1990 AJHSME Problems/Problem 4: Difference between revisions
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==Problem== | ==Problem== | ||
Which of the following could '''not''' be the | Which of the following could '''not''' be the units digit <nowiki>[one's digit]</nowiki> of the square of a whole number? | ||
<math>\text{(A)}\ 1 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8</math> | <math>\text{(A)}\ 1 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8</math> | ||
Revision as of 15:57, 29 September 2017
Problem
Which of the following could not be the units 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing
