1990 AMC 8 Problem 4
Attempt Problem 4 of the 1990 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1990 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
4.
Which of the following could not be the units digit [one’s digit] of the square of a whole number?
Answer: E
Small hint:
The units digit of a square depends only on the units digit of the number being squared
Big hint:
Square each of the digits through and record only the units digit of each result
Solution:
The units digit of a square is determined by the units digit of the number squared. Squaring through gives units digits .
So a square can only end in or ; it can never end in or . Among the choices, only is impossible.
Thus, the correct answer is E .
Problem 4 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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