TOMORROW's maths competition ?? (1 Viewer)

[susie_]

Is anyone doing the maths competition tomorrow ?
Do we need to study for it :S

 

[FBJ]

Yeah I'm doing it, I created a thread about it, you mean the AMC, right?

 

[LetsBReasonable]

I have an ext maths exam the day after so the maths comp is probably the last thing on my mind atm. Is this the one where all the questions are multiple choice? Because I heard from someone that we can't use calculators...

 

[FBJ]

Yes, this is multichoice for first 25 qs, for last 5, select a number from 0 to 999.

 

[kev-kun]

Ohhh... the AMC one... well you can't really study for it. Its just based on math skills if I recall so.
Yeah I'm doing it ==

 

[seanieg89]

Study won't change much, just get a good nights rest. Marks pretty much come from general aptitude / how well you can figure stuff out on the day.

 

[kev-]

Does anyone have a few of the hard AMC questions that they want to chuck up here? one of the 0-999 questions would be awesome because I never know how to even start to attempt them.

 

[Demento1]

AMC 2009 SENIOR Q 26:

The reciprocals of 4 positive integers add up to 19/20. Three of these integers are in the ratio 1:2:3. What is the sum of the four integers?

 

[seanieg89]

AMC 2009 SENIOR Q 26:

The reciprocals of 4 positive integers add up to 19/20. Three of these integers are in the ratio 1:2:3. What is the sum of the four integers?

42?

 

[Demento1]

42?

That's right.

 

[kev-]

does anyone want to post up a solution? :/

 

[johnpap]

Let the integers in the ratio 1:2:3 be a,2a and 3a and let the 4th integer be b, then 11/6a + 1/b = 19/20.
Note b>1 as 1/b < 19/20, so 1/b <= 1/2, so if a>=5, then 11/6a + 1/b <= 11/30 + 1/2 < 19/20. Hence it suffices to check a=2,3,4. Luckily a=2 gives 1/b = 19/20 - 11/12 = 1/30,
Hence (2,4,6,30) is a solution set, so find the sum of the integers 2+4+6+30 = 42.
There are normally lots of ways to do these things, but normally just trying easy stuff like bounding arguments or divisibility, even just trying to encode all the information in a set of equations is enough to get the job done.

 

[Ealdoon]

So what did everyone think of the mathematics competition?

 

[kev-kun]

Lol it was like... Ok first 10 questions... easy.... next 10 ok.... next 5 was wow? and the last 5 was just guessing marathon because our time was cut , but I think the last question was like 250-something

 

[chocolatelatte]

omg lol.. it was horrible :-( basically the questions from 1-20 were okay (cept i got stuck on q10 which was ugh). 20-25 were asldkjaslkjdsa, got 21,22,25 (not sure if correct tho) and the only question I got out of the last 5 was q26 not looking forward to my results at all

 

[Ealdoon]

omg lol.. it was horrible :-( basically the questions from 1-20 were okay (cept i got stuck on q10 which was ugh). 20-25 were asldkjaslkjdsa, got 21,22,25 (not sure if correct tho) and the only question I got out of the last 5 was q26 not looking forward to my results at all

Haha, you are not alone!

 

[mirakon]

omg lol.. it was horrible :-( basically the questions from 1-20 were okay (cept i got stuck on q10 which was ugh). 20-25 were asldkjaslkjdsa, got 21,22,25 (not sure if correct tho) and the only question I got out of the last 5 was q26 not looking forward to my results at all

that actually looks good and by no means is that bad

 

[Ealdoon]

Did everyone get their booklet collected? Strange, I thought we were allowed to take them.

 

[chocolatelatte]

Did everyone get their booklet collected? Strange, I thought we were allowed to take them.

Nope. Your school gets disqualified if anyone takes a booklet home (at least that's what a teacher said).

 

[Ealdoon]

Nope. Your school gets disqualified if anyone takes a booklet home (at least that's what a teacher said).

Do you know why?