Latest CTS Aptitude Question SOLUTION: how many zeros are there from 1 to 10000?

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(#M40001382) CTS Numerical Ability question Keep an EYE

how many zeros are there from 1 to 10000?

Solution

for solving this problem first we would break the whole range in 5 sections
1) from 1 to 9
Total number of zero in this range = 0
2) from 10 to 99
Total possibilities = 9*1 = 9 ( here 9 is used for the possibilities of a non zero integer)
3) from 100 to 999 - three type of numbers are there in this range
a) x00 b) x0x c) xx0 (here x represents a non zero number)
Total possibilities
for x00 = 9*1*1 = 9, hence total zeros = 9*2 = 18
for x0x = 9*1*9 = 81, hence total zeros = 81
similarly for xx0 = 81
total zeros in three digit numbers = 18 + 81 +81 = 180
4) from 1000 to 9999 - seven type of numbers are there in this range
a)x000 b)xx00 c)x0x0 d)x00x e)xxx0 f)xx0x g)x0xx
Total possibilities
for x000 = 9*1*1*1 = 9, hence total zeros = 9*3 = 27
for xx00 = 9*9*1*1 = 81, hence total zeros = 81*2 = 162
for x0x0 = 9*1*9*1 = 81, hence total zeros = 81*2 = 162
for x00x = 9*1*1*9 = 81, hence total zeros = 81*2 = 162
for xxx0 = 9*9*9*1 = 729, hence total zeros = 729*1 = 729
for xx0x = 9*9*1*9 = 729, hence total zeros = 729*1 = 729
for x0xx = 9*1*9*9 = 729, hence total zeros = 729*1 = 729
total zeros in four digit numbers = 27 + 3*162 + 3*729 = 2700
thus total zeros will be 0+9+180+2700+4 (last 4 is for 4 zeros of 10000)
= 2893

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Asked In CTS Anil (13 years ago)

Solved Read Solution (2)

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Read Solution (2) :

dhiresh  (13 years ago)

10 20 30 40 50 60 70 80 90=no of zero=9
means b4 100 total no of zero=9
110 120 130 140 150 160 170 180 190 =no of zero=9
means after 100 and before 200 no zero=9
similarly ..no of zero between 200 and 300 =9
and so on...
no of zeros between 900 and 1000=9
and some zeros at 100 200 300........900
so total no of zero before 1000=10*9+9*2=12*9=108
means before 1000 no of zeros=108 so before 2000=108
similarly....
..............
before 10000 no of zeros=108
and some at 1000 2000 3000 .......9000 and one 10000
so total no of zeros became=108*9+9*3+4=972+27+4=1003
1003 is the ans

Is this solution Helpfull? Yes (2) | No (17)  

ANUPAM JAISWAL  (7 years ago)

From 1-100=11
from1-1000=11*10+1=111
from 1-10000=111*10+1=1111
so the No. Of zero from 1-10000 is 1111

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