In a set of numbers from 100 to 1000

[tejal777]

In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit "5"?ans:288

Can somebody proceed as below and get the ans.?
100 to 1000 we have 901 integers out of which 451 are odd.From there deduct 500-599 series i.e 100 more nos and get to 351...after that i got stuck:(

[StaceyKoprince]

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Thanks!

[tejal777]

source:Gmat club test

[kinjal.nandy]

from 100 to 110 there are 5 odd no.s 101,103,105,107,109...we need to remove 105 so we are left with 4 such digits
from 100 to 200 in one series we would have 4X10 =40 but we have included 150 series so need to subtract 4 such digit
40-4=36
now from 100 to 1000 we would remove 500 series hence we are left with 8 such series...100,200,300,400,600,700,800,900
hence the total no. would be 36x8=288

[JonathanSchneider]

I like the reasoning above. In fact, the math can be simplified to 4x9x8.

Well done.

[kramacha1979]

Might be an easier way

0,1,2,3,4,5,6,7,8,9 - total of 10 digits

_ _ _ three places to fill can leave 100 and 1000 b/c both are even

1st place any digit except 0 and 5 - 8 choices
2nd place any digit except 5 - 9 choices
3rd place any digit except and even - only 4 choices ( 1,3,7,9)

8*9*4 = 288

[JonathanSchneider]

nice approach! good use of the "slot method"!