Harvard University Admission Interview Tricks

Harvard University Admission Interview Tricks | Find the Value of k=?

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Күн бұрын

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@ericwiddison7523 Ай бұрын

I started by noting that k^2-k^3=k^2(1-k). If there is an integer solution then k must be a squared factor of 150, which is 5^2*6. Because we have 1-k as a factor, this hints that k

@ScholarTutors Ай бұрын

Yes. Thanks for the comments 👍. Are you a maths teacher 💖?

@zahidhussain251 Ай бұрын

This seems to be more logical i.e. finding a number whose square is a factor of 150. The only numbers we can come up with is 5 or -5. So let's see which gives us the correct answer.

@un-heungjung549 Ай бұрын

IF) K=5 ===> 125-25+150=0 (x)

@ericwiddison7523 Ай бұрын

@@zahidhussain251 That's what I said.

@Игорьййй-ь3р 3 күн бұрын

-5 В уме, за примерно 3 секунды) Сразу понятно что К должно быть отрицательным для изменения знака, дальше интуитивно решил проверить 5, так и оказалось.

@ScholarTutors 3 күн бұрын

Good 👍. Thanks for the comments Are you a professor of maths 💖?

@Игорьййй-ь3р 2 күн бұрын

@@ScholarTutors Нет, я IT из России. В школе учился еще в СССР ))

@nikolayplatnov5148 10 күн бұрын

Very easy. K must be a negative figure. For simplicity a=-k. a^2+a^3= a(a^2+1)= 150 =25×6 a=5. k=-5.

@ScholarTutors 9 күн бұрын

Yes. Thanks for the comments 👍. Are you a professor of maths 💖?

@user-hy6sp7qe9k Ай бұрын

k^2-k^3=k^2(1-k) suggests to search for square integer factor of 150. It's not a guaranteed but promising approach because it's an interview question.

@ScholarTutors Ай бұрын

Great 👍. Thanks for the comments. Are you a maths teacher 💖?

@RH-ro3sg Ай бұрын

obviously, k*k -k*k*k > 0 is only possible for k < 1 (when looking only at real numbers at first). In order to arrive quickly at a first solution, k=-5 seems a prime candidate because -( -5^ 3)= 125, right in the ballpark of the rhs , and -5 turns out to be a solution indeed. Then of course, there should be 2 other solutions, possibly complex, that could be easily obtained by dividing the polynomial by the x=-5 root and solving the remaining quadratic equation, but I'm not going to bother with those. Why not? Mainly, because I'm lazy right now and on free time, and it's such a boring exercise that won't teach me anything new. And I'll use the excuse of the notation of the initial equation, (k*k - k*k*k suggests to me we are only looking for an elementary 'natural' solution, in contrast to x^2-x^3). Not exactly sound scientific or mathematical reasoning perhaps, but still :) ... of course, if I actually had do this stuff for an exam or such, it'd be different.

@ScholarTutors Ай бұрын

Wow, thanks for the comments 👍 Are you a professor of maths 💖?

@sunnysharma5166 Ай бұрын

After solving in mind,k=-5

@ScholarTutors Ай бұрын

Yes. But it has other complex solutions. Thanks for the comments 👍 Are you a maths teacher 💖?

@sunnysharma5166 Ай бұрын

@@ScholarTutors No,I just love to solve maths in free time whether it is easy or hard doesn't matter or else I enjoy the solution

@ГригорийРайцес 3 күн бұрын

Тоже самое! В уме за 1 мин!

@user-db1sn8gd8g Ай бұрын

My "solution" was much simpler and intuitive method. Common sense says that a smaller amount minus a larger amount equals a positive result can only be possible if the minus sign becomes a plus sign. Since there are 5 total Ks then it must be a negative number to obtain a positive number. ergo -5

@ScholarTutors Ай бұрын

Great 👍. Thanks for the comments Are you a maths teacher 💖?

@zahidhussain251 Ай бұрын

I want to make a slight correction to your intuitive reasoning. Actually there are not 5 Ks, but 2Ks and then 3Ks. Taking your logic but restricting it to K^3 being negative K must be negative. K^2 will be positive regardless of sign of K. Having said that I have an answer but still no solution. And the one given here is not valid because there is no logical explanation how we came up with 25 + 125

@highpath4776 29 күн бұрын

@@zahidhussain251 25 + 125 is 150. I guess we could split the 150 any way we like, as you say reasoning not given (I presume the 5sq x 5 fell to mind )

@un-heungjung549 Ай бұрын

조건에 '실수'라는 게 있었나? '허수'는 안된다는 조건 없던 것 같던데... 판별식을 사용했다는 것은 '실수'라는 건데...문제가 좀 있네..ㅎㅎ 2개의 '허수'가 더 존재해야 올바른 정답이 아닐지.. 이걸 어떻게 번역해야 할 지 몰라서 ...암튼, 2개의 답이 더 있어야 될 듯싶네요.

@ScholarTutors Ай бұрын

Great 👍. Thanks for the comments Are you a maths teacher 💖?

