Columbia University Science Honors Program ENTRANCE EXAMINATION

Colleges & Universities Columbia University
3341

For the circle and tangent line:

X+Y = R and X^2+Y^2=R are equal at the point of tangency. The only possible values for X and Y are (0,0) or (1,1) but you can’t have a radius of 0 for a circle so its 1+1=2 so R=2.

I accidentally marked 1 instead of 2 (stupid mistake ik) because x=1 but I later realized it was asking for r.

3342

Oh rip I thought 440 was in base 10. No wonder I got a weird polynomial.

3343

Thank you @JumpyJLizard

3344

Guys what were #11, #13, and #6 on the challenge math?

3345

@ADITYAEMPIRE yeah i’m pretty sure you need to use y=x too like CSGO2022 did, but i think it’s just second nature for smart people lol can’t relate ;-;
and i’m pretty sure i misbubbled at least once too, almost didn’t catch myself when i did it for the third problem on the easy math section rip
@CSGO2022 np
also can you tell us which problems you do remember? i think we had a compilation a little while back, lemme bring it up

3346

1 the ratio one - 5/4

2 the penny problem - 15

14 with the 0 year old - 102

15 with the acid solution - 25%

xxx with the base that was not base 10 - 8

xxx with the circle and the line on the coordinate plane - 2

xxx with the circle and the chord perpendicular to the radius - 12sqrt3

xxx with the man running and walking at 4 mph - 9/4

xxx with (another) man who walked 1/2 a mile slower and faster - 15 miles

xxx with 8x - 3a^2 or smth - 16/3 iirc

xxx classic painted cube one - 488

xxx the rate problem with variables - 10a/r

any more?

3347

I think you got them all!

3348

i got 12, forgot 3 ;-;

3349

I’m pretty sure the other three were already discussed a few pages back

3350

wait really i’ll check
if i can’t find it, could you do me a favor and remind me of what they were? sorry

3351

@JumpyJLizard The mixture one?

3352

no that one was there
yeah i can’t remember the other 3 for the life of me

3353

@ADITYAEMPIRE i think that one’s near the bottom

3354

I asked another senior who got in as a sophomore and he said to get in you have to get everything on the Challenge Math correct (I doubt it)

3355

^^

3356

@ADITYAEMPIRE yeah i think someone commented a while ago about how they got 7-8 on the last part but still got in or smth
and i think the first question is on the top?

3357

@JumpyJLizard omg ya oops didnt see it lol. I’ve been searching my head for the other questions and i cant seem to find any :frowning:

3358

lol that’s what i do on my AMCs ;-;

3359

@JumpyJLizard Did u qualify for AIME?

3360

yup and yup
you?