Harvard University Admission Entrance Tricks | X=? & Y=?

[@fernandoreescolar418]

Analyzing the expression (X+Y)(X-Y), we come to the conclusion that both terms can only be even numbers. So only the pair 18-2 can be a solution.

[@percussion44]

can you elaborate?

[@fernandoreescolar418]

In principle at least one of the factors must be an even number. But if one of the factors is even then (X,Y) is (even, even) or (odd, odd) and in both cases both factors would be even.

[@samiodeh3785]

Wrong sir ​@@fernandoreescolar418

[@srininaidoo]

​@@fernandoreescolar418 X is 10 Y is 8

[@dupontfra]

@@fernandoreescolar418 Or we could say that the difference between X+Y and X-Y is 2Y which is even. So if X+Y is even minus even is even, therefore X-Y is even

[@MrPoornakumar]

The condition is that the sum of factors should be even (if x, y ∊ N). Only (18, 2) satisfy this condition, that yields x=10 and y=8.

[@sakshikausal]

Using Pythagoras law In right angled triangle sides 6,8,10 x² = y²+ 6² 10² = 8² +6²

[@pavelvancouver1214]

I have also got this idea. The problem can be solved in just two steps. A triangle having sides with 3:4:5 ratio is referred to as Egyptian Triangle The thing that any math teacher must tell their students in Grade 5. .

[@digbycrankshaft7572]

Should be 10^2=8^2+6^2

[@carolwhite6979]

x*x - y*y= 36 x*x = 36 + y*y x*x = 36 + ( and here I ran basic times table to 8.... 8 squared is 64) x*x = 36 + 64 = 100 x = 10

[@suresh1227]

x X x = 36 + y X y so x = 6 if y= 0 when y is 1, 2, 3, 4,5,6,7 then we do not get a number which will have a root which is a whole number when y = 8 , then y X y = 64 x X x = 36 + 64 x X x = 100 so x = 10 , y= 8 or x = 6 , y= 0

[@73p3ro]

6 x 0 = 0

[@tungyeeso3637]

The trick is you need to have a pair of even numbers in order to attain an outcome of natural numbers as the solution.

[@beekeeper-m5q]

It's true

[@nbkenkere1685]

x=6 and y =0 is the simplest answer !

[@chakradharamappini579]

X^2-y^2=36 X^2-y^2=6^2 X^2=6^2+y^2 We know 3,4,&5 are Pythagorean triplets. 6 can be converted to 3x2. so to eliminate 2 from 6, Divide both sides by 4 (X/2)^2= 3^2+(y/2)^2 It means x/2= 5 & y/2=4 => X=10 Y=8

[@rajkunargupta5183]

X=6 & Y=0

[@IfeanyiOzor2022]

You are doing a great work, keep it on.

[@ImranAli-bk3nj]

Amazing 😍

[@stevensanders9846]

You left out 6x6 which would solve that (x,y) =(6,0). However there seems to be a debate whether 0 is a natural number or not.

[@attiylanen]

But given the requirement that x+y > x-y, 6x6 cannot be an option.

[@attiylanen]

Then again, (x+y)(x-y) = 6x6 when 0 ∈ N, so I think you are correct.

[@stevensanders9846]

@attiylanen The requirement should be that x+y >= x-y if 0 is a natural number

[@ohmy9261]

Okay but (6+6)(6-6) doesn't that just give you 0?

[@stevensanders9846]

@ohmy9261 you misunderstood my response. What I said is that x=6, y=0 solves the equation if 0 is considered a natural number

[@geoffreystone4849]

X=10, Y=8. 100 minus 64 = 36. Simples

[@Sindhi001]

(X x X) - (Y x Y) =36 (10 x10) - (8 x 8) = 36 (100) - (64) = 36 X = 10 and Y=8

[@r8rdarklord]

x2 = 36 + y^2 => x = SQRT(36+y2) Now if y2 = 64 => y = 8 since y belongs to N => x = 10

[@thionga8774]

I have no specific formula for solving the problem. But by common-sense inspection and intuition, 100 - 64 = 36. 100 happens to be 10 square, and 64 is 8 square... So "x" must therefore be 10, and "y" equals 8. Or, "x" could be 6, and "y" equals 0. How's that for a quick solution.

[@Sindhi001]

X=10 Y=8 10x10=100 8x8=64 100-64=36 (6x6)

[@MIT-sf2ud]

Since x,y are naturals integers Why you forgot the first case X=6 and Y= 0 (6+0)*(6-0)= 36

[@RyanLewis-Johnson-wq6xs]

X^2-Y^2=36 X=±10, Y=± 8 X=± 6, Y = 0 (X,Y)=(10,8)

[@komandos.020]

İ am from Azerbaydjan.Veru useful.Thanks

[@Sindhi001]

(10x10=100) - (8x8=64) = 100-64 =36

[@HuseyinTosun-jd4px]

(X-Y).(X+Y)=36 , (10-8).(10+8)=36

[@goyopinto4381]

Another solution would be 6 and 0. However, since the Solution must be natural Numbers, 0 is rejected. I got the Solution 0 and 6 using derivatives, however 0 is not a natural Number and the 6,0 are not correct.

[@ARABGULF4444]

X*x-y*y= 100 - 64 X= +-100 , y= +-6 Or, x=+-6, y=0

[@sofianikolidou5640]

Thank you 🎉❤

[@himchanjeong4679]

Could you kindly provide the source of your claim that this question is from ‘Harvard University Admission Exam’? I am not sure whether they have a written format of entrance exam.

