20 is 20% smaller than 25. 25 is 25% larger than 20.
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Posted Mar 16, 2021, 2:47 PM UTC
3.7K117
So many people miss OP point it’s a bit frustrating
Edit: original top comments have been downvoted to oblivion
Edit2: wow TIL that there are several interesting ways to find out all possible combinations, I’m so impressed with all of the contributors
Original noob calculation:
The example above has 0 relation with “x of y = y of x”. This will yield 3 set of numbers but OP has only 2 set: 25 and 20
First and second are
X = Y * (1-X/100)
Y = X * (1+Y/100)
However these 2 equations are actually the same. Hence, there are multiple (but very constrained) set of number that can satisfy the statement above
50 is 50% smaller than 100. 100 is 100% bigger than 50
However, with the formula above, you will see that you cannot just pull random number like “100” and “30”. Hence, it is not x of y = y of x
If you still don’t get it: try repeating OP wording above with just 2 numbers and you will realise it’s impossible unless you use the formula above
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Interestingly, these two examples seem to be the only ones that satisfy this equation (if we constrain ourselves to integers between 0 and 100). I wrote this messy java program to confirm.
public static void main(String[] args){
for(float i = 1; i <= 100; i++){
for(float j = 1; j <= 100 ; j++){
if(i * (1-(j/100)) == j && j * (1+(i/100)) == i ) System.out.print("["+ j + ";" + i + "]");
}
}
}
Which prints:
[20.0;25.0][50.0;100.0]
30
That is awesome, I did paper calculation and I agree these are the only 2 possible positive integer sets
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Any above 100?
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75 and 300 is the only other set that I was able to find under 1.000.000, but a clever algorithm that does not brute force the results can probably search a much bigger space.
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y - xy/100 = x
100y - xy = 100x
xy - 100y + 100x = 0
xy - 100y + 100x - 10000 = -10000
(x-100)(y+100) = -10000
since 10000 has 23 factors there are 45 possible integer solutions
23
Line 3 should have +100x but this is a really interesting way to find out all numbers!
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Fixed it
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There are 13 non-negative integer solutions:
0 0
20 25
50 100
60 150
75 300
80 400
84 525
90 900
92 1150
95 1900
96 2400
98 4900
99 9900
This is also: 0 <= X < 100, Y = 100*X / (100 - X)
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Thanks for the clarity.
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Sir, this is a Wendy's.
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GME to the moon yet?
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Reminding me of finite math in high school. There are times you can’t remember the formula, but if you understand the concept enough, you can use the simpler examples and extrapolate from there and reverse engineer the formula, if that makes any sense.
I would just plug number like 1,2 and 10 into what I thought was the right formula and if it doesn’t balance, see how far off my answer is from the expected answer and then tweak it until everything adds up.
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That's a perfect example of shower thought :)
Nothing new discovered, unnecessary for life but enlightening inside.
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Not unnecessary though. Very big deal in the stock market.
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I fully agree.
But for some reason, the mods didn't think so :(
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“Eleven plus two” is an anagram of “twelve plus one”.
-Lemino.
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What the FUCK is this shit why wasn't I told about this my life is based on LIES and SECRECY
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And Friday the Thirteenth is an anagram for " Dearie The Thrifty Nth "
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What kind of math fuckery is this?
(Seriously, though, the amount of people that don't understand this is astounding.)
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You are 100% correct.
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That is 100% greater than 50% correct.
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Looking at the comments, I understand now how some people find the SATs hard.
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It was definitely hard to pass when for 6 years straight of school you had math teachers who wanted to "grade as a group" and spend the last 5 minutes of class trying to speed teach the lesson.
Principals at both schools did, nothing. I single handedly made a math teacher quit Sophomore year for telling her how useless and incompetent she was and how she's wasting our time like a sack of shit. The replacement math teacher was even worse than her.
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guys guys listen
20% of 25 is 5, so 20 is 20% smaller than 25 (25-5)
25% of 20 is 5, so 25 is 25% bigger than 20 (20+5)
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Thats why losind 30% of 100k isn't the same as earning 30% off of 70k.
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Wow. Legit amused by this. Good work op
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90 is 90% smaller than 900, 900 is 900% larger than 90.
40 is 40% smaller than 66 2/3, 66 2/3 is 66 2/3% larger than 40.
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I think about stuff like this all the time. It’s so different sounding when you compare fractions and decimals and percent. It’s billed as the easy math we learned in grade school, then they use it to rip us off the rest of our lives. All ads hope to do this.
