Finley’s friends all chipped in to buy her a wedding gift. At first, ten friends agreed to contribute the same amount. Then two “friends” dropped out. The remaining eight had to add another dollar each to cover the cost of the gift. How much did the gift cost?
Imagine an HIV test that is 95% accurate (false positive rate of 5%) and around 2% of the tested population is infected with HIV. What is the probability that you actually have HIV when your test comes back positive?
I hesitated to add this because it’s poorly worded, ambiguous and the answer could be almost anything. I prefer teasers with a single answer, but there you go.
If you came up with a different answer and can explain how you did it, don’t think you’re wrong. It’s probably just as valid. Feel free to share yours in the comments.
My answer for the first number is 2.
Here’s how I got it.
The generic rule for a number in the sequence is: 2^(n – 1) + 1, where n is the position in the sequence.
Note: The teaser doesn’t specify the position of 17. In this case, it’s fifth.
Position 1: (so n = 1) is 2^(1 – 1) + 1 = 2
Position 2: 2^(2 – 1) + 1 = 3
Position 3: 2^(3 – 1) + 1 = 5
Position 4: 2^(4 – 1) + 1 = 9
Position 5: 2^(5 – 1) + 1 = 17
For the curious, the next 5 numbers of the sequence would be:
Hans made a meandering journey from Paris to Roye. On the first day, he went half of the distance. On the second day, he went one third of the remaining distance. On the third day he went three quarters of the remaining distance. The next day he traveled half of the remaining distance and was left with 5 kilometers to get to Roye. How far was the entire journey?
Day 1 – 60 km (60 km remaining)
Day 2 – 20 km (40 km remaining)
Day 3 – 30 km (10 km remaining)
Day 4 – 5 km (5 km remaining)
Day 5 – 5 km (arrives in Roye)
On a remote (imaginary) island, there are 11 snakes and a single mouse. As you’d expect, snakes eat the mice. But contrary to what you’d expect, when a snake eats a mouse, it turns into one.
The snakes live by only two rules:
1. Don’t get eaten.
2. Eat mice as long as rule #1 isn’t violated.
How many snakes and mice will there be left on the island?