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 $30$ thin rods, one each of every integer length from $1$ cm through $30$ cm. She places the rods with lengths $3$ cm, $7$ cm, and $15$ 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?

$\text{(A) 16}\qquad\text{(B) 17}\qquad\text{(C) 18}\qquad\text{(D) 19}\qquad\text{(E) 20}$

Solution

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