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How to tackle Math Olympiad questions - 2

In the last article we talked about some general practices that will stand you in good stead while taking part in the Maths Olympiad (or any exam/test in general). In this edition, we'll talk about various additional techniques that could help you perform better in Math Olympiads.

Most of the time the questions in such competition are of the objective type question. This can make things simpler for you (on the other hand, depending on the ingenuity of the question setter, it can also make it harder for you).  The way it makes it easier for you is in two ways

  • One is that you can easily check if the answer you compute is part of the options provided to you
  • The second is that sometimes, just sometimes, you can do some amount of guessing to eitherget the right answer, or narrow down your possibilities

For example, take the following question taken from http://www.edugain.com

Question: The number 11449 can represented by a 107 x 107 square grid. Out of the following numbers,

which number can not be represented on the square grid?

a. 14641           b. 90601

c. 9216             d. 16122

Here, you could work out the square root of all the numbers and try to figure out the answer, but a quicker way may be to notice that a square number cannot end in 2. In addition, the question reads "which number", which implies there is only one choice that is true.

So the answer here is obviously d) - 16122

Similarly, in a lot of these cases, you can eliminate at least one of the choices - there can be many variants that you could identify by just looking at the question. Ask yourself some mental questions like "Can the answer be an odd number?" etc. Of course, each mental question you ask yourself will be specific to that question.

Sometimes, a question can seem rather hard at a quick glance, but if you read it once more slowly, you can probably see past the apparent complexity into a simple solution.

Consider the question (also taken from http://www.edugain.com)

Question: Archana's roll number is a two digit number. Her friend Balvinder's roll number has the same digits as Archana's roll number, but with digits interchanged. If they add their roll number, and divide the sum by 11. Find the remainder of this division.

a. 1              b. 2

c. 0             d. Can not be determined without knowing the roll number

At first glance, it may seem really hard - how can you know without really trying? Here you can use one of two methods. One is not really what I would call mathematical, but if you are pressed for time, you could easily use it for such question. And what's that technique?

It's simple - all you do is try it out on a couple of example numbers. Imagine that Archana's roll number is 61. Then Balvinder's roll number would be 16. Add 61 and 16, and you get 77. The remainder when 77 is divided by 11 is 0.

However, you also need to know how to solve this directly (after all, you are here because you want to learn mathematics).

The way to do that is to think of it as follows

Archana's number has two digits - say they are "ab" where a and b could be any of 0,1,2,3,4,5,6,7,8 or 9.

You can represent it mathematically as

10a + b

Then Balvinder's number would be "ba" - mathematically you would say

10b + a

Add them up

10a + b + 10b + a = 11a + 11b = 11(a+b)

This is of course divisible by 11 leaving a remainder of 0.

Simple, and more satisfying to do it this way, isn't it?

So you should always keep in mind that no matter how hard the question looks, it is very likely that you have already been taught the tricks to solving it. There may be a few questions that may use concepts you haven't been taught yet (to identify the really advanced students), but there's not much you can do about that. For a majority of the questions though, you already know all the techniques you need to solve them. It's just a question of identifying them and applying them.

You should also know your strengths and use them appropriately. For instance, you may be very good with spatial questions and at visual data - then go for the geometry or figure related questions first. If numbers dance in your head, go for the arithmetic questions. Get them out of the way, and then move on to the other sections.

One final note, that I mentioned in the previous article. Once you've found a solution, put it back in the question and double check that your solution is indeed right.


56 comments

  1. Posted by Mapesu Clementine Ramahuma| 2012-02-22 01:34:14

    i believe having read this article will help me a lot! I have been unsuccessful in all olympiads tests that i wrote, i have always failed to go to round two. But tonight i,ve learnt something and i hope and pray that i qualify to write this year because if i do, i,ll surely go far. Thanks a lot for the help i,ll keep peeping for those awesome tips and advices. You rock!

  2. Posted by RM| 2012-04-17 20:10:54

    Great Article ..
    It would be great to have these tips coming ..

