Pre-RMO was conducted on 12th October 2014 in Mumbai, India

I have posted the questions in this set. There are 20 questions in total (the questions are numbered according to set A).

If you haven't appeared for the pre-RMO, you can take this set as a test. Try to complete the paper within the time limt, that is 2 hrs 30 min.

**Update:** Answers have been added to the final note in this set. Be sure to check them out !!!!!

If you have found a nice way to solve any question, do post the worked solution in the comments below the question. Hoping to see some creative solutions !!!!!

For those who wrote the exam, how did it go?

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## Comments

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TopNewesthii pranshu

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Thanks @Pranshu Gaba this set helped me a lot..

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You're welcome! I'm glad it helped. Are you appearing for the math olympiad this year?

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Yes

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I am in 12th now, so I am not eligible to apply for RMO this year. I wouldn't be able to share any RMO questions. However, I look forward to developing and sharing cool new problems!

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Hello there, It's good to find a community full of Enthusiastics in Mathematics. I'm, providing an Analysis of this year and last year's Pre RMO paper here. Feel free to discuss the same here.

2014 Paper

2013 Paper

(Please note that there's a small mistake in solution to Q18, I'll correct it as soon as possible.)

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Ok, the mistake in Q.18 is corrected.

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And I think that in question number 18, it should be that f (n) = n for the rest of the prime numbers.

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That's correct. I had the same thing in mind, however missed out in typing.

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In the 16th question, the diagram could be drawn such that P, Q and R lie between AI, BI and CI respectively. So the diagram won't be that messy.

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That's right, but I had taken the points to be on the extended lines AI,BI and CI (Without taking into consideration the easier case). Now that raises a question which I missed out in the discussion. There are 8 possibilities for the points P, Q, R as it is not explicitly mentioned in the question whether the points P, Q, R lie on the segment AI, BI, CI or them extended. The answer will vary accordingly. However it should be safely assumed that one should either take the three points dividing the segments internally or externally. In both cases, answer is $55^0$

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The results are out!!!!! The cutoff is only 40/100 lol !

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hey ! Im in the 10th grade and i qualified for RMO .. Presently I have only the past year papers to solve ..and i am clueless about which bookks to refer to ! .. Please help..

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i didn't expect it to be so low.

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Anyways :p

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I got 19 :)

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which one didn't you get.

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I made a silly mistake in the questionn where we were asked to find the number of solutions to xy = x+ y + gcd (x, y), where x <=y. God knows why I included (3,2) as a solution.

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What do think the cut off marks will be this year for qualifying for RMO 2014?

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i think it should be around 8 questions as last year's paper was simpler than this year and last year the cutoff was around 9 questions.

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I really felt that the last year's paper was slightly more difficult. Anyways, the cutoff probably wouldn't exceed 10 (but don't curse me if it does!), so you'd probably qualify.

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Wat is pre rmo and rmo? Is there a difference?

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Should u show the solution as well in the paper? Pls help me I'm new to this and wat is pre Rmo?

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Only the final answer must be shown in the paper. You can refer to the HBCSE website for more info.

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Can you tell me how you'd prepared for RMO/pre-RMo

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Isn't it supposed to be 6 questions?how did it become 20?

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The pre-rmo has 20 questions to be solved in 2 and a half hours. If you qualify in the pre-rmo, you are eligible to appear for the RMO which has around 6 questions to be solved in 3 hours.

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Dude but I am directly writing rmo There is no pre rmo and all I'm from bangalore

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@Shiv Kumar I think you wrote the Association of Mathematics Teachers of India's NMTC Contest and if you had got selected for the second round then irrespective of qualifying the second round you can pay $Rs.~20$ and get to write RMO. This is what happens in Chennai, all as I know, Isn't it @Krishna Ar and I forgot to write it this year, totally, well next year is the only remaining year for me to write, isn't it IDK..can we write it afetr schools too . Now IDK the matter in bangalore ..just a guess...and a query..

Arya

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@Arya Samanta From next year onwards standard 12th students aren't eligible to write pre-rmo.

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@Shiv Kumar In mumbai you first have to write pre-rmo which consists of 20 questions. If you qualify, you are eligible to write RMO.

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even i gave pre-rmo. how many questions did you get correct?

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I didn't get the answer key, so I am not sure, but I am expecting around 17. What about you?

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How many marks do you think that the cut off will be for qualifying for RMO?

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How many are you getting correct? the answer key has been published on the website.

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How can you write pre-RMO now..?I think you are in a college (from your age-18)

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Greater than 12. Did a silly mistake in the paper. Can I qualify with this score?

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