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too high to understand
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This is why I failed math
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20% of 25 is 25% of 20.
X% of Y is Y% of X.
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But the only reason the OP works is because 20% of 25 is also equal to 25-20. ie. (25, 20) is a solution to xy=100(x-y). If we rearrange to (x+100)(y-100)+10000=0 you can see there are finitely many integer solutions, all of which correspond to factors of 10000.
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I was just posting another fun fact with percentages. :-)
That's really interesting!
Here are all of the positive solutions:
https://www.wolframalpha.com/input/?i=%28x%2B100%29%28y-100%29%2B10000%3D0
x == 0, y == 0
x == 25, y == 20
x == 100, y == 50
x == 150, y == 60
x == 300, y == 75
x == 400, y == 80
x == 525, y == 84
x == 900, y == 90
x == 1150, y == 92
x == 1900, y == 95
x == 2400, y == 96
x == 4900, y == 98
x == 9900, y == 99
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Yep, this is different from X% of Y = Y% of X. It's actually Y - X% of Y = X (X is Y minus X% of Y) which when re-arranged give that equation you gave (with of course % -> /100).
The "less than" and "more than" parts is what make this special, most people are just reading it too quickly and assuming it's the same.
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Anyone else just nod in agreement, because you’re too lazy to do the math yourself?
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I think almost everyone is capable of verifying this as they read the sentence since the numbers involved divide really nicely
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Still too lazy to do that much numbers in my head
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It's a maths troll!
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Exactly. And this comes up with investment all the time, especially during a down turn.
If you have $100 and lose 20% of it, you are down to $80. Then it goes up 20%, now you have $96.
You lost 4% overall, but everyone will party and celebrate like making %20 was the greatest thing ever.
True story, check out 2019, and all the people bragging about their huge yearly gains. They ignore the 20% drop in Dec 2018.
Went over to 2019 and there was a lot but yea checked it out
r/2019
That is a wild subreddit. Created in 2011, and it's not about shitposting before covid/2020 like I was expecting.
Yes, but this doesn't take into account the magic of rebalancing. Most large investors are not solely invested in stocks. They'll do something like 50/35/15% in stocks, bonds and alternatives. When equities fall relative to the rest of the portfolio, they sell bonds and buy more stocks. When stocks go up, they liquidate those positions and shift money to bonds.
In a scenario where stocks go up one year, then down the next, this means that you're continuously buying at the bottom and selling at the top. Rather than losing money, a rebalanced portfolio can actually pump extra returns from a sideways up-and-down market.
Another way to think about this is to imagine a hypothetical investment that in any random year either doubles or falls in half. Naively, you'd think this isn't a very good investment. Over the long run the halving years will cancel out the doubling years. But what you can do is keep one quarter of your total wealth invested. When it doubles, take money out. And when it halves put money back in. Over any 25 year period, you'll make money nearly 90% of the time, with median return of 600%+ on your initial investment.
That’s a really clear and insightful explanation!
The only metric that counts is the “current portfolio value” in relation to “amount of cash invested”.
The value the portfolio had yesterday is irrelevant if you did not sell anything.
Yes. A stock I have dropped 25 % over a few days (ouch, and no, not gme or any of those) and have slowly gone back up so now I am only down 10 % of my invested money compared to current value.
But simce nothing is sold, I have actually lost no money (yet)
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I thought...everybody knew this.
Or F me I guess to read the 10-15 classics including Fooling people all the time and the Extraordinary delusional people and madness of crowds and all the rest modern takes on pump and dumps like Tim Sykes dvds.
Damn I wish we would get back the old wsb before 500k sub not this brainwashed idiots straight from r/politics who manage to explain everything with false or fake info.
Fuck me when I mentined about my gas short position with 100x leverage it was removed because I said Fuck in in. But everybody agrees to buy gme and if you disagree you a bot or hedge fund(??????).
It went from idiots who understand the conundrum on betting on the unpredictable future to buy ONLY this one stock. Fuck jnug. Fuck all the etfs. Fuck gas, oil gold, fuck all the best penny stocks in the last 10 years playing them up AND down. Fuck 1000% move in a day. Just gme gme gme.
Seriously FUCK THAT SUB.
You uh... You okay, bud?
You have done an excellent job at wasting my time.
I feel you man. I was a member too long before the GameStoppening. I miss all the loss porn.
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