Difference between revisions of "1990 AJHSME Problems/Problem 4"
5849206328x (talk | contribs) (Created page with '==Problem== Which of the following could '''not''' be the unit's digit <nowiki>[one's digit]</nowiki> of the square of a whole number? <math>\text{(A)}\ 1 \qquad \text{(B)}\ 4 …') |
|||
| Line 15: | Line 15: | ||
{{AJHSME box|year=1990|num-b=3|num-a=5}} | {{AJHSME box|year=1990|num-b=3|num-a=5}} | ||
[[Category:Introductory Number Theory Problems]] | [[Category:Introductory Number Theory Problems]] | ||
| + | {{MAA Notice}} | ||
Revision as of 23:05, 4 July 2013
Problem
Which of the following could not be the unit's digit [one's digit] of the square of a whole number?
Solution
We see that 
, 
, 
, and 
, so already we know that either 
is the answer or the problem has some issues.
For integers, only the units digit affects the units digit of the final result, so we only need to test the squares of the integers from 
through 
inclusive. Testing shows that 
is unachievable, so the answer is 
.
See Also
| 1990 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
