Discussion
If you have two straight sticks of length 3.44 feet and 2.20 feet, what is the minimum length (in feet) that you can measure?
Answer: B
The minimum length is 0.04 feet.
With two sticks you can measure any length of the form \(3.44a + 2.20b\) for whole numbers \(a, b\) (laying sticks end to end, or one against the other). The smallest positive length obtainable that way is their highest common factor.
\[ \begin{aligned} \text{HCF}(344, 220) &= \text{HCF}(220, 124) \\ &= \text{HCF}(124, 96) = \text{HCF}(96, 28) \\ &= \text{HCF}(28, 12) = 4 \end{aligned} \]
So in feet the answer is \(4/100 = 0.04\). The value 0.4 is the same digits out by a factor of ten, and 0.2 or 0.1 cannot be built from 3.44 and 2.20 at all, since neither divides both lengths.
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