The Trickiest 1% Question: In a room of 100, 99% are left-handed. How many must leave to get 98%?

In a room of 100 people, 99% are left-handed. How many left-handed people have to leave the room to bring that percentage down to 98%?

This question is from an Instagram reel by the page The 1% Club (also a TV show). They claim only 1% of people can get this question right in 30 seconds. Frankly, I thought the answer was 1 at first, but after a more careful thought for about 10 seconds, I got it and saw why this was a very tricky and counter-intuitive question.

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#math #algebra #1percentclub

[bprpmathbasics]

1 ÷ 0 = 0? (a 3rd grade teacher & principal both got it wrong), Reddit r/NoStupidQuestions

[avinotion]

I'm glad to see that a lot of people didn't go through the entire process, and rather know or have come to the conclusion that in order to double the percentage of right-handed people, you need to halve the total number.

[brianwade]

I thought about it like this. At the beginning there is one right-handed person in the room. How many left-handed people do I need for there to be 2% right-handed people in the room? Clearly I need 49. Therefore I have to remove 50 left-handed people. I did all this in about 5 seconds.

[Starchaser]

50 people. That stumped me for a hot minute before i realized what happens when you remove a person.

[Crazy-mxdc]

I thought about it like this:
When you want 100 people with 98% left handed, you need 98 left handed and 2 right handed people.
Then I divided both by two so there’s only one right handed person. That left me with 49 left handed people.
And 99-49=50, so 50 left handed people have to leave.

[StephenMarkTurner]

The small change from 99 to 98 obscures the large relative change from 1 to 2. This is a good general lesson.

[sassymuffinzzz]

This is the first one on your videos that I figured out immediately. My brain went to one person is 1% in the initial scenario, so for someone to be 2% of the group there would need to be half the total people.

[Violaetor]

Quick intuitive approach - equation balancing, you want to double the number of right handed people, inversely, you need to half the number of left handed.

[zdhshue]

Percentage = x/ (x+1), set percentage to 98/100 which is = to 49/50=x/(x+1), x ist equal to 49. So 50 left handed ppl had to leave since 99-50 is 49

The multi marker skills are impressive

[SaucyCinemaFilm]

Go in the opposite direction: start with 1 right-handed person. How many lefties do you need to bring in to the room to get to a ratio of 100:2 (given that the max number of righties is 1)?

[adamsmith]

Easier mathematical manipulation if you recast as right-handed percentage. 1 right-handed person in the room with 99 left-handed is 99% left handed or 1% right handed. So to go down to 98%-left is to go up to 2%-right. Equation is almost the same but much quicker to solve since there is always 1 right handed peron and "x" left-handed people need to leave ther room

1/(100-x) = 0.02 Note it is easier if you recall that 0.02 = 2/100 = 1/50

1/(100-x) = 1/50 So 100-x = 50. x=50

[mamta]

It feels good to be a part of that 1% club

[teelo]

50. Had to pull out a calculator and guess-and-check. Never would have been able to figure that out on the spot on a gameshow.

[jorggradert]

Only one person right handed. 2% right-handed = 1/50 so 50 left-handed have to leave the room.

[FundamSrijan]

Better method to solve that algebra -
(99-x) / (100-x) = 98/100
Add and subtract 1 from 99 - x
(100-x-1) / (100-x) = 98/100
[(100-x) / (100-x)] - [1/(100-x)] = 98/100
1 - 1/(100-x) = 98/100
1 - 98/100 = 1/(100-x)
(100-98)/100 = 1/(100-x)
2/100 = 1/(100-x)
1/50 = 1/(100-x)
50 = 100-x
x = 100-50 = 50 Ans.

[CoffeeSipper]

I solved it in 10 seconds:

If they are 100 people every person is 1%, half of those and every person equals 2% so they need to be 49 out of 50.

[monroeclewis]

I solved it mentally with algebra. The hardest part was remembering the numbers, keeping them in mind. Here ‘s the equation: 99–x/ 100–x = 98/100. It took me more than 30 seconds to do it, though. Still, not bad for an octogenarian!

[tchevrier]

I used a slightly different method.
99 are left handed so that means 1 is right handed. 1 out of 100 equals 1%
1 out of 50 total equals 2%. That means 50 less Total people.

[nickcellino]

Another problem is asking how to bring the percentage down to 96%. The answer is 75 left-handed people must leave the room leaving 1 right-handed person and 24 left-handed people. 24 out of 25 is 96%. The easier way to calculate this is to concentrate on the number of right-handed persons which is always one. 1=4x/100 which equals 25 so there are 24 left-handed and 1 right-handed so 75 of 99 left-handed must leave the room. In the problem given the equation would be 1=2x/100 which equals 50 so there is 1 right-handed and 49 left-handed (49 out of 50 is 98%) so 50 left-handed must leave the room. This math is easier than what is shown.