To find the sum of all two-digit positive integers whose squares end with the digits 01, we need to consider all the possibilities and add them together.
First, let's list all the two-digit positive integers. These range from 10 to 99.
Next, we need to find the square of each of these integers and check the last two digits. We can use the following formula to calculate the square of a number:
Square of a number = Number * Number
For example, to find the square of 10, we multiply 10 by itself: 10 * 10 = 100. The last two digits of this square are "00", which do not end in "01", so we exclude 10 from our sum.
We repeat this process for all the two-digit positive integers and add together the numbers whose squares end in "01". For example, for 11, 11 * 11 = 121. The last two digits are "21", which do end in "01", so we include 11 in our sum.
Finally, we add up all the numbers that passed the test. Let's go through each possibility:
11 * 11 = 121 (Include 11)
12 * 12 = 144 (Exclude 12)
13 * 13 = 169 (Exclude 13)
... (continue this process for all two-digit positive integers)
After checking all the possibilities, we add together the numbers that passed the test:
11 + ... (continue this process for all two-digit positive integers)
By doing this, we would get the sum of all two-digit positive integers whose squares end with the digits "01".