Official Guide Explanation:
Problem Solving #D19




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Solution and Metadata

Question: D19
Page: 22
Difficulty: 4 (Moderately Easy)
Category 1: Geometry > Triangles > Length of sides

Explanation: The limitations on the length of a side of a triangle are that it must be greater than the difference between the lengths of the other two sides, and less than the sum of the lengths of the other two sides. Since two sides of the triangle are 2 and 7, k must be greater than 5 and less than 9. Since k is an integer, the only possible values are 6, 7, and 8. However, the question tells us that k is less than 7, meaning that 6 is the only possibility. Choice (A) is correct.

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