Difference between revisions of "1961 AHSME Problems/Problem 28"
Rockmanex3 (talk | contribs) (Solution to Problem 28) |
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== Problem 28== | == Problem 28== | ||
| − | If <math>2137^{753}</math> is multiplied out, the units' digit | + | If <math>2137^{753}</math> is multiplied out, the units' digit in the final product is: |
<math>\textbf{(A)}\ 1\qquad | <math>\textbf{(A)}\ 1\qquad | ||
| Line 7: | Line 7: | ||
\textbf{(C)}\ 5\qquad | \textbf{(C)}\ 5\qquad | ||
\textbf{(D)}\ 7\qquad | \textbf{(D)}\ 7\qquad | ||
| − | \textbf{(E)}\ 9</math> | + | \textbf{(E)}\ 9</math> |
==Solution== | ==Solution== | ||
Revision as of 03:51, 17 March 2020
Problem 28
If 
is multiplied out, the units' digit in the final product is:
Solution
has a unit digit of 
.
has a unit digit of 
.
has a unit digit of 
.
has a unit digit of 
.
has a unit digit of .
Notice that the unit digit eventually cycles to itself when the exponent is increased by 
. It also does not matter what the other digits are in the base because the units digit is found by multiplying by only the units digit. Since 
leaves a remainder of after being divided by , the units digit of is , which is answer choice 
.
See Also
| 1961 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 27 |
Followed by Problem 29 | |
| 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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
