2014 Taiwan Selection Test for PMWC and EMIC Preliminary Round Paper I (Time Allowed : 60 Minutes)

Write down all answers on the answer sheet. Each problem is worth 5 points and the total is 100 points. 1. 6 72 125 = 2. 2 7 27 72 272 727 2727 7272+ + + + + + + = 3. 5 605 1605 21605 721605+ + + + = 4. (9999 11118888 22227777 33336666 44445555 55554444 66663333+ + + + + + +

77772222 88881111 99990000) 9+ + = 5. 93339 87655 31113 37035 + = 6. 1.2014 0.3993 0.3993 0.7986 0.7986 4999 + + =

7. 1 2 4 8 16 32 64 128 256 5120.01 0.04 0.09 0.18 0.32 0.42 0.49 0.64 0.81

+ + + + + + + + + =+ + + + + + + + 8. 201420142014 201420142017 201420142015 201420142015 = 9. 11231 12341 13451 14561 15671 16781 17891 18911 19121+ + + + + + + + =

10. 1 1 1 1 1 1 1 17 14 28 31 62 124 248 496+ + + + + + + =

11. 1 1 1 11007 1008 1008 1009 1009 1010 2013 2014

+ + + + = "

12. 1 20 39 58 20152 4 6 2014

+ + + + + =+ + + +"

"

13. 1 1 1 1 1 115 50 500 5000 50000 500000

=

14. 2 2 2 2 2 22014 1995 1976 1957 1938 1919

361 + + =

15.

2012 2012 2012(1 2012)(1 )(1 ) (1 )2 3 2014

2014 2014 2014(1 2014)(1 )(1 ) (1 )2 3 2014

+ + + +=

+ + + +"

"

16. (10000 2014 2014 0.2014)(2014 2014 0.2014 0.20142014)+ + + +

(10000 2014 2014 0.2014 0.20142014)(2014 2014 0.2014)+ + + + =

17. 2 2 2 260 60 60 60

10 1 11 1 12 1 30 1+ + + + = "

18. 2 2 2 2 22000 2002 2004 2006 2008

1999 2001 2001 2003 2003 2005 2005 2007 2007 2009+ + + + +

2 2 22010 2012 20142009 2011 2011 2013 2013 2015

+ + =

19. 1 1 1150 151 152 151 152 153 199 200 201

+ + + = "

20. 11 11 11 11 11 11 99911234

=