Problem: The symbol 25b25_{\mathrm{b}}25b represents a two-digit number in the base bbb. If the number 52b52_{\mathrm{b}}52b is double the number 25b25_{\mathrm{b}}25b, then bbb is:
Answer Choices:
A. 777
B. 888
C. 999
D. 111111
E. 121212 Solution:
52b=5 b+2,25b=2 b+552_{\mathrm{b}}=5 \mathrm{~b}+2,25_{\mathrm{b}}=2 \mathrm{~b}+552b=5 b+2,25b=2 b+5. Since 52b=2(25b),5 b+2=2(2 b+5)∴b=852_{\mathrm{b}}=2\left(25_{\mathrm{b}}\right), 5 \mathrm{~b}+2=2(2 \mathrm{~b}+5) \therefore \mathrm{b}=852b=2(25b),5 b+2=2(2 b+5)∴b=8