If k is an Integer and 2 < k < 7, for how many Different Values GMAT Problem Solving

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?

(A) one
(B) two
(C) three
(D) four
(E) five

Correct Answer: A
Solution and Explanation:
Approach Solution 1:

You must use the information supplied in the question to solve this GMAT problem. These concerns cover numerous mathematical disciplines. This question concerns algebra. Because of how the options are presented, it is difficult to select the optimal option. Candidates must comprehend the correct approach to obtaining the required response. Only one of the five supplied alternatives is correct.
It is asked in the question that how many alternative values of k exist for a triangle with sides measuring 2, 7, and k if k is an integer and 2 < k < 7.
When the lengths of two sides of a triangle are A and B, the third side's length is equal to the difference between A and B plus the sum of A and B.
Hence, we can write: If a triangle has sides 2, 7, and k. 7 - 2 < k < 7 + 2
Reduce to obtain: 5 < k < 9
According to our information, k is an integer, and 2 < k < 7.
Hence, k = 6 is the only value of k that may satisfy the inequality 5 < k < 9.

A is the correct answer.

Approach Solution 2:

You must use the information supplied in the question to solve this GMAT problem. These concerns cover numerous mathematical disciplines. This question concerns algebra. Because of how the options are presented, it is difficult to select the optimal option. Candidates must comprehend the correct approach to obtaining the required response. Only one of the five supplied alternatives is correct.

It is asked in the question that how many alternative values of k exist for a triangle with sides measuring 2, 7, and k if k is an integer and 2 < k < 7.
|7-2| < k < |7+2|
or 5 < k < 9
thus k = 6, 7, 8, but 2 < k < 7
therefore, k = 6

A is the correct answer.

Approach Solution 3:

You must use the information supplied in the question to solve this GMAT problem. These concerns cover numerous mathematical disciplines. This question concerns algebra. Because of how the options are presented, it is difficult to select the optimal option. Candidates must comprehend the correct approach for obtaining the required response. Only one of the five supplied alternatives is correct.

It is asked in the question that how many alternative values of k exist for a triangle with sides measuring 2, 7, and k if k is an integer and 2 < k < 7.

The triangle inequality theorem, which asserts that the lengths of any two sides of a triangle (in this case, sides 2 and k) added together must be longer than the length of the third side of the triangle, can be used (in this case, 7).

So, we can see:
2 + k > 7
k > 5
The only integer value of k that is more than 5 but less than 7 is 6, since k < 7.

A is the correct answer.

“If k is an integer and 2 < k < 7, for how many different" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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