The digits 1 to 9 are arranged in three rows in such a way that each row contains three digits, and the number formed in the second row is twice the number formed in the first row; and the number formed in the third row is thrice the number formed in the first row. Repetition of digits is not allowed. If only three of the four digits 2, 3, 7 and 9 are allowed to use in the first row, how many such combinations are possible to be arranged in the three rows?
A
4
B
3
C
2
D
1
Correct Answer: Option C
Explanation
1. **Understand Constraints:** We need three 3-digit numbers using digits 1-9 exactly once. Row 2 = $2 \times$ Row 1; Row 3 = $3 \times$ Row 1. Row 1 uses only digits from {2, 3, 7, 9}.
2. **Apply Bounds (The Elegant