Read-Host always outputs a string.
In order to treat the output as a number, you must explicitly convert it to one:
$a = Read-Host "What is your name?"
# Note: Add error handling with try / catch
# and a retry loop to deal with invalid input.
[int] $b = Read-Host "Enter a 2 digit number"
[int] $c = Read-Host "Enter a 3 digit number"
The above type-constrains variables $b and $c to integer values (by placing the [int] cast to the left of the target variable in the assignment), which automatically converts Read-Host's [string] output to [int].
To spell it out with a concrete example that prompts until a two-digit (decimal) number is entered:
do {
try {
[int] $b = Read-Host "Enter a 2 digit number"
} catch {
continue # Not a number - stay in the loop to prompt again.
}
if ($b -ge 10 -and $b -le 99) { break } # OK, exit the loop.
} while ($true)
Note: Strictly speaking, the [int] cast accepts anything that would work as a number literal in PowerShell, which includes hexadecimal representations, such as 0xA, as well as number with a type suffix, such as 10l - see this answer for more information.
As for what you tried:
Except for -, all the operators used in your code have string-specific overloads (meaning); note that it is sufficient for the LHS to be of type [string] to trigger this behavior.[1]
-lt / -ge perform lexical comparison with strings; e.g., '10' -gt '2' yields $false, because, in lexical sorting, string '10' comes before string '2'.
-and / -or treat empty strings as $false, and any nonempty string as $true; e.g.,
'0' -and '0' is $true, because '0' is a nonempty string.
+ performs string concatenation; e.g., '1' + '0' is '10'.
* performs string replication; e.g., '1' * 3 is '111' - the LHS is repeated as many times as specified by the number on the RHS; note that '1' * '3' works the same, because the RHS is coerced to an [int] in this case.
- is the only exception: it always performs a numeric operation, if possible; e.g, '10' - '2' yields 8, because both operands were implicitly converted to [int]s.
[1] Typically, it is the LHS of an operation that determines its data type, causing the RHS to be coerced to a matching type, if necessary.