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Consecutive integers

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Consecutive integers

by venmic » Mon Sep 05, 2011 1:11 pm
In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit "5"?

please explain

288
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by knight247 » Mon Sep 05, 2011 1:56 pm
If we are looking at odd numbers then the last digit of that number would end in 1 3 5 7 9

1000 is an even number so we don't need to consider it. Lets consider numbers till 999.

For the last digit we can have 1 3 5 7 9 but 5 is not allowed so we have 1 3 7 9= 4 options

For the middle digit we can 0 1 2 3 4 6 7 8 9. All the digits except 5 which equals 9 options

For the first digit we can have 1 2 3 4 6 7 8 9. All except 5 and zero. We cannot include zero as that would make the number a two digit number. so 8 options

So we have 4*9*8=288
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