1969 AMC 12 Problem 3

Attempt Problem 3 of the 1969 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1969 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

3.

If N,N, written in base 2,2, is 11000,11000, the integer immediately preceding N,N, written in base 2,2, is:
1000110001
1001010010
1001110011
1011010110
1011110111
Answer: E
Concepts:number baseplace valuewhole number operations
Small hint:
Subtract 11 from the binary number
Big hint:
Borrow through the three trailing zeros
Solution:
Subtracting 11 from 11000211000_2 requires borrowing through the three trailing zeros. Thus 110002−12=101112. 11000_2-1_2=10111_2.
Therefore, the correct answer is E.
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