Difference between revisions of "2019 AMC 10B Problems/Problem 2"

(Created page with "hey guys")
 
(Video Solution 1)
(21 intermediate revisions by 18 users not shown)
Line 1: Line 1:
hey guys
+
{{duplicate|[[2019 AMC 10B Problems|2019 AMC 10B #2]] and [[2019 AMC 12B Problems|2019 AMC 12B #2]]}}
 +
 
 +
==Problem==
 +
 
 +
Consider the statement, "If <math>n</math> is not prime, then <math>n-2</math> is prime." Which of the following values of <math>n</math> is a counterexample to this statement?
 +
 
 +
<math>\textbf{(A) } 11 \qquad \textbf{(B) } 15 \qquad \textbf{(C) } 19 \qquad \textbf{(D) } 21 \qquad \textbf{(E) } 27</math>
 +
 
 +
==Solution==
 +
 
 +
Since a counterexample must be a value of <math>n</math> which is not prime, <math>n</math> must be composite, so we eliminate <math>\text{A}</math> and <math>\text{C}</math>. Now we subtract <math>2</math> from the remaining answer choices, and we see that the only time <math>n-2</math> is '''not''' prime is when <math>n = \boxed{\textbf{(E) }27}</math>.
 +
 
 +
~IronicNinja
 +
 
 +
minor edit (the inclusion of not) by AlcBoy1729
 +
 
 +
==Video Solution (HOW TO THINK CRITICALLY!!!)==
 +
https://youtu.be/CgZnUftXoig
 +
 
 +
~Education, the Study of Everything
 +
 
 +
==See Also==
 +
{{AMC10 box|year=2019|ab=B|num-b=1|num-a=3}}
 +
{{AMC12 box|year=2019|ab=B|num-b=1|num-a=3}}
 +
{{MAA Notice}}

Revision as of 13:23, 29 May 2023

The following problem is from both the 2019 AMC 10B #2 and 2019 AMC 12B #2, so both problems redirect to this page.

Problem

Consider the statement, "If $n$ is not prime, then $n-2$ is prime." Which of the following values of $n$ is a counterexample to this statement?

$\textbf{(A) } 11 \qquad \textbf{(B) } 15 \qquad \textbf{(C) } 19 \qquad \textbf{(D) } 21 \qquad \textbf{(E) } 27$

Solution

Since a counterexample must be a value of $n$ which is not prime, $n$ must be composite, so we eliminate $\text{A}$ and $\text{C}$. Now we subtract $2$ from the remaining answer choices, and we see that the only time $n-2$ is not prime is when $n = \boxed{\textbf{(E) }27}$.

~IronicNinja

minor edit (the inclusion of not) by AlcBoy1729

Video Solution (HOW TO THINK CRITICALLY!!!)

https://youtu.be/CgZnUftXoig

~Education, the Study of Everything

See Also

2019 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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 AMC 10 Problems and Solutions
2019 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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 AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png