What percentage of numbers from 1 to 70 have squares that end in the digit 1?A. 20 %B. 25 %C. 15 %D. 16 %

To solve this question, we need to identify the numbers from 1 to 70 whose squares end in the digit 1.

Step-by-step solution:
Determine the possible last digits of squares: To find numbers whose squares end in 1, we need to first observe the last digits of the squares of integers from 0 to 9 (since the last digit of any number only depends on the last digit of that number).

0^2 = 0
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 6
5^2 = 5
6^2 = 6
7^2 = 9
8^2 = 4
9^2 = 1
From this, we see that the squares of numbers ending in 1 or 9 will have squares ending in 1. Therefore, a number whose square ends in 1 must have a last digit of either 1 or 9.

List the numbers from 1 to 70 that end in 1 or 9: The numbers from 1 to 70 that end in 1 or 9 are:

Numbers ending in 1: 1, 11, 21, 31, 41, 51, 61
Numbers ending in 9: 9, 19, 29, 39, 49, 59, 69
Count the numbers: There are 7 numbers ending in 1 and 7 numbers ending in 9, making a total of 7 + 7 = 14 numbers whose squares end in 1.

Calculate the percentage: There are 70 numbers in total (from 1 to 70). The percentage of numbers whose squares end in 1 is:

(14 / 70) * 100 = 20%

Final Answer:
The percentage of numbers from 1 to 70 whose squares end in the digit 1 is 20%.

So, the correct answer is A. 20%.