1952 AHSME Problems/Problem 43
Problem
The diameter of a circle is divided into equal parts. On each part a semicircle is constructed. As
becomes very large, the sum of the lengths of the arcs of the semicircles approaches a length:
equal to the semi-circumference of the original circle
equal to the diameter of the original circle
greater than the diameter, but less than the semi-circumference of the original circle
that is infinite
greater than the semi-circumference
Solution
Let our two digit number be . Its value is
. The number formed by interchanging its digits is BA and has value
.
Setting AB equal to
times the sum of the digits yields
We now must relate AB to BA. Note that
Using this in the first equation yields
Therefore,
is
times the sum of its digits and our answer is
.
See also
1952 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 42 |
Followed by Problem 44 | |
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