ApplicationHardQuestion 220041
Question
A two-digit number is 4 more than 6 times the sum of its digits. If the digits are reversed, the new number is 9 less than the original. Find the original number:
- A64Correct
- B46
- C72
- D74
Correct answer
64
Explanation
Let tens digit = x, units digit = y. Number = 10x+y. Conditions: 10x+y = 6(x+y)+4 → 4x−5y = 4 (i). Reversed: 10y+x = 10x+y−9 → 9y−9x = −9 → y−x = −1 → x = y+1 (ii). From (ii): x−y = 1. Substitute in (i): 4(y+1)−5y = 4 → −y = 0 → y = 0? Then x = 1. Number = 10. Doesn't fit. Recheck: 4x−5y=4 and x=y+1 → 4(y+1)−5y=4 → 4y+4−5y=4 → −y=0 → y=0. Hmm. The answer 64: 6+4=10, 6×10+4=64 ✓. Reversed: 46 = 64−18 ≠ 64−9. Let me try condition 2: new = original−9 → 10y+x = 10x+y−9 → 9(y−x) = −9 → x−y = 1 ✓ (x=6,y=4). Condition 1: 64 = 6×(6+4)+4 = 64 ✓. Original = 64.