Explanation

Take the task of creating 2-digit numbers and break it into stages.

Stage 1: Select a digit for the TENS position.
We can choose any digit from 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 1 in 9 ways

[Aside: we cannot choose 0 for the tens position, because numbers like 03 and 07 are not considered 2-digit numbers]

Stage 2: Select a digit for the UNITS position.
In most cases, the UNITS digit can be any of the following: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
HOWEVER, for this question, the units digit must be DIFFERENT from the tens digit we selected in stage 1
So, once select a digit in stage 1, we cannot re-use it in stage 2.
So, we can complete stage 2 in 9 ways

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a 2-digit number) in (9)(9) ways (= 81 ways)

So, we have:
Quantity A: 81
Quantity B: 80


Answer: A

Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.

Cheers,
Brent
_________________

Brent's approach is probably better, but if you get stuck, you could say there is 90 two digit numbers (# of values in arithmetic series that increments by 1 = last # - first # + 1 --> so for this problem --> 99-10+1 = 90) then list out all the two digit numbers which have the same first and last digit (11,22,33....99) and count them (there are 9). Then find the difference, 90-9 = 81.

A is 81
B is 80

Answer is A

Here is my approach.
calculate the total number between 10-100 inclusive, 100-10+1=91
and then from there subtract all number which unit digit equal ten, such as , 11,22,33, which is 9.
= 91-9=82.
A is the answer.

I'm not sure about my approach.

This was the approach I took, except the question asks for the number of positive two digit numbers. So instead of counting from 10 to 100, it's 10 to 99. So 99-10+1 = 90, and then you subtract out the 9 multiples of 11, giving you 90-9 = 81.

yeah forgot that
Thanks for the explanation

hey, what if i wanna go from units to tens, in that case unit number could be chosen from 0-9 meaning 10 numbers and for tens i have 8 numbers, so wouldn't 10*8 be 80? any reason why i can't do it this way?

Two digits Number means 10 to 99
Here, I can't repeat the same digit placed on the tens digit. So, technically 11,22,33,44, 55,66,77,88,99 are those two digits number we can't use.
Again, 10-99 it holds 91 numbers and we have to delete 9 same numbers.
So, 91-9=82

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