Question

Which of the following could not be the units digit [ones digit] of the square of a whole number?

$1$

$4$

$5$

$6$

$8$

Answer: E

Concepts:units digit perfect square

Difficulty rating: 800

Solution:

The units digit of a square is determined by the units digit of the number squared. Squaring $0$ through $9$ gives units digits $0,$ $1,$ $4,$ $9,$ $6,$ $5,$ $6,$ $9,$ $4,$ $1$ .

So a square can only end in $0,$ $1,$ $4,$ $5,$ $6,$ or $9$ ; it can never end in $2,$ $3,$ $7,$ or $8$ . Among the choices, only $8$ is impossible.

Thus, the correct answer is E .

1990 AMC 8 Problem 4

Answer: E

Difficulty rating: 800

Solution:

Problem 4 in Other Years