Difference between revisions of "2017 AMC 10A Problems/Problem 6"
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| + | ==Problem== | ||
Joy has <math>30</math> thin rods, one each of every integer length from <math>1</math> cm through <math>30</math> cm. She places the rods with lengths <math>3</math> cm, <math>7</math> cm, and <math>15</math> cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod? | Joy has <math>30</math> thin rods, one each of every integer length from <math>1</math> cm through <math>30</math> cm. She places the rods with lengths <math>3</math> cm, <math>7</math> cm, and <math>15</math> cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod? | ||
<math>\text{(A) 16}\qquad\text{(B) 17}\qquad\text{(C) 18}\qquad\text{(D) 19}\qquad\text{(E) 20}</math> | <math>\text{(A) 16}\qquad\text{(B) 17}\qquad\text{(C) 18}\qquad\text{(D) 19}\qquad\text{(E) 20}</math> | ||
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| + | ==Solution== | ||
Revision as of 14:28, 8 February 2017
Problem
Joy has 
thin rods, one each of every integer length from 
cm through cm. She places the rods with lengths 
cm, 
cm, and 
cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?