@kvadromir 3 күн бұрын

25+125. К=-5

@ScholarTutors 3 күн бұрын

Wow, thanks for the comments 👍 Where are you watching from 💖?

@kvadromir 2 күн бұрын

@@ScholarTutors I'm from Russia.

@Mrpallekuling Ай бұрын

Short solution: k^2 (1-k) = 150 = 2*3*5*5. Thus, k*2 = 25 => k=5 or k=-5. If k=5 => k^2 (1-k) = -100 no good. Thus, k=-5

@ScholarTutors Ай бұрын

Yes. You got it. But it has other complex solutions. Where are you watching from 💖?

@Mrpallekuling Ай бұрын

@@ScholarTutors Hi. Denmark!

@ЛюбовьРыжкова-ы6о Күн бұрын

А куда делась еще одна скобка (к +5)?

@ScholarTutors Күн бұрын

Great 👍. Thanks for the comments Where are you watching from 💖?

@champion1 14 күн бұрын

(-5×-5)-(-5×-5×-5)=25-(-125)=150.

@ScholarTutors 14 күн бұрын

Great 👍. Thanks for the comments. Are you a professor of maths 💖?

@SmirnovOleg1394 8 күн бұрын

Задача решается в уме за1,5 минуты. Я не учитель и не профессор математики. Просто советская школа.

@arturkowalski5151 Ай бұрын

In mind, in 5 seconds, k=-5.

@ScholarTutors Ай бұрын

Great 👍. Thanks for the comments Are you a maths teacher 💖?

@ohmreggienius Ай бұрын

k = -5 or k = 3 + (root21)i or k = 3 - (root21)i 😁

@ScholarTutors Ай бұрын

Thanks for the comments 👍. Where are you watching from 💖?

@highpath4776 29 күн бұрын

thought there might be three roots in a cube expression, wasnt certain how to get it low enough to work - did you use logs?

@alfiodimauro8210 Ай бұрын

credo che nessuno abbia detto di trovare solo soluzioni reali, pertanto, visto che parliamodi Harvard credo che le soluzioni siano da cercare nel campo dei complessi.

@ScholarTutors Ай бұрын

Great. Thanks for the comments 👍 Where are you watching from 💖?

@AdegbeyeArafatOluwaseun Ай бұрын

Nice one

@ScholarTutors Ай бұрын

@@AdegbeyeArafatOluwaseun thanks 😊

@ЭтоЯ-э9и5х 9 күн бұрын

Без решения сразу видно,-5)))))

@ScholarTutors 9 күн бұрын

Yes. Thanks for the comments 👍 Where are you watching from 💖?

@reforgedall5251 16 күн бұрын

-5 is one of 3 roots...

@ScholarTutors 15 күн бұрын

Yes. Thanks for the comments 👍 Where are you watching from 💖?

@TheNizzer Ай бұрын

8min! -5 by inspection in a few seconds. Anyone using the suggested method would be rejected instantly.

@ScholarTutors Ай бұрын

Yes. Thanks for the comments 👍 Are you a maths teacher 💖?

@highpath4776 29 күн бұрын

Would you do a Ln log transformation (or log one) for a general solution method if k not an integer

@次野先生 22 күн бұрын

k³-k²+150=0. 이하 3차방정식 (k+5)(k²--6k+30)=0

@ScholarTutors 22 күн бұрын

Great 👍. Thanks for the comments. Are you a maths teacher 💖?

@次野先生 22 күн бұрын

@@ScholarTutors retire

@shrimpmmv Ай бұрын

Without watching yet, by trial and error in my head, I discovered k = -5. I would probably use the Ruffini method to factorize the expression and discover the other solutions, but i am too lazy ahhaha

@ScholarTutors Ай бұрын

Great. Thanks for the comments 👍 Are you a maths teacher 💖?

@shrimpmmv Ай бұрын

@@ScholarTutors Nope. I am studying computer engineering

@MathMastery_Minds Ай бұрын

Great

@ScholarTutors Ай бұрын

Thank you so much 💖, bro.

@rooksman64 Ай бұрын

way too long of a solution k has to be negative and further you can do a substitution

@ScholarTutors Ай бұрын

@rooksman64 yes. Thanks for the comments ❤❤❤

@Elf20122 Ай бұрын

I startet with - 10 and than I tried -5 and it worked.

@ScholarTutors Ай бұрын

Great 👍 . Thanks for the comments Where are you watching from 💖?

@emfunke Ай бұрын

2k-3k=150 -k=150 K=-150

@emfunke Ай бұрын

Never; I misread the problem.

@emfunke Ай бұрын

Nevermind; I misread the problem.

@ScholarTutors Ай бұрын

Okay 👍

@ScholarTutors Ай бұрын

Are you a maths teacher 💖?

@Brown-hb2ld Ай бұрын

Correct ,same as my

@rodrigoprado9710 Ай бұрын

Cool

@ScholarTutors Ай бұрын

Yes. Thanks for the comments 👍 Are you a maths teacher 💖?

