Difference between revisions of "1987 AJHSME Problems/Problem 20"
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Revision as of 23:53, 4 July 2013
Problem
"If a whole number is not prime, then the whole number
is not prime." A value of
which shows this statement to be false is
Solution
To show this statement to be false, we need a non-prime value of such that
is prime. Since
and
are prime, they won't prove anything relating to the truth of the statement.
Now we just check the statement for . If
or
, then
is
or
, which aren't prime. However,
makes
, which is prime, so
proves the statement false.
See Also
1987 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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.