# How many five digit integers (10,000-99,999) are divisible by 5?

• May 31st 2010, 11:31 PM
taurus
How many five digit integers (10,000-99,999) are divisible by 5?
When I did it I got 2000*10-2000=18000. But I was marked wrong but cant see where I went wrong.
• May 31st 2010, 11:52 PM
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Quote:

Originally Posted by taurus
When I did it I got 2000*10-2000=18000. But I was marked wrong but cant see where I went wrong.

The answer is indeed 18000. I don't know why it got marked wrong.
• Jun 1st 2010, 01:08 AM
simplependulum
The minimum is $10000$ and the maxumum is $99995$ so the total number is :

$\frac{99995-10000}{5} + 1$

$= 18000$
• Jun 1st 2010, 01:41 AM
Quote:

Originally Posted by taurus
When I did it I got 2000*10-2000=18000. But I was marked wrong but cant see where I went wrong.

Maybe it was not the final answer that was marked wrong.
Possibly a certain method was being examined to arrive at the answer.

You either calculated the amount of non-zero numbers up to 100,000 divisible by 5
and got 20,000, by dividing 100,000 by 5 as every 5th number is a multiple of 5....
then you subtracted the amount of numbers up to 10,000 divisible by 5 and got 2,000.
Subtracting these gives 18,000.

Unfortunately, this is the amount of non-zero numbers from 10,001 to 100,000 inclusive that are divisible by 5.
It is of course good enough, but doesn't answer the question directly.
The examiner may have thought this is what you did.

Then again, you may have done the following...
Your answer is good enough because you can start from 0, thereby finding the amount of numbers from 0 to 99,999 divisible by 5
and the amount of numbers from 0 to 9,999 divisible by 5.

Maybe the examiner didn't think through your method.

From 10,000 to 99,999 the numbers divisible by 5 end in 0 or 5.
The first (most significant) digit can be any of nine from 1 to 9.
The 2nd digit can be any of 10.
The 3rd digit can be any of 10.
The 4th digit can be any of 10.
The 5th digit can be either of 2.

That's 9(10)(10)(10)2=18,000