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)
at

11 comments:

  1. Anonymous29 May 2012 at 15:45

    Why is Q23 4? :(

    ReplyDelete
  2. Anonymous29 May 2012 at 18:22

    Can someone explain Q26?

    ReplyDelete
  3. Anonymous29 May 2012 at 20:15

    where can i get the questions from for free?

    ReplyDelete
  4. Sng Chong Hao Ernest29 May 2012 at 20:24

    Why is q35 12? Can someone explain

    Random Sec 1 student

    ReplyDelete
  5. Anonymous30 May 2012 at 18:26

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

    ReplyDelete
  6. Anonymous30 May 2012 at 22:54

    I thought (A) is wrong for Q8?

    ReplyDelete
  7. Anonymous31 May 2012 at 13:10

    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.

    ReplyDelete
  8. Lee Zheng Han31 May 2012 at 15:35

    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)!!!

    ReplyDelete
  9. Unknown31 May 2012 at 20:27

    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

    ReplyDelete
  10. Lee Zheng Han1 June 2012 at 17:44

    Oh yeah! I damn confused...

    ReplyDelete
  11. zabachi4 June 2012 at 08:10

    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

    ReplyDelete