Harvard University Admission Entrance Exam Tricks.
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- Опубликовано: 8 фев 2025
- This is an interesting question with amazing concepts!
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This is one of those problems where the powers of 2 up to the 32nd power come handy to know, especially when all computing is based on binary language.
I love the way you divide and conquer when multiplying. I never learned that method. We just did it straight on. Your method is better.😊
1024x1024 is much faster to calculate than writing (1000+24)^2 and simply multiple with (10+5). Done in 3 min instead 7 min.
Good, step by step calculation, no calculator but with much time and patience.
I appreciate your feedback! 👍
(4×16)^4_16^5=16^2×16^4-16^5=16×16^5-16^5=16^5(16-1)=16^5×15=15 728 640. Меньше преобразований и быстрее решается.
I think there is an easier solution approach. This reduces to 15* (16^5), if you group the expression in powers of 16.
Came to say this. The solution give in the video is way to complicated
That was impressive. You gave me a new way to figure out these types of equtions that I never thought of. It looked like it would be a lot faster than the method I would have used. It has been over 40 years since I took math course and I rarely do math by hand any more.
Thanks
Harvard University Admission Entrance Exam: 64⁴ - 16⁵ =?
64⁴ - 16⁵ = (4³)⁴ - (4²)⁵ = 4¹² - 4¹⁰ = 4¹⁰(4² - 1) = 4¹⁰(16 - 1) = 15(2²⁰) = 15[(2¹⁰)²]
2¹⁰ = (2⁵)² = 32² = (30 + 2)² = 900 + 120 + 4 = 1024 = 2(512), (2¹⁰)² = 4(512²)
512² = (500 + 12)² = 500² + 2(12)(500) + 12² = 25(10⁴) + 12(10³) + 144
64⁴ - 16⁵ = 15[(2¹⁰)²] = 15[4(512²)] = 60(512²) = 60[25(10⁴) + 12(10³) + 144
= 15(10⁶) + 72(10⁴) + 8640 = 15728640
2^24-2^20= 15*2^20=15*1024*1024
@TWJRPGGamming= True!
If one wishes a less laconic statement of the solution, it can be developed as such:
16 = 2^4 ; 64 = 2^6 ;
64^4 = (2^6)^4 = 2^24 ;
(16)^5 = (2^4)^5 = 2^20 ;
hence :
(64)^4 - (16)^5 = 2^24 - 2^20
............................ = 15 x 2^20
............................= 15 x (2^10)^2
[Rem.: 2^10 is known as a KiB and equals 1024]
............................ = 15 x 1024^2
thus, either by calculator or by hand:
(64)^4 - (16)^5 = 15'728'640
_____ .
I wrote the same thing. Thanks.
Solution in 4 easy steps:
Given: 64^4 - 16^5
(I) = (16*4)^4 - 16^5
(II) = 16^4 * 4 ^ 4 - 16^5
(III) = 16^4 * 16 * 16 - 16^5
(IV) = 16^5 * (16 - 1)
==> 15 728 640
64^4 =16^4х4^4
16^4х(4^4-16)
65536х240=15728640
16x16x16x16x16 - 16x16x16x16
=10,48,576 - 65,536
=9,83,040
Good review of exponent math!
I stopped at 15 * 16^5. The rest is calculating, not mathematics. 😁
I think I can do faster 64x64x64x64-16x16x16x16x16 on a piece of paper
I would use base 4
Thank you so much. I like your sums. Solving by myself.
If this is an entrance exam, how much time would you have spent by just solving this one problem if you do it this way?
Very good 😁
Thank you very much 🙏♥️🙏
Ocham's razor. Just figure it out with a pencil and paper. Even Harvard students can do that.
Excellent!!!
Many thanks!
Why Harvard don't have calculater?
Because any idiot can stick it in a calculator,but not everyone understands the maths behind it.
Because if you can't do it without a calculator, you don't know what you are doing.
The secret is out --> Harvard is merely a safety school.
@@johnshaw6702not necessarily. You can do the simpler ones manually and complex one with calc and still know what you’re doing
@@life_score Doing it by hand makes it stick. Besides, how do you think they check if the calculator is correct. I write software for a living and math libraries had to do some fancy adjustments to ensure that answers produced were correct. Computers may be good at math, but they didn't always have a chip dedicated to math.
Whoa!! Thats well done Sir! I'd have to watch that twice to keep up. I'm sure Boeing's got a great career path for you. Nah wait, Maybe NSA or the CIA....Hmmm, maybe no. Hey, Call Elon!!!Bet he has a spot!
Thanks a ton! Hope so!
Antes de que termines de hacer este video yo ya lo habia resuelto en la forma tradicional y en la mitad de tiempo que tu tardaste...La distancia entre 2 puntos es la linea recta, no lo olvidemos....
( 16 x 4 ) x (16x 4 ) x ( 16 x 4 ) x ( 16 x 4 ) - ( 16 x 16 x16 x16 x16 ) = ?
Το κάνεις με το επιστημονικό κομπιουτεράκι και το λύνεις σε 5 δευτερόλεπτα
This is round arround 2^24-2^20 does it all. =2^20(2^4-1) = 15*2^20. That's it
Who said the answer have to be in base 10 ? :p
2^24 = 1 0000 0000 0000 0000 0000 0000b (24 zero in base 2)
2^20 = 1 0000 0000 0000 0000 0000b (20 zéro in base 2)
sub = 1111 0000 0000 0000 0000 0000b
(64x64x64x64= 16,777,216) (16x16x16x16x16=1,048,576) 16,777,216 - 1,048,576 = 15,728,640
Of course, I didn't go to Harvard.
En başta hepsini tek tek çarpsaydı daha hızlı biterdi 🫣
Last you said 15 724 640 😂
😂😂😂
64⁴-16⁵=(2⁶)⁴-(2⁴)⁵=2²⁴-2²⁰=2²⁰×(2⁴-1)=2²⁰×(16-1)=2²⁰×15
Ну или так. Ну это работает, если можно к одному значению подвести. А если нет? Если вместо 16 стояла бы 13, а вместо 64, скажем, 61? И накрылась ваша лавочка.
Ну так решаем же именно то, что дано, а не в общем виде, я тоже решила именно так!@@mukhomor9937
COOL
4¹²-4¹⁰=4¹⁰(4²-1)
Hello, int Harvarduniversity You Learn to Build an Atombombe, with Count Atoms Perhaps.
Perhaps Since Corona ist Such Extremes.
Lg Sven Balzer
16 la puterea 3
Такой простой задаче посвящать видео ?? 😊
And why do we need to learn this when calculators were invented before my birth
Warum so kompliziered??????
1/4
Zero.
jesus, why is it so hard =POWER(64;4)-POWER(16;5)
But the actual answer is - 983 040.
No, this answet ist OK.
The correct answer is 2^screw it I’m going to get drunk
If this is the Harvard U. Admission exam, then I am seriously worried about US education system
Why?
De ce sa te complici atat?Pui mana pe creion ,calculezi efectiv numerele ,faci scaderea si gata ,ai rezultatul !Asa ,consumi pagini de hartie degeaba!Ati luat-o razna rau de tot!
Bruh milan engineering school is way harder lol
You make it too complicated with this method
That took me two lines and I skipped 7.22 of your video. Did you do it the quick way?
The rest of us need to learn from first principles
Bro what are you even doing?
512
Helllooom
♥️👍♥️
❤❤❤❤❤❤❤🇹🇳
This is not a Harvard admission entrance exam. You are a liar. I'm gone for good!
In english, please
1/4