If x and y are two digits and the number 4x5y790 is divisible by 11, then what is the remainder, if x + y is divided by 11?

Question

If x and y are two digits and the number 4x5y790 is divisible by 11, then what is the remainder, if x + y is divided by 11?

1. A. 1
2. B. 3
3. C. 5
4. D. 7 (Correct answer)

Correct Answer

Option D — 7

Detailed Solution & Explanation

The correct answer is Option D (7).

Key Points

• For 4x5y790 to be divisible by 11, the alternating digit sum must be a multiple of 11: (4 + 5 + 7 + 0) − (x + y + 9) = 7 − (x + y).
• This is divisible by 11 when x + y = 7 (or 18); in both cases the remainder of (x + y) ÷ 11 is 7.

Additional Information

• The alternating-sum rule for 11 pins x + y ≡ 7 (mod 11), giving remainder 7 → Option D.