1965 AMC 12 Problem 15

Attempt Problem 15 of the 1965 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 1965 AMC 12 solutions, or check the answer key.

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

15.

The symbol 25b25_b represents a two-digit number in the base b.b. If the number 52b52_b is double the number 25b,25_b, then bb is:
77
88
99
1111
1212
Answer: B
Concepts:number baseplace valuelinear equation
Small hint:
Translate 25b25_b as 2b+52b+5 and 52b52_b as 5b+25b+2
Big hint:
Solve 5b+2=2(2b+5)5b+2=2(2b+5)
Solution:
In ordinary notation, 25b=2b+525_b=2b+5 and 52b=5b+2.52_b=5b+2. Thus 5b+2=2(2b+5),5b+2=2(2b+5), so b=8.b=8.
Therefore, the correct answer is B.
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