How many integers between [10] and [500] begin and end in [3]?
A). [11]
B). [12]
C). [10]
D). [13]
E). [9]

To find how many integers between 10 and 500 begin and end with the digit 3, we need to consider the three-digit and two-digit numbers separately.

Step 1: Three-digit numbers
We are looking for integers between 100 and 500 that begin and end with the digit 3. These numbers are of the form 3 _ 3, where the middle digit can be any digit from 0 to 9. So, the possible numbers are:

303, 313, 323, 333, 343, 353, 363, 373, 383, 393
This gives us 10 possible numbers.

Step 2: Two-digit numbers
We also need to consider two-digit numbers between 10 and 99 that begin and end with the digit 3. These numbers are of the form 3 _ , where the middle digit is also 3. So, the only number is:

33
This gives us 1 possible number.

Step 3: Total Count
Now, adding the results from both steps:

10 numbers from the three-digit range (303 to 393)
1 number from the two-digit range (33)
Thus, the total count is 10 + 1 = 11.

Final Answer:
The correct answer is A) 11.