  3. Posted by risa| 2012-08-16 06:27:31

    thank you article, now i could win the amc for sure!!! :)

  4. Posted by anoushka puri| 2012-11-17 19:51:28

    wonderful! help ful tips!

  5. Posted by mohak singh| 2013-12-16 10:09:27

    I prefer that more questions should be there for practising otherwise its an amazing site for me......

  6. Posted by ananya| 2014-03-06 19:17:27

    Good trick and explanation

  7. Posted by Pulkit| 2014-08-05 22:25:48

    this is very nice

  8. Posted by Tlotlo Lekgoba | 2016-05-06 18:38:21

    These tips will definitely come out handy. I can't wait for the math olympiad second round next week .

  9. Posted by Anuj| 2016-05-12 08:04:37

    This is great :)

  10. Posted by TJ13| 2016-08-30 19:01:49

    helped me a lot:)

  11. Posted by som| 2016-10-10 06:54:19

    very nice

  12. Posted by som| 2016-10-10 06:54:34

    very nice

  13. Posted by shreyansh| 2016-11-06 11:35:29

    this relaxed my mind

  14. Posted by Pratik Dash, Chandigarh | 2016-12-25 14:09:13

    I can't wait for imo round 2 with these tips in handy

  15. Posted by HimanshU Kumar| 2017-01-04 10:44:21

    Very helpful!!

  16. Posted by Ankur Saha | 2017-01-27 15:59:12

    Thanks to help me.??

  17. Posted by Sidaster| 2017-02-23 23:14:07

    I am still confused

  18. Posted by Sidaster| 2017-02-23 23:15:38

    I do love this article but my it is a little to complex.

  19. Posted by Sanjib chaki| 2017-03-18 13:49:44

    Nice.can you send me how to send articles?

  20. Posted by Aloysius| 2017-03-26 02:22:55

    I suggest the first question should be rephrased.
    "...which number can not be represented on the square grid?" should be "...which number can not be represented on a square grid?"
    But it is very

  21. Posted by Ata| 2017-04-20 02:38:10

    This is very helpful I'm definitely going to use this????

  22. Posted by andiswa| 2017-04-22 04:04:09

    This article was very helpful, helped me get a few tips on how to handle the upcoming second round.  Highly appreciated ????

  23. Posted by Nguy?n Nh?t Linh| 2017-05-01 16:48:53

    that is useful.

  24. Posted by somya| 2017-05-12 10:26:44

    these tips are exellent and very helpful.......
    more tips should keep coming
    a very very very thankyou forthese tips

  25. Posted by somya| 2017-05-12 10:26:48

    these tips are exellent and very helpful.......
    more tips should keep coming
    a very very very thankyou forthese tips

  26. Posted by somya| 2017-05-12 10:26:48

    these tips are exellent and very helpful.......
    more tips should keep coming
    a very very very thankyou forthese tips

  27. Posted by somya| 2017-05-12 10:26:48

    these tips are exellent and very helpful.......
    more tips should keep coming
    a very very very thankyou forthese tips

  28. Posted by Anurag| 2017-08-20 02:08:51

    good and effective article

  29. Posted by Neha| 2017-08-27 06:29:28

    your paper IdNO:U-121110-30-6744-IMO(1)
    Question NO:5 not understaning.
    please give me detail explanition.

  30. Posted by Pgmn| 2017-11-03 16:18:24

    What a wonderful  article is this  . It is really helpfhelpful

  31. Posted by DR. MRITYUNJOY GHOSH| 2017-11-21 09:45:43

    Fine

  32. Posted by Jacob| 2017-12-09 19:48:06

    I belive that if you are in a lower level of psmo this information is useful to get possable one or two more correct answers but if you are already doing well foe example top 20% like I am well this i

  33. Posted by Ahaan| 2017-12-18 09:06:57

    v helpful. hopefully I get into imo level 2

  34. Posted by Lohitashwan| 2017-12-18 12:47:49

    I'm gonna rock at SASMO next year!

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