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

 
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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
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"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>
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<math>\textbf{(A)}\ 9 \qquad \textbf{(B)}\ 12 \qquad \textbf{(C)}\ 13 \qquad \textbf{(D)}\ 16 \qquad \textbf{(E)}\ 23</math>
  
 
==Solution==
 
==Solution==
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Now we just check the statement for <math>n=9,12,16</math>.  If <math>n=12</math> or <math>n=16</math>, then <math>n-2</math> is <math>10</math> or <math>14</math>, which aren't prime.  However, <math>n=9</math> makes <math>n-2=7</math>, which is prime, so <math>n=9</math> proves the statement false.
 
Now we just check the statement for <math>n=9,12,16</math>.  If <math>n=12</math> or <math>n=16</math>, then <math>n-2</math> is <math>10</math> or <math>14</math>, which aren't prime.  However, <math>n=9</math> makes <math>n-2=7</math>, which is prime, so <math>n=9</math> proves the statement false.
  
<math>\boxed{\text{A}}</math>
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Therefore, the answer is <math>\boxed{\textbf{A}}</math>, 9.
  
 
==See Also==
 
==See Also==

Latest revision as of 15:44, 24 May 2023

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

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

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.

Therefore, the answer is $\boxed{\textbf{A}}$, 9.

See Also

1987 AJHSME (ProblemsAnswer KeyResources)
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

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