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Which of the following gives all possible values of x in the figure ab : Problem Solving (PS)
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# Which of the following gives all possible values of x in the figure ab

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Re: Which of the following gives all possible values of x in the figure ab [#permalink]
third side rule simple
sum <7 and >1
IMO B

Bunuel wrote:

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

PS05602.01
Quantitative Review 2020 NEW QUESTION

Attachment:
2019-04-26_1739.png
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Re: Which of the following gives all possible values of x in the figure ab [#permalink]

Solution

Given
In this question, we are given
• The diagram of a triangle PQR, with side lengths PQ = 3, QR = 4, and PR = x

To Find
We need to determine
• Among the given choices, which range defines all possible values of x.

Approach & Working
We know that, for any given triangle, sum of any two sides is always greater than the third side.

Therefore, we can say
• 3 + 4 > x
Or, x < 7

Similarly, x + 4 > 3
Or, x > 1

Combining the two results, we can conclude 1 < x < 7.

Hence, the correct answer is option B.

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Re: Which of the following gives all possible values of x in the figure ab [#permalink]
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Bunuel wrote:

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

PS05602.01
Quantitative Review 2020 NEW QUESTION

Attachment:
2019-04-26_1739.png

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

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Re: Which of the following gives all possible values of x in the figure ab [#permalink]
Top Contributor
Bunuel wrote:

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

PS05602.01
Quantitative Review 2020 NEW QUESTION

Attachment:
2019-04-26_1739.png

A property of a triangle is: The length of the third side must be greater than the difference of the other two sides and less than the sum of those two sides.

So, $$4 - 3 < x < 4 + 3$$ $$= 1 < x < 7$$

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Re: Which of the following gives all possible values of x in the figure ab [#permalink]
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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