Question

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

Answer 1

Hint: we have to find the percentage of the numbers whose squares end with digit 1. So, the numbers whose squares end with digit one are the numbers whose unit digit is 1 or 9. We will first find the numbers which end with 1 or 9 and then find their percentage.

Complete step by step answer:
We will find the numbers whose unit digit is 1 or 9 because the numbers that end with 1 or 9 have their squares which end with 1.
So, from 1 to 10 there are only 2 numbers that end with 1 or 9. They are 1, 9.
Similarly, from 11 to 20. The numbers are 11 and 19.
From 21 to 30. The numbers are 21 and 29.
From 31 to 40 the numbers are 31 and 39.
From 41 to 50 the numbers are 41 and 49.
From 51 to 60 the numbers are 51 and 59.
From 61 to 70 the numbers are 61 and 69.
So, the total numbers that have 1 or 9 at their unit places are 14.
Now, we will find the percentage of x of y using the formula $\dfrac{x}{y} \times 100$. Here, x is 14 and y is the total number, which is 70.
$ = \dfrac{{14}}{{70}} \times 100$
$ = $$\dfrac{{1400}}{{70}}$
\[ = 20\% \]
The percentage of numbers from 1 to 70 which have the squares that end with digit 1 is 20%.

So, the correct answer is “Option A”.

Note:
Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by whole and multiply by 100. In this case also we have used this formula of percentage.