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the citizen of planet OZ are 6 fingered and they developed the number system in base 6.A certain street in OZ has 1000 buildings and they are numbered 1 to 1000.How many no. of 3's are used?Express your answer in base 10.
a.144
b.54
c.108
d.36
Read Solution (Total 6)
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- 3's in 1 to 1000 is 300
Change to base 6
3*6^2+0*6^1+0*6^0= 3*36=108 - 14 years agoHelpfull: Yes(15) No(2)
- in unit's place, the 3's are:
3, 13, 23, 33, 43, 53
103, 113, 123 , 133, 143, 153
...
703, 713, .... 773
=> total number of 3's in unit's place is 6*6 = 36
in 10's place (that's 8 in decimal), the 3's are:
30, 31, 32... 35
130, 131, ... 135
...
730, 731, .... 735
=> total number of 3's in 10's place is 6*6 = 36
in 100's place (that's 64 in decimal), the 3's are:
300, 301, ... 305
310, 311 ... 315
...
370, 371 .... 375
=> total number of 3's in 100's place is 6*6 = 36
thus, the total number of 3's in total is 36 + 36 + 36 = 108
- 14 years agoHelpfull: Yes(12) No(4)
- number of times 6 appears from 1 to 1000 = 300
express 300 in base 6 i.e 3*6^2=108. answer is C. - 14 years agoHelpfull: Yes(2) No(2)
- 108
- 14 years agoHelpfull: Yes(1) No(2)
- c
- 14 years agoHelpfull: Yes(1) No(2)
- 108
- 14 years agoHelpfull: Yes(1) No(3)
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