Tuesday, 29 May 2012

SMO 2012 (Junior Section) Answers

SMO 2012 Junior Special Round Participants List
COP for Special Round - 8, about 4.7% (~185/3959 participants) selected
1. D
2. E
3. B
4. B
5. A
6. D
7. D
8. B
9. D (*C)
10. C
11. 4
12. 25
13. 9
14. 2996
15. 110
16. 93
17. 50
18. 35
19. 58
20. 1818
21. 4
22. 375
23. 3
24. 23
25. 108
26. 468
27. 240
28. 200
29. 3150
30. 6720 (half cut not allowed) / 40320 (half cut allowed) (*840 - does not consider horizontal cut)
31. 27
32. 1
33. 12
34. 1977 (*1976 - answer should be odd number)
35. 12
Answers contributed by: Lim Jeck and Lim Min
*Answers updated on 1 Sep 2012, after checking the Solution Book

SMO (Junior) Previous Years' Cut-off Points (Inclusive of Round 2 scores)
Update: 2012 Gold (17), Silver (8), Bronze (6), HM (5), Round 2(8)
2011 Gold (12), Silver (9), Bronze (7), HM (6), Round 2 (11), Top 30 (~34)
2010 Gold (24), Silver (9), Bronze (8), HM (5)
2009 Gold (11), Silver (7), Bronze (6), HM (5)
2008 Gold (23), Silver (14), Bronze (11), HM (10)
2007 Gold (20), Silver (14), Bronze (11), HM (10)

11 comments:

Anonymous said...

Why is Q23 4? :(

Anonymous said...

Can someone explain Q26?

Anonymous said...

where can i get the questions from for free?

Sng Chong Hao Ernest said...

Why is q35 12? Can someone explain

Random Sec 1 student

Anonymous said...

Shouldn't q24 be 24? Correct me if I'm wrong

Anonymous said...

I thought (A) is wrong for Q8?

Anonymous said...

Q8 is (B). Factorize b out of the RHS of the equation and divide both sides by b. From there use some contradictions to solve it.

Lee Zheng Han said...

For question 8, a=b⌊a/b⌋-b{a/b}=b⌊a/b⌋-a+b⌊a/b⌋=2b⌊a/b⌋-a. Hence,a=b⌊a/b⌋. Therefore,(A),(B), (D),(E) is then obviously not the answer...
So, question 8 is (C)!!!

WittyP said...

In response to Zheng Han, you are wrong, because by saying that statement C is incorrect, you are implying that if b is a rational number, a is an irrational number, which clearly does'nt make sense.

And the answer IS (B), and here is a counterexample to statement B: a=3, b=3/2.

3=(3/2)⌊3/(3/2)⌋.
Therefore statement B is false

Lee Zheng Han said...

Oh yeah! I damn confused...

zabachi said...

Solutions to selection questions from SMO 2012 (Junior).

Q6.
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=482268

Q11.
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=481872

Q13.
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=481874

Q14.
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=481861

Q15.
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=481649

Q16.
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=481645

Q17.
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=481651

Q18.
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=481644

Q19.
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=481653

Q21.
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=481885

Q23.
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=482279

Q31.
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=482277