what is the value of (x – 2y) for the minimum value of y?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 3.
44 = 11 × 4
Divisibility rule of 4: the last two digits are divisible by 4
⇒ y8 ÷ 4
⇒ y = 0 [minimum]
Divisibility rule of 11: If the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or divisible by 11
⇒ (4 + 0 + 9 + 4 + 8) - (5 + 6 + x + 0)
⇒ 25 - 11 - x = 0, 11
⇒ 14 - x = 0, 11
⇒ x = 3
⇒ (x – 2y) = (3 - 2 × 0) = 3