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The reversed numbers (Posted on 2005-09-16) Difficulty: 2 of 5
Both a and b are four-digit numbers and one is obtained from the other by reversing the digits.

Determine them, knowing that 2 * (a + b) = 5 * (b - 1).

Show your reasoning.

See The Solution Submitted by pcbouhid    
Rating: 4.5000 (4 votes)

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Solution Two answers | Comment 5 of 7 |
The problem asks for a and b such that 2a=3b-5. Obviously, b must be odd so 3b-5 is even. Writing a=1000w+100x+10y+z we get 2000w+200x+20y+2z= 3000z+300y+30x+3w-5. Equating the larger terms, 2w=3z, which allows for w=3 or w=9 since w must be odd so b is odd.

If w=3, z=2, and the equality implies 170x=280y, so x=y=0, producing a=3002 and b=2003.

If w=9, z=6, and we et 170x=280y+10, so x=5 and y=3, giving a=9536 and b=6359.

  Posted by Old Original Oskar! on 2005-09-16 19:30:53
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