[@madurappankalyanaraman8015]

x=10 y=8 is the answer X² - y² =10² -8² 100 - 64 = 36.

[@RRRSSS1111]

X=10 y=8. Or just in a second x=6 and Y 0. Can do it.

[@afshinfathi6388]

great

[@jrwilliams5509]

What about 6 x 6 = 36?

[@i_am_sb]

If x+y=x-y,y=0

[@ameermirza2]

x=6, y=0 gives the right solution

[@gopinathrao1550]

x=10, y=8 6, 8 and 10 are pyrhagorean triplets.

[@borisbeletskiy4681]

Вот именно что там решать если знаешь квадраты чисел от двух до десяти

[@themr.maoandleopardmaoshow8745]

You can get 10 and 8 in your head through substitution in less than a minute.

[@sanaeelalioui6980]

You didn't apply the rule of multiple two negative numbers that are positive and you didn't put it in the probabilities

[@ellalan-u7g]

I think a simple way was elongated to confuse, if you do math like this everything is going like a big problem.

[@CharlesChen-el4ot]

x + y = 18 x- y = 2 x = 10 y = 8

[@ManiBoukhmis]

Très bien

[@modmafiya]

10. And. 8

[@rajeshvyas934]

X=10 Y=8

[@jeancorneillembuyi]

Where is 6 x 6?

[@ЛилияСуглобова-м1ъ]

It is immediately clear that both x^2 and y^2 should be sguare numbers , then we have 100- 64=36, so x=10, and y=8

[@PandithGautha]

you are missing ONE obvious solution : x=6 and y=0 !!

[@nagalakshmidevi7022]

Zero is not a natural number. x and y are natural numbers

[@PandithGautha]

@@nagalakshmidevi7022 there is no such restriction imposed in the question.So anyhting that logically satisfies the equation , will do the JOB !

[@adgf1x]

x,y=(10,8)

[@michaeljin101]

Ramanujan would first list these solutions: x=6,y=0 and x=-6, y=0

[@AYEMYINT-w6y]

X=13/2 Y=5/2

[@Ajaykumar123_rcm]

X=13/2. Y=5/2

[@tigermanhappy7875]

Let X=Y+ n, plug into the equation, you can quick immediately get the answers

[@virginiadepaula3478]

Congratulation! Solution is very well expressed

[@geetavansiya3376]

=10^2-8^2=(10-8)(10+8)=(2)(18)

[@nusretgulmammadov5144]

X=8 y=5

[@petercircee4692]

6x6

[@vijayasrinivasan8924]

X=10; y=8

[@dr4g0n76]

Binomial. Then you can do it in your head.

[@nenora]

Noce

[@davidgardner9001]

Long winded confusing waffle. It was a simple mental arithmetic question. A few seconds thought yielded X= 10 and Y = 8.

[@badzarbi4702]

X=6 and Y=0

[@dardoburgos3179]

X= 6, Y= 0.

[@JayPatel-hp9df]

? x=10 Y= 8.

[@jayanthits6742]

X=10 and y=8

[@Евгений-л9ф2н]

Why make things so complicated?😂 100-64=36. X=10, Y =8.

[@Radioayandeh]

No need to calculation, x=10 & y= 8

[@urubatandurval5245]

x=10 e y=8

[@ARABGULF4444]

I mean x= 10, y=6

[@ksmyth999]

Why would Harvard set such a trivial problem? A 12 year old could answer this.

[@vasanthosangadi2896]

🙏🇮🇳🚩😊👌✌

[@КириллФеоктистов-м7л]

Это же элементарно....

[@pavelvancouver1214]

Уравнение описывает так называемый египетский треугольник со сторнами, кратными 3, 4, 5.

[@tharstonsachin]

Ai b mama marry karsnawada a vawa danne na.

[@sunilsood7079]

What is the real life use of this?

[@kennethkan3252]

x^2-y^2=36 (x+y)(x-y)=36 36=1×36), (-1)×(-36) 36=2×18,(-2)×(-18) 36=4×9, (-4)×(-9) 36=6×6, (-6)(-6) (x+y)(x-y)=6×6 x+y=6, x-y=6, 2y=6-6, y=0,x=6 x+y=-6 x-y=-6 2×=(-6)+(-6) 2×=-12 ×=-6, y=0 x+y=9 x-y=4 2y=9-4 y=2.5 x=6.5 x+y=-9 x-y=-4 2y=(-9)-(-4) y=-2.5, x=-6.5

[@kennethkan3252]

(x+y)(x-y)=36 36=18x2 x+y=18 x-y=2 2y=18-2 y=8, x=10 y=-8, x=-10

[@kennethkan3252]

(x+y)(x-y)=36×1 (x+y)=36 (x-y)=1 2y=36-1 y=17.5, x=18.5 y=-17.5, ×=-18.5

[@さすらいのまーん]

how about also x=6, y=0 x=-6 , y=0

[@Billts]

Ωραία άσκηση κατανοητη

[@nguoiviet7925]

Phần sau làm quá dài dòng, nên xét tính chẵn, lẻ của x, y

[@nationalist6045]

X = 10 Y = 8

[@cabasantbab]

X=10 Y= 8

[@srininaidoo]

X = 10 Y = 8