Question

What percentage of numbers from $1$ to $70$ have squares that end in the digit $1$ ?

• A. $1\%$
• B. $14\%$
• C. $20\%$
• D. $21\%$

Answer 1

The correct option is C $20\%$

for a square to end with'1' it's root should have

either '1' or '1' as ones digit.

i.e. $1^2=1$ $9^2=81$ ${11}^2=121$

$\therefore$ no. of squares that end with 1 before ${70}^2\Rightarrow$

$n(1^2,9^2,{11}^2,{19}^2,{21}^2,{29}^2,{31}^2,{39}^2,{41}^2,{49}^2,{51}^2,{59}^2,{61}^2,{69}^2)$

[10 of squares that and with '1' before ${10}^3$] = 14

Percentage = $\frac{[no.ofsquaresnumber1-70thathavesquaresthatandwith1]}{70}\times 100$

$=\frac{14}{70}\times 100$

percentage = 20%

$\therefore$ 20 % of number from 1-70 have squares that

and with digit '1'.