Difficult elementary school math problems

Many math problems are fascinating. Often they are also difficult, so that only those who have high enough education can understand their beauty. But sometimes a really simple problem – such that anyone with just the elementary school knowledge can solve it – can be quite cute as well. Most elementary school math questions are truly boring, but it’s possible to add some spice to this mass.

1 (I knew this earlier) “Dried cucumbers”:
Cucumber contains 99% of water. A box of cucumbers weighs 100kg. During winter storage, cucumbers dried out so that they now contain only 98% of water. How much does the box weigh now?

2 (I got this today, which inspired me for this post) “Probability for doctors”:
Assume a test for a rare disease (which affects 1 person in a million) is 99.99% accurate. A patient tests positive. What are the probabilities he actually has the disease?

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