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Which of the following gives all possible values of \(x\)

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by Brent@GMATPrepNow » Wed Aug 14, 2019 4:02 pm
BTGmoderatorLU wrote:Source: Official Guide

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Which of the following gives all possible values of \(x\) in the figure above?

A. \(1 < x < 4\)
B. \(1 < x < 7\)
C. \(3 < x < 5\)
D. \(4 < x < 7\)
E. \(5 < x < 12\)

The OA is B
IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B

Applying the above rule, we get: 4 - 3 < x < 4 + 3
Simplify: 1 < x < 7

Answer: B

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by Scott@TargetTestPrep » Sun Aug 18, 2019 6:28 pm
BTGmoderatorLU wrote:Source: Official Guide

Image

Which of the following gives all possible values of \(x\) in the figure above?

A. \(1 < x < 4\)
B. \(1 < x < 7\)
C. \(3 < x < 5\)
D. \(4 < x < 7\)
E. \(5 < x < 12\)

The OA is B
In any triangle, the length of the third side must be more than the difference of the other sides and less than the sum of those two sides. Therefore, we have:

4 - 3 < x < 4 + 3

1 < x < 7

Answer: B

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