Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus
During AMC testing, the AoPS Wiki is in read-only mode and no edits can be made.

Difference between revisions of "2008 iTest Problems/Problem 4"
m (→‎See also)
Line 8: Line 8:
  
 
== See also ==
 
== See also ==
 +
 +
ghgkjhgjghaopsisgreat

Revision as of 19:29, 7 May 2015

Problem

The difference between two prime numbers is $11$. Find their sum.

Solution

We know that any prime number, excluding $2$, is congruent to $1 \pmod 2$. Thus, if both of the primes are not $2$, their difference would be congruent to $0 \pmod 2$. Because $11 \equiv 1 \pmod 2$, one of the primes must be $2$. It follows that the other prime must then be $13$. Therefore, the sum of the two is $13+2=\boxed{15}$.

See also

ghgkjhgjghaopsisgreat

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2008_iTest_Problems/Problem_4&oldid=70140"