and... if you know binary numbers well because you're a developer and have used them.... you know that 2^16 is 65536, so 2^15 is 32768 and 2^14 is 16384 so 16384 - 1 is 16383, just multiply by 32 for 524256 (or double it 5 times if you don't have paper to write out the multiplication)
@@紫瞳-w6t maybe, but 2^20 isn't used as often as 2^8 or 2^16 or even 2^32, so it's not quite as easy for those of us that don't have our 2^ numbers memorised
This seems like an inefficient way to do this problem. I did it in my head in about a minute, in a manner that's similar but I think easier to track and calculate mentally: 2^19 - 32 = 2^19 - 2^5 = (2^20 - 2^6)/2 = [1/2] * [(2^10)^2 - (2^3)^2 ] = [1/2] * [1024^2 - 8^2] = [1/2] * [1000^2 + 24*1000*2 + 24^2 - 8^2] = 1,000,000/2 + 48,000/2 + 4*144/2 - 64/2 = 500,000 + 24,000 + 288 - 32 = 524,256 There are other ways to do this that are equally or even slightly easier, so I'm not claiming this is "the best" way to do it. It boils down to personal preference. And also not saying everyone should do it as a mental math problem. I just dislike calculators when not necessary, and don't like to go find pencil and paper while watching a video - and just find it more fun to see what I can do "tools free". But the point is, you can break this up into a problem that a decent high school freshman student can do pretty easily. No "tricks" needed, and not at all exclusive to "Stanford University caliber" students.
this is a simple arithmetic problem that should be done by multiplication. 2^19=512*1024 512000 10240 2048+ 524288 32- 524256 Answer All that algebra is a waste of time and time is short in an exam.
@@davidseed2939 I don't think that would be an acceptable solution. The descriptors include things like "interview question", "algrebra problem", "simplification aptitude test", and "math olympiad" - as well as "exam question". Of course, these days who knows how accurate that is or what reflects ACTUAL use; people attach labels just to maximize views, regardless of the context of how problem was originally used. BUT: (1) the way it's presented to US, it is certainly meant to require simplification, and NOT to just be an elementary/middle school arithmetic problem. (2) Out of the five descriptors I cited, only for the last one (the one you described) would it be appropriate to treat it as an exercise in long multiplication. For all the other ones, you are required to demonstrate a deeper understanding (specifically, of use of exponents for simplifying expressions). Still not a deep problem, by any means - but one that at least requires algegra 1 level understanding.
2^19 - 32 = 2^19 - 2^5 = 2^5 * (2^14 - 1 )= 2^5 * ( 2^7 + 1) * (2^7 - 1) = 32 * 129 * 127 = 524256, 3 items question is simple enough to calculate directly.
I’m glad you found a simpler way to solve the problem! Thanks for sharing it with everyone! 🚀🙏✅👏
and... if you know binary numbers well because you're a developer and have used them.... you know that 2^16 is 65536, so 2^15 is 32768 and 2^14 is 16384
so 16384 - 1 is 16383, just multiply by 32 for 524256 (or double it 5 times if you don't have paper to write out the multiplication)
@@andrewhughes8687
2^10=1024，2^19=[(2^10)^2]/2=(1024^2)/2，by using binary numbers would be simpler.
@@紫瞳-w6t maybe, but 2^20 isn't used as often as 2^8 or 2^16 or even 2^32, so it's not quite as easy for those of us that don't have our 2^ numbers memorised
256 au carré que multiplie 2 au cube moins 32 = 524256
use multiplication
512x1024=524,288
-32
524256
This seems like an inefficient way to do this problem. I did it in my head in about a minute, in a manner that's similar but I think easier to track and calculate mentally:
2^19 - 32 =
2^19 - 2^5 =
(2^20 - 2^6)/2 =
[1/2] * [(2^10)^2 - (2^3)^2 ] =
[1/2] * [1024^2 - 8^2] =
[1/2] * [1000^2 + 24*1000*2 + 24^2 - 8^2] =
1,000,000/2 + 48,000/2 + 4*144/2 - 64/2 =
500,000 + 24,000 + 288 - 32 =
524,256
There are other ways to do this that are equally or even slightly easier, so I'm not claiming this is "the best" way to do it. It boils down to personal preference. And also not saying everyone should do it as a mental math problem. I just dislike calculators when not necessary, and don't like to go find pencil and paper while watching a video - and just find it more fun to see what I can do "tools free". But the point is, you can break this up into a problem that a decent high school freshman student can do pretty easily. No "tricks" needed, and not at all exclusive to "Stanford University caliber" students.
this is a simple arithmetic problem that should be done by multiplication.
2^19=512*1024
512000
10240
2048+
524288
32-
524256
Answer
All that algebra is a waste of time and time is short in an exam.
@@davidseed2939 I don't think that would be an acceptable solution.
The descriptors include things like "interview question", "algrebra problem", "simplification aptitude test", and "math olympiad" - as well as "exam question".
Of course, these days who knows how accurate that is or what reflects ACTUAL use; people attach labels just to maximize views, regardless of the context of how problem was originally used. BUT:
(1) the way it's presented to US, it is certainly meant to require simplification, and NOT to just be an elementary/middle school arithmetic problem.
(2) Out of the five descriptors I cited, only for the last one (the one you described) would it be appropriate to treat it as an exercise in long multiplication.
For all the other ones, you are required to demonstrate a deeper understanding (specifically, of use of exponents for simplifying expressions). Still not a deep problem, by any means - but one that at least requires algegra 1 level understanding.