Question

A number becomes a perfect square when we subtract 1 from it. Which of the given options cannot be the last digit of that number?
A. 2
B. 4
C. 5
D. 0

Answer 1

Hint: We first try to find the relation between the unit digits of a number and its square number. From the list we find the number which can’t be the last of the given number.

Complete step-by-step answer:
We first try to find the unit digit of a square number.
The final digit for a number can be in the range of $0-9$.
Let us assume it as variable $a$ for the unit digit of the number. Then $a\in \left[ 0,9 \right]$.
We try to find the unit digit of the square number which is denoted by $A$.
If $a$ is 0 then $A$ will be also 0.
If $a$ is 1, 9 then $A$ will be also 1.
If $a$ is 2, 8 then $A$ will be also 4.
If $a$ is 3, 7 then $A$ will also be 9.
If $a$ is 4, 6 then $A$ will be also 6.
If $a$ is 5 then $A$ will be also 5.
The unit digit of the square number has to be from 0, 1, 4, 5, 6, 9.
It cannot be 2, 3, 7, 8.
A number becomes a perfect square when we subtract 1 from it. Therefore, the number’s unit digit can’t be 3, 4, 8, 9. The correct option is B.
So, the correct answer is “Option B”.

Note: The square number’s digit number is not important to decide about the unit digit. The unit digit is only responsible for the solution of the problem.