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Which of the following gives all possible values of x in the

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Carcass
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Which of the following gives all possible values of x in the [#permalink] New post   23 May 2020, 01:56
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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
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B
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Which of the following gives all possible values of x in the [#permalink] New post   23 May 2020, 14:20
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Carcass wrote:
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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


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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Re: Which of the following gives all possible values of x in the [#permalink] New post   09 Dec 2023, 02:25
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Theory: Each Side of the Triangle is between the | Difference of the other two sides | and Sum of the other two sides

=> |PQ - QR| < PR < PQ + QR
=> |3 - 4| < x < 3 + 4
=> |-1| < x < 7
=> 1 < x < 7

So, Answer will be B
Hope it helps!
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Re: Which of the following gives all possible values of x in the [#permalink]
09 Dec 2023, 02:25
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