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Column Bases (Posted on 2004-12-15) Difficulty: 3 of 5
All of the following relationships are correct, except one. Determine the wrong answer and explain why the others are correct.
A) 5612 ~ 1475
B) 4657 ~ 1210
C) 4326 ~ 1080
D) 2474 ~ 755
E) 1781 ~ 737

See The Solution Submitted by Juggler    
Rating: 2.0000 (2 votes)

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Solution Second Stab | Comment 2 of 7 |
B is the wrong answer. 
For the first group of numbers, let the "thousands" column be base 6, the "hundreds" column be base 8, the "tens" column be base 9, the the ones column can be anything greater than 7.

Then the first column translates to the second column perfectly except for B):
A) 5612 ~ 1475  
B) 4657 ~ 1300
C) 4326 ~ 1080
D) 2474 ~ 755
E) 1781 ~ 737



For example:
5612 ---> 5*6^3 + 6*8^2 + 1*9 + 2 = 1475 in decimal
4657 ---> 4*6^3 + 6*8^2 + 5*9 + 7 = 1300 in decimal
4326 ---> 4*6^3 + 3*8^2 + 2*9 + 6 = 1080 in decimal
2474 ---> 2*6^3 + 4*8^2 + 7*9 + 4 = 755 in decimal
1781 ---> 1*6^3 + 7*8^2 + 8*9 + 1 = 737 in decimal

Edited on December 15, 2004, 8:43 pm

Edited on December 15, 2004, 8:44 pm

Edited on December 15, 2004, 8:45 pm
  Posted by Larry on 2004-12-15 20:38:22

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