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Pre-RMO 2014

This note has been used to help create the RMO Math Contest Preparation wiki

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?

Note by Pranshu Gaba
2 years, 5 months ago

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even i gave pre-rmo. how many questions did you get correct? Sai Prasanth Rao · 2 years, 5 months ago

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@Sai Prasanth Rao I didn't get the answer key, so I am not sure, but I am expecting around 17. What about you? Pranshu Gaba · 2 years, 5 months ago

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@Pranshu Gaba How many marks do you think that the cut off will be for qualifying for RMO? Mihir Chakravarti · 2 years, 5 months ago

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@Mihir Chakravarti I am sorry but I do not have any idea regarding that. Anyways, the results will out by 31 October. Pranshu Gaba · 2 years, 5 months ago

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@Pranshu Gaba How many are you getting correct? the answer key has been published on the website. Sai Prasanth Rao · 2 years, 5 months ago

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@Sai Prasanth Rao I am getting 18. What is your score? Pranshu Gaba · 2 years, 5 months ago

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@Pranshu Gaba 11 (ashamed) Sai Prasanth Rao · 2 years, 5 months ago

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@Pranshu Gaba How can you write pre-RMO now..?I think you are in a college (from your age-18) Krishna Ar · 2 years, 5 months ago

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@Krishna Ar I am currently studying in 11th grade, and my actual age is 16, so I can write pre-RMO. Pranshu Gaba · 2 years, 5 months ago

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@Pranshu Gaba Didntkno' Dat ...Ok :D Krishna Ar · 2 years, 5 months ago

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@Pranshu Gaba Greater than 12. Did a silly mistake in the paper. Can I qualify with this score? Sai Prasanth Rao · 2 years, 5 months ago

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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.) Siddhesh Naik · 2 years, 5 months ago

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@Siddhesh Naik Ok, the mistake in Q.18 is corrected. Siddhesh Naik · 2 years, 5 months ago

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@Siddhesh Naik And I think that in question number 18, it should be that f (n) = n for the rest of the prime numbers. Shourya Pandey · 2 years, 5 months ago

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@Shourya Pandey That's correct. I had the same thing in mind, however missed out in typing. Siddhesh Naik · 2 years, 5 months ago

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@Siddhesh Naik 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. Shourya Pandey · 2 years, 5 months ago

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@Shourya Pandey 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 \(55^0\) Siddhesh Naik · 2 years, 5 months ago

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hii pranshu Kishan Chaudhary · 1 year, 5 months ago

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Thanks @Pranshu Gaba this set helped me a lot.. Krishna Shankar · 1 year, 8 months ago

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@Krishna Shankar You're welcome! I'm glad it helped. Are you appearing for the math olympiad this year? Pranshu Gaba · 1 year, 8 months ago

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@Pranshu Gaba Yes Krishna Shankar · 1 year, 8 months ago

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@Krishna Shankar All the best! Pranshu Gaba · 1 year, 8 months ago

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@Pranshu Gaba Thanks and keep updating such good stuff's Krishna Shankar · 1 year, 8 months ago

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@Krishna Shankar Sure!

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! Pranshu Gaba · 1 year, 8 months ago

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@Pranshu Gaba Sure Krishna Shankar · 1 year, 8 months ago

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The results are out!!!!! The cutoff is only 40/100 lol ! Shourya Pandey · 2 years, 5 months ago

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@Shourya Pandey 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.. Gaurav Sharma · 2 years, 4 months ago

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@Shourya Pandey i didn't expect it to be so low. Sai Prasanth Rao · 2 years, 5 months ago

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@Sai Prasanth Rao Anyways :p Shourya Pandey · 2 years, 5 months ago

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@Shourya Pandey you started preparing for minor test 2? Sai Prasanth Rao · 2 years, 5 months ago

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@Sai Prasanth Rao Kind of. Shourya Pandey · 2 years, 5 months ago

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I got 19 :) Shourya Pandey · 2 years, 5 months ago

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@Shourya Pandey which one didn't you get. Sai Prasanth Rao · 2 years, 5 months ago

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@Sai Prasanth Rao 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. Shourya Pandey · 2 years, 5 months ago

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@Shourya Pandey did you include (2,3)? by the way are you from PACE Sai Prasanth Rao · 2 years, 5 months ago

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@Sai Prasanth Rao Ya I am from PACE nerul :) Shourya Pandey · 2 years, 5 months ago

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@Shourya Pandey Ru from pace? Isn't pace in bangalore? Shiv Kumar · 2 years, 5 months ago

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@Shourya Pandey you were the topper right? Sai Prasanth Rao · 2 years, 5 months ago

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@Sai Prasanth Rao Yup. Shourya Pandey · 2 years, 5 months ago

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@Shourya Pandey congratulations. Sai Prasanth Rao · 2 years, 5 months ago

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Wat is pre rmo and rmo? Is there a difference? Shiv Kumar · 2 years, 5 months ago

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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? Shiv Kumar · 2 years, 5 months ago

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@Shiv Kumar Only the final answer must be shown in the paper. You can refer to the HBCSE website for more info. Pranshu Gaba · 2 years, 5 months ago

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@Pranshu Gaba Can you tell me how you'd prepared for RMO/pre-RMo Krishna Ar · 2 years, 5 months ago

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@Krishna Ar I solved the last year's pre-RMO paper, as well as lots of questions on Brilliant ! Pranshu Gaba · 2 years, 5 months ago

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Isn't it supposed to be 6 questions?how did it become 20? Shiv Kumar · 2 years, 5 months ago

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@Shiv Kumar 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. Sai Prasanth Rao · 2 years, 5 months ago

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@Sai Prasanth Rao Dude but I am directly writing rmo There is no pre rmo and all I'm from bangalore Shiv Kumar · 2 years, 5 months ago

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@Shiv Kumar The pre Rmo is for Mumbai region only. They introduced it here so that they don't have to waste their time correcting the RMO papers of students who get really very low marks. Shourya Pandey · 2 years, 5 months ago

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@Shiv Kumar @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 :) Arya Samanta · 2 years, 5 months ago

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@Arya Samanta @Arya Samanta From next year onwards standard 12th students aren't eligible to write pre-rmo. Sai Prasanth Rao · 2 years, 5 months ago

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@Sai Prasanth Rao I can't write PRE-RMO and RMO too? if that is so..it then ..it..damn it! Arya Samanta · 2 years, 5 months ago

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@Arya Samanta In bangalore u have to just pay 120 and u can write I think it's only for our school fiitjee integrated!! I didn't write anything and in Dec ill write rmo Shiv Kumar · 2 years, 5 months ago

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@Shiv Kumar @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. Sai Prasanth Rao · 2 years, 5 months ago

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What do think the cut off marks will be this year for qualifying for RMO 2014? Mihir Chakravarti · 2 years, 5 months ago

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@Mihir Chakravarti 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. Sai Prasanth Rao · 2 years, 5 months ago

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Comment deleted Mar 15, 2015

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@Mihir Chakravarti @mihir Chakravarti I too got 11 questions correct. The count could have been higher for me as I too made some blunders. My friends had given the pre-rmo last year and last to last year. They said that 11 questions were more than enough to qualify. I am riding on this hope. Sai Prasanth Rao · 2 years, 5 months ago

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@Sai Prasanth Rao 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. Shourya Pandey · 2 years, 5 months ago

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@Shourya Pandey i felt the last year's paper to be simpler. I could solve around 15 questions. Sai Prasanth Rao · 2 years, 5 months ago

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