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False Positive HIV Test

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?

29%

To read more about this, see the False Positive Paradox page on Wikipedia.

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Paula and Quincy

Paula had four times the money that Quincy had, but after Paula gave Quincy $33, Quincy had 3 times as much as Paula.

How much did they each start with?

Paula had $48 and Quincy had $12.

If Q is the amount Quincy had, then 3(4Q – 33) = Q + 33

Solved, Q = 12.

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How to Save Gas

If you could chose to increase the average fuel economy of a car, which of these would save the most fuel?

1. 10mpg -> 12mpg
2. 12mpg -> 15mpg
3. 15mpg -> 20mpg
4. 20mpg -> 30mpg
5. 30mpg -> 60mpg

It turns out they all save the same amount of fuel.

If you travel 100 miles:

100 / 10 = 10 gallons used
100 / 12 = 8 1/3 gallons used

10 – 8 1/3 = 1 2/3 gallons saved

100 / 30 = 3 1/3 gallons used
100 / 60 = 1 2/3 gallons used

3 1/3 – 1 2/3 = 1 2/3 gallons saved

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All Words From Nine Letters to One

What 9-letter word can have a letter removed to make a new word and repeat the process until a single letter remains?

startling
starting
staring
string
sting
sing
sin
in
i

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You’re Halfway There

You’re standing 11 feet away from a doorway and with each step you move halfway to the doorway. How many steps will it take for you to get to the doorway?

Technically, the answer is infinity. If you keep going halfway, you’ll never actually make it to the doorway.

But in practice, after 10 steps you’ll be 1/8th of an inch to the doorway and anyone behind you would say to stop being a baby and take a real step through the doorway already.

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Dry As a Bone

Milton was out for a walk when it started to rain. He did not have an umbrella and wasn’t wearing a hat. His clothes were soaked, yet not a single hair on his head got wet. How did this happen?

Milton sadly suffers from alopecia, more commonly known as baldness. The old coot was as bald as a ping pong ball, leaving not a single hair on his head to get wet.

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Finley’s Flaky Friends

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?

$40.

Let x be the amount the ten friends initially agreed to pay. We can then make the following equation:

10x = 8x + 8

Solving for x gives us $4, thus the gift cost 10 × $4, or $40.

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How to Stay Dry?

A group of ten people are going out for pizza but only two of them have an umbrella to keep them dry. Somehow they are able to walk all the way to the pizza place without getting wet. How?

It’s not raining.

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The 22nd and 24th Presidents of the U.S.

The 22nd and 24th presidents of the United States of America had the same parents, but were not brothers. How is this possible?

It was the same guy! Grover Cleveland is the only president in history to serve two, non-consecutive terms.

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Kevlar, Fire Escapes and Wipers, Oh My!

What do computer compilers, kevlar, fire escapes and windshield wipers all have in common?

They were all invented by women.

A variation of this brain teaser includes laser printers (they were invented by Gary Starkweather) and bulletproof vests (invented by Casimir Zeglen using silk, though modern vests use Kevlar, so it’s halfway right).

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