Question: If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 7, and k?
- one
- two
- three
- four
- five
Correct Answer: A
Solution and Explanation:
Approach Solution 1:
It is known in the triangle inequality theorem that-
The total of the smaller two sides of a triangle must be greater than the greatest side.
For k values 3,4,5, and 6, the only triangle possible is 2,7, and k = 6 because only 2 + 6 > 7. For k values 3,4, and 5,
The total of the smaller two sides is smaller than the third side; consequently, 6 is the only possible value of k that meets that criteria.
The number of different values of k is there a triangle with sides of lengths 2, 7, and k = one.
Approach Solution 2:
It's easy to answer the following equation and the arithmetic method can also be used in this situation. This can be explored in the following manner:
\(|7-2| < k < |7+2|\)
or 5 < k < 9
thus k = 6, 7, 8, but 2 < k < 7
therefore, k = 6
The number of different values of k is there a triangle with sides of lengths 2, 7, and k = one.
“If k is an integer and 2 < k < 7, for how many different values” - is a topic of the GMAT Quantitative reasoning section of the GMAT exam. The topic has been taken from the book “GMAT Official Guide Quantitative Review”. The candidates must possess solid knowledge of mathematics in order to solve GMAT Problem Solving questions. The candidates can follow GMAT Quant practice papers to become familiar with several sorts of questions that will help them to score better in the exam.
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