Difference between revisions of "1965 AHSME Problems/Problem 15"
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− | + | == Problem == | |
+ | |||
+ | The symbol <math>25_b</math> represents a two-digit number in the base <math>b</math>. If the number <math>52_b</math> is double the number <math>25_b</math>, then <math>b</math> is: | ||
+ | |||
+ | <math>\textbf{(A)}\ 7 \qquad | ||
+ | \textbf{(B) }\ 8 \qquad | ||
+ | \textbf{(C) }\ 9 \qquad | ||
+ | \textbf{(D) }\ 11 \qquad | ||
+ | \textbf{(E) }\ 12 </math> | ||
+ | |||
+ | == Solution == | ||
+ | |||
+ | We begin by noting that <math>25_b = 2b+5</math> and <math>52_b = 5b+2</math>. The problem tells us that <math>2*25_b=52_b</math>, so <math>2(2b+5)=5b+2</math>. Solving for b yields the answer <math>\boxed{\textbf{(B) }8}</math>. | ||
+ | |||
+ | ==See Also== | ||
+ | {{AHSME 40p box|year=1965|num-b=14|num-a=16}} | ||
+ | {{MAA Notice}} | ||
+ | |||
+ | [[Category:Introductory Number Theory Problems]] |
Latest revision as of 16:58, 18 July 2024
Problem
The symbol represents a two-digit number in the base
. If the number
is double the number
, then
is:
Solution
We begin by noting that and
. The problem tells us that
, so
. Solving for b yields the answer
.
See Also
1965 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.