Easy math puzzles

Quote: unJon

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What makes you think Tom is saying two ties is 2t and not t^2? It’s the same answer since t=2

Good point. However, I'm sticking with my answer, but admit it is subject to interpretation.

Quote: unJon

This one will be truly easy for those on this forum, but it’s an old classic and I used to use it as an interview question (updated for the current crisis):

With 10% of the population having COVID-19, the world is in extreme crisis. Thankfully, a new Pharma company has just created an instant COVID-19 test that is 90% accurate. World leaders have mandated that everyone take the test in the hopes this will enable the virus to finally be contained. You dutifully show up at Walmart (wearing your N95 mask and staying six feet away from everyone else) to get tested in the pharmacy. Bad news: the test is positive for COVID-19.

What is the probability you actually have COVID-19?

This is a classic problem in conditional probability.

I never liked the "picture equations", because...

Quote: Wizard

This is a classic problem in conditional probability.

I never liked these either, because you have to assume that the condition for which you are testing is uniform - in this case, the probability that you have COVID-19 is 10%.

I punted on the symbols problem from the very beginning, because I thought there were just too many ways to interpret the combinations of symbols.

Suppose that you could determine that a shoe represents the number 5. Do two shoes right beside each other represent 2*5 = 10, or 5*5 = 25, or a double-digit-symbol = 55? With that much ambiguity in the symbols -- even without the hidden shoes and straps added to the man (which I didn't see) -- I just thought the numerous ways to reverse-interpret a set of equations was not something I wanted to try.

Quote: Doc

I punted on the symbols problem from the very beginning, because I thought there were just too many ways to interpret the combinations of symbols.

Suppose that you could determine that a shoe represents the number 5. Do two shoes right beside each other represent 2*5 = 10, or 5*5 = 25, or a double-digit-symbol = 55? With that much ambiguity in the symbols -- even without the hidden shoes and straps added to the man (which I didn't see) -- I just thought the numerous ways to reverse-interpret a set of equations was not something I wanted to try.

Almost always, two symbols = 2 x one symbol in these.

Except for this most recent one and the joke in the bottom line, aren't these picture puzzles just designed to start fights about order of operations? They lay out 3 items of various values, then combine them on a line with both + and * operations. Apparently there's a big age-based divide there, with PEMDAS being replaced by a left-to-right approach.

Answer: 30

LOL, I went from the first puzzle straight to the last post.

Time for a fresh problem.

A rectangle bisects a cylinder, going through the center of the bottom and top. The perimeter of the rectangle is 6. What is the maximum volume of the cylinder?

I will show the working out, if this is correct.
Note: I had "two answers" and this one seemed the most likely to me

Edit (about 3 pm):
I think the answer by the Joeman below is lot better than mine, because:
1. He found the answer more efficiently than me (I used a "trial and error" type of way),
2. He can prove that his answer is correct with a formula/method.