# 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?

## Comments

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TopNewesteven i gave pre-rmo. how many questions did you get correct? – Sai Prasanth Rao · 2 years ago

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– Pranshu Gaba · 2 years ago

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

– Mihir Chakravarti · 2 years ago

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

– Pranshu Gaba · 2 years ago

I am sorry but I do not have any idea regarding that. Anyways, the results will out by 31 October.Log in to reply

– Sai Prasanth Rao · 2 years ago

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

– Pranshu Gaba · 2 years ago

I am getting 18. What is your score?Log in to reply

– Sai Prasanth Rao · 2 years ago

11 (ashamed)Log in to reply

– Krishna Ar · 2 years ago

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

– Pranshu Gaba · 2 years ago

I am currently studying in 11th grade, and my actual age is 16, so I can write pre-RMO.Log in to reply

– Krishna Ar · 2 years ago

Didntkno' Dat ...Ok :DLog in to reply

– Sai Prasanth Rao · 2 years ago

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

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 · 1 year, 12 months ago

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– Siddhesh Naik · 1 year, 11 months ago

Ok, the mistake in Q.18 is corrected.Log in to reply

– Shourya Pandey · 1 year, 11 months ago

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

– Siddhesh Naik · 1 year, 11 months ago

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

– Shourya Pandey · 1 year, 11 months ago

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.Log in to reply

– Siddhesh Naik · 1 year, 11 months ago

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 \(55^0\)Log in to reply

hii pranshu – Kishan Chaudhary · 1 year ago

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Thanks @Pranshu Gaba this set helped me a lot.. – Krishna Shankar · 1 year, 3 months ago

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– Pranshu Gaba · 1 year, 3 months ago

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

– Krishna Shankar · 1 year, 3 months ago

YesLog in to reply

– Pranshu Gaba · 1 year, 3 months ago

All the best!Log in to reply

– Krishna Shankar · 1 year, 3 months ago

Thanks and keep updating such good stuff'sLog in to reply

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, 3 months ago

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– Krishna Shankar · 1 year, 3 months ago

SureLog in to reply

The results are out!!!!! The cutoff is only 40/100 lol ! – Shourya Pandey · 1 year, 12 months ago

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– Gaurav Sharma · 1 year, 11 months ago

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..Log in to reply

– Sai Prasanth Rao · 1 year, 12 months ago

i didn't expect it to be so low.Log in to reply

– Shourya Pandey · 1 year, 12 months ago

Anyways :pLog in to reply

– Sai Prasanth Rao · 1 year, 12 months ago

you started preparing for minor test 2?Log in to reply

– Shourya Pandey · 1 year, 11 months ago

Kind of.Log in to reply

I got 19 :) – Shourya Pandey · 2 years ago

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– Sai Prasanth Rao · 1 year, 12 months ago

which one didn't you get.Log in to reply

– Shourya Pandey · 1 year, 12 months ago

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.Log in to reply

– Sai Prasanth Rao · 1 year, 12 months ago

did you include (2,3)? by the way are you from PACELog in to reply

– Shourya Pandey · 1 year, 12 months ago

Ya I am from PACE nerul :)Log in to reply

– Shiv Kumar · 1 year, 12 months ago

Ru from pace? Isn't pace in bangalore?Log in to reply

– Sai Prasanth Rao · 1 year, 12 months ago

you were the topper right?Log in to reply

– Shourya Pandey · 1 year, 12 months ago

Yup.Log in to reply

– Sai Prasanth Rao · 1 year, 12 months ago

congratulations.Log in to reply

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

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HBCSE website for more info. – Pranshu Gaba · 2 years ago

Only the final answer must be shown in the paper. You can refer to theLog in to reply

– Krishna Ar · 2 years ago

Can you tell me how you'd prepared for RMO/pre-RMoLog in to reply

– Pranshu Gaba · 2 years ago

I solved the last year's pre-RMO paper, as well as lots of questions on Brilliant !Log in to reply

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

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– Sai Prasanth Rao · 2 years ago

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.Log in to reply

– Shiv Kumar · 2 years ago

Dude but I am directly writing rmo There is no pre rmo and all I'm from bangaloreLog in to reply

– Shourya Pandey · 2 years ago

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.Log in to reply

@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 agoLog in to reply

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

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– Arya Samanta · 2 years ago

I can't write PRE-RMO and RMO too? if that is so..it then ..it..damn it!Log in to reply

– Shiv Kumar · 2 years ago

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 rmoLog in to reply

@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 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 ago

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– Sai Prasanth Rao · 2 years ago

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.Log in to reply

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@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 ago

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– Shourya Pandey · 1 year, 12 months ago

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.Log in to reply

– Sai Prasanth Rao · 1 year, 12 months ago

i felt the last year's paper to be simpler. I could solve around 15 questions.Log in to reply