counting

[vipulgoyal]

How many integers between 135900 and 557600 have tens digit 5and units digit 2?

ans not given

[Anju@Gurome]

How many integers between 135900 and 557600 have tens digit 5 and units digit 2?

Deleted.
Using combinatorics is way to cumbersome for this problem.
Follow Mitch's post below for a better solution.

[GMATGuruNY]

How many integers between 135900 and 557600 have tens digit 5and units digit 2?

ans not given

The integers all look like this:
XXXX52.

Thus, only the first 4 digits change.
The smallest option for the first 4 digits is 1359.
The greatest option for the first 4 digits is 5575 (since 557652 is beyond the threshold of 557600).
Thus, we need to count the number of integers between 1359 and 5575, inclusive.

To count consecutive integers, use the following formula:
Number of integers = biggest - smallest + 1.
Thus, between 1359 and 5575, inclusive:
Number of integers = 5575 - 1359 + 1 = 4217.

Since there are 4217 options for the first 4 digits, the number of integers between 135900 and 557600 with a tens digit of 5 and a units digit of 2 = 4217.

[vipulgoyal]

thanks experts, Anju 599952 comes in your counting which is greter then thrshold , Mitch's explaination seems valid any take on it ???

[Anju@Gurome]

thanks experts, Anju 599952 comes in your counting which is greter then thrshold , Mitch's explaination seems valid any take on it ???

Yes, my explanation had this flaw which I didn't notice. I've deleted my post.
Mitch's explanation is the ideal solution for this problem.

[vipulgoyal]

Guys got 2 sec solution

557600-135900/100 = 4217

[beatthe800]

How many integers between 135900 and 557600 have tens digit 5and units digit 2?

ans not given

The integers all look like this:
XXXX52.

Thus, only the first 4 digits change.
The smallest option for the first 4 digits is 1359.
The greatest option for the first 4 digits is 5575 (since 557652 is beyond the threshold of 557600).
Thus, we need to count the number of integers between 1359 and 5575, inclusive.

To count consecutive integers, use the following formula:
Number of integers = biggest - smallest + 1.
Thus, between 1359 and 5575, inclusive:
Number of integers = 5575 - 1359 + 1 = 4217.

Since there are 4217 options for the first 4 digits, the number of integers between 135900 and 557600 with a tens digit of 5 and a units digit of 2 = 4217.

What is the idea behind adding 1 in the equation marked in bold