Difference between revisions of "1987 AJHSME Problems/Problem 20"
5849206328x (talk | contribs) (New page: ==Problem== "If a whole number <math>n</math> is not prime, then the whole number <math>n-2</math> is not prime." A value of <math>n</math> which shows this statement to be false is <mat...) |
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==Problem== | ==Problem== | ||
| − | "If a whole number <math>n</math> is not prime, then the whole number <math>n-2</math> is not prime." A value of <math>n</math> which shows this statement to be false is | + | "If a whole number <math>n</math> is not [[prime]], then the whole number <math>n-2</math> is not prime." A value of <math>n</math> which shows this statement to be false is |
<math>\text{(A)}\ 9 \qquad \text{(B)}\ 12 \qquad \text{(C)}\ 13 \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 23</math> | <math>\text{(A)}\ 9 \qquad \text{(B)}\ 12 \qquad \text{(C)}\ 13 \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 23</math> | ||
| Line 15: | Line 15: | ||
==See Also== | ==See Also== | ||
| − | + | {{AJHSME box|year=1987|num-b=19|num-a=21}} | |
[[Category:Introductory Number Theory Problems]] | [[Category:Introductory Number Theory Problems]] | ||
| + | [[Category:Logic Problems]] | ||
Revision as of 18:40, 30 May 2009
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 | ||
