smc q

For the following question (q11 smc 2014):

How are you supposed to figure out that 2047 = 23 x 89 within the time constraint? Or is the answer worked out by elimination?

If the latter, arent you first meant to exhaust all possible "factors" of 127 first? But then that would be a huge time sink as well...

And what would be the most time efficient way of answering these "figure out the factors" questions - the only strategy that comes to my mind is just memorising the prime factorisations of certain numbers.

(edited 1 month ago)

Reply 1

mqb2766

The other ones are easy to see theyre prime
3,7,31,127
(the last one just try dividing by 3,5,7,11 - divisibility rules), so it had to be E

(edited 1 month ago)

Reply 2

mosaurlodon

I get that the first 3 are easy as in you can see theyre prime in like a few seconds
but for 127 - wouldnt you have to check 13,17,19,21... and all those weird numbers to check if theyre a factor? And even with the divisibility rules, checking 127 would take a couple of minutes right?
Unless im just slow.

Im trying to aim for BMO in the smc, and not sure If I should focus so much on being as fast as possible to get more time to answer the last qs (so practice in timed conditions) or a more problem solving approach to answer the last qs (practicing untimed but just with the hard qs).

(edited 1 month ago)

Reply 3

mqb2766

To check for prime/divisibility you only need to check the prime numbers up to sqrt(n), so for 127 its 2,3,5,7,11 and all are simple digit/divisibility rules, but not hard to do the longer way.

Similar for 2047 if you really wanted to. Youd need to check primes up to 43 and 2,3,5,7,11 are easy. Then its just a case of trying 13,17,19,23, ... and the latter would give.

Reply 4

mqb2766

Original post by mosaurlodon

I get that the first 3 are easy as in you can see theyre prime in like a few seconds
but for 127 - wouldnt you have to check 13,17,19,21... and all those weird numbers to check if theyre a factor? And even with the divisibility rules, checking 127 would take a couple of minutes right?
Unless im just slow.
Im trying to aim for BMO in the smc, and not sure If I should focus so much on being as fast as possible to get more time to answer the last qs (so practice in timed conditions) or a more problem solving approach to answer the last qs (practicing untimed but just with the hard qs).

For the second point, Id practice both timed and untimed so try get as much as done in the 90 mins, but for questions you dont get done, spend extra time trying to do them without looking at the answer. Its also worth seeing if you can answer questions different ways. Problem solving can certainly help so simplify the problem, work back from answers, spot magic numbers, work through problems for specific values ...

Just post some questions if youre unsure / want to check if there are different ways of doing it. If you search, I went through last years smc in a "problem solving" way and many of the first 20 questions (roughly) can be approached in an elementary/problem solving/quick way.

(edited 1 month ago)

Reply 5

mosaurlodon

last time I got 84 so barely scrapped a gold since my timing was so bad and didnt even really touch the last 4 qs, but now I can prob answer most of them, with reasonable accuracy so some progress I guess (except the long/confusingly worded qs - those really seem to make my brain shut off or eat time, either that or the hard geometry problems).

I actually went through your post about last years smc, it was quite helpful :smile:

, I also like this one youtuber called Dice Cup who breaks down the problems in a way I can understand which is nice.

RN, im doing a q on the volume of 2 cubes that are infused together and its really confusing me, might post that one tomorrow If I cant crack it today.

(edited 1 month ago)

Reply 6

mqb2766

Original post by mosaurlodon

last time I got 84 so barely scrapped a gold since my timing was so bad and didnt even really touch the last 4 qs, but now I can prob answer most of them, with reasonable accuracy so some progress I guess (except the long/confusingly worded qs - those really seem to make my brain shut off or eat time, either that or the hard geometry problems).
I actually went through your post about last years smc, it was quite helpful :smile:

, I also like this one youtuber called Dice Cup who breaks down the problems in a way I can understand which is nice.
RN, im doing a q on the volume of 2 cubes that are infused together and its really confusing me, might post that one tomorrow If I cant crack it today.

Practice is the main thing, but it can be worth posting questions / solutions even if you get them right as there are often different ways of doing questions. Last year the bmo threshold was 106 which corresponds to getting 21 questions right, so youve got to have the time to go for pretty much all the questions.

The hard geometry questions will improve with practice. Again just post them if you want a hint about getting started. Common things are sketching extra radii / right angles to tangents, setting up pythagoras with an unknown on two sides, using similar triangles, recognising 30-60-90 and 45-45-90 ...