@rodrigoprado9710 Ай бұрын

I'm Just a doctor - anesthesiologist

@Alamaths Ай бұрын

@@rodrigoprado9710wow, thanks for the comments 👍.

@Donna_Rosa_de_Alvadorez 12 күн бұрын

Я со своими учениками это в 9 классе только что прошла.

@ScholarTutors 11 күн бұрын

Great 👍. Thanks for the comments Where are you watching from 💖??

@emfunke Ай бұрын

Nevermind; I misread the problem.

@kno6ndg7 Ай бұрын

-5. Took me 7 seconds. Harvard has very low entry threshold, if a slow guy like me can do it.

@ScholarTutors Ай бұрын

Thanks for the comments 👍 Where are you watching from 💖?

@Ньярлатхотеп-ъ9у 19 күн бұрын

К=(-5). Время решения 30 секунд. )))

@ScholarTutors 19 күн бұрын

Great 👍. Thanks for the comments Where are you watching from 💖?

@BoKha777 15 күн бұрын

15 секунд ))) Сразу видно 150= 125+25

@АндрейПетрович-н6б 27 күн бұрын

-5,

@ScholarTutors 26 күн бұрын

Great 👍. Thanks for the comments Where are you watching from 💖?

@ПашаПитецкий 14 күн бұрын

Гарно,але довго 😊

@ScholarTutors 14 күн бұрын

Yes. Thanks for the comments 👍 Are you a maths teacher 💖?

@ПашаПитецкий 14 күн бұрын

@ScholarTutors Hi, my friend, I'm not teaching, I'm interesting, and I like you think

@Corpoint 11 күн бұрын

Странно что в Гарварде решают примеры школьной программы, да ещё только в действительной области

@ScholarTutors 10 күн бұрын

Yes. Thanks for the comments 👍 Are you a professor of maths 💖?

@Corpoint 8 күн бұрын

@ScholarTutors нет, почему вы так решили?

@nafisatsulaiman-cd2xm Ай бұрын

Thanks so much sirr 😊

@ScholarTutors Ай бұрын

@@nafisatsulaiman-cd2xm thank you so much, dear 😘 ❤️

@petergomes8788 Ай бұрын

-5.

@ScholarTutors Ай бұрын

Thank you so much for the comments 👍 Where are you watching from 💖?

@hafedhsaif2090 Ай бұрын

You should stop making these issues so direct.

@ScholarTutors Ай бұрын

Thank you so much 💖.

@cosimo7770 26 күн бұрын

Terrible solution. Student would fail admission. Maths requires insight and creativity, not blind application of rules which is all YT tutors can do. Mentally, within 1 second, (1-k) must be positive. So k= -5 for then k²(1-k) = 150.

@ScholarTutors 26 күн бұрын

Great 👍. Thanks for the comments. Are you a maths teacher 💖?

@SrisailamNavuluri Ай бұрын

Some body said k=- 5 which is real.

@ScholarTutors Ай бұрын

Yes. But it has other complex solutions. Where are you watching from 💖?

@SrisailamNavuluri Ай бұрын

@@ScholarTutors you are right.If you are interested for real number solutions,there is only one solution

@thomasharding1838 Ай бұрын

Negative 5. Let's keep it real, people! Do I get into Harvard?

@ScholarTutors Ай бұрын

Thanks for the comments 👍. Are you a maths teacher 💖?

@БерикМ-у6п 3 күн бұрын

k=x

@ScholarTutors 3 күн бұрын

Great 👍. Thanks for the comments. Are you a maths teacher 💖?

@usmanazhar7073 Ай бұрын

K=-5

@ScholarTutors Ай бұрын

Yes. Thanks for the comments 👍 Are you a professor of maths 💖?

@usmanazhar7073 Ай бұрын

@@ScholarTutors no, just solved it in my min

@ConnorRybka Ай бұрын

-5 way too easy

@ScholarTutors Ай бұрын

Great 👍. Thanks for the comments Where are you watching from 💖?

@ВладимирЮвчик Ай бұрын

-150

@ScholarTutors Ай бұрын

Great 👍. Thanks for the comments Where are you watching from 💖?

@DavidChadderton-g7d Ай бұрын

K = 1/150

@ScholarTutors Ай бұрын

Great 👍. Thanks Thanks the comments Where are you watching from 💖?

@DavidChadderton-g7d Ай бұрын

@@ScholarTutors Ballarat.

@Kinnlinntunplays Ай бұрын

I already got this by guessing.the answer is 5.lol.

@Kinnlinntunplays Ай бұрын

I meant -5 sorry

@ScholarTutors Ай бұрын

Okay 👍. Thanks for the comments. Where are you watching from 💖?

@Kinnlinntunplays Ай бұрын

@@ScholarTutors since the answer of the equation is supposed to be negative(cuz is the value of k was positive)(this is case 1)but the answer of this equation is positive(case 2)the the value of k must be in negative cuz negative numbers multiplying toghether will get an positive answer so if negative 5 is k then -5 times -5 - negative 5 to the power -5 which is the answer of 150 Btw I watched your vids daily.i enjoyed it