Difference between revisions of "1987 AJHSME Problems/Problem 20"

Revision as of 22:53, 4 July 2013

Problem

"If a whole number $n$ is not prime, then the whole number $n-2$ is not prime." A value of $n$ which shows this statement to be false is

$\text{(A)}\ 9 \qquad \text{(B)}\ 12 \qquad \text{(C)}\ 13 \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 23$

Solution

To show this statement to be false, we need a non-prime value of $n$ such that $n-2$ is prime. Since $13$ and $23$ are prime, they won't prove anything relating to the truth of the statement.

Now we just check the statement for $n=9,12,16$ . If $n=12$ or $n=16$ , then $n-2$ is $10$ or $14$ , which aren't prime. However, $n=9$ makes $n-2=7$ , which is prime, so $n=9$ proves the statement false.

$\boxed{\text{A}}$

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.

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 [[Category:Introductory Number Theory Problems]]
 [[Category:Logic Problems]]
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Difference between revisions of "1987 AJHSME Problems/Problem 20"

Revision as of 22:53, 4 July 2013

Problem

Solution

See Also