#5**+1 **

^{There was a flat containing boxes of apples having a total weight of 100 kg. An analysis showed that the apples were 99% moisture, by weight. After two days in the sun, a second analysis showed that the moisture content of the apples was only 98%, by weight. What was the total weight of the apples after 2 days, in kg?}

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My statistics professor often posed questions like this to reinforce the importance of paying attention to how a question presents data and correctly interpreting data that results from analysis.

**Solution:**

\(\text {The first analysis shows the apples are 99% water. The weight of the water is then}\\ \left(0.99\cdot 100\right) = 99 ~ kg\\ \text {Let x be the weight of the water lost after exposure to the sun. }\\ \left(0.99 \cdot 100-0.98(100-x)\right)=x\\ \begin{aligned}99-(98-0.98x)&=x\\99-98+0.98x&=x\\1+0.98x&=x\end{aligned}\\ \begin{aligned}1+0.98x-0.98x&=x-0.98x\\1&=0.02x\\x&=50\\\end{aligned}\\ \text { }\\ 100-x=100-50=50 ~ kg \leftarrow \text { The total weight of the apples after 2 days}\\\)

The correct solution appears paradoxical. It’s not, but it is counter-intuitive.

This question is known as the * Potato Paradox*. We genetically enhanced Chimps refer to it as the

GA

GingerAle
12-sep-2018