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Question
How many numbers are there between 1 and 1000 (both inclusive) which are divisible neither by 2 nor by 5?
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Solution
From 1 to 1000, the numbers ÷ by 2 = 500
The number ÷ by 5 = 200
And the numbers ÷ by 10 = 100(5 × 2 = 10)
So number ÷ by 2 or 5 = 500 + 200 – 100 = 600
Total numbers from 1 to 1000 = 1000
So the number of numbers which are ÷ neither by 2 nor by 5
= 1000 – 600
= 400
Three-digit numbers:
| Hundred's | Ten's | Unit |
The unit place can be filed in 4 ways using the digits 1, 3, 7, 9.
Hundred’s place can be filled in 9 ways excluding 0.
Ten’s place can be filled in 10 ways using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Therefore, the required number of 3 digit numbers neither divisible by 2 nor by 5 is = 9 × 10 × 4 = 360.
There is only one 4-digit number, but it is divisible by 2 and 5.
Therefore, required numbers using fundamental principle of addition = 4 + 36 + 360 = 400
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