Question: If x – 1, x + 6, x + 7 are 3 side lengths of a triangle, what is the value of x?

1. 4
2. 5
3. 6
4. 7
5. 8

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

The approach used to solve this question is using the Pythagorean Triples and they are as follows:
(3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), (33, 56, 65), (16, 63, 65), (48, 55, 73), (36, 77, 85), (13, 84, 85), (39, 80, 89), and (65, 72, 97)
In this question, we could try (5, 12, 13). Consider (x+6) first in the given equation, as it is easier to make 12 by adding 6. So let’s presume x = 6,
Then (x + 7) = 13 and (x – 1) = 5
Therefore, the value of x = 6.

Approach Solution 2:
According to the Pythagorean Theorem, if you expand
\((x-1)^2+(x+6)^2=(x+7)^2\)
You get:
\(x^2-2x+1+x^2+12x+36=x^2+14x+49,\)
And then when you simplify, you get \(x^2-4x-12=0\)
From (x – 6) (x + 2) = 0, x = 6
Therefore, the value of x = 6.

“If x – 1, x + 6, x + 7 are 3 side lengths of a triangle, what is the value of x?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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