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

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Bunuel
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Which of the following gives all possible values of x in the figure ab [#permalink] New post   26 Apr 2019, 06:41
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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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BrentGMATPrepNow
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Which of the following gives all possible values of x in the figure ab [#permalink] New post   Updated on: 25 Apr 2021, 13:05
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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



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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Originally posted by BrentGMATPrepNow on 26 Apr 2019, 10:07.
Last edited by BrentGMATPrepNow on 25 Apr 2021, 13:05, edited 1 time in total.
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Re: Which of the following gives all possible values of x in the figure ab [#permalink] New post   27 May 2019, 19:17
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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


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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

Answer: B
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Re: Which of the following gives all possible values of x in the figure ab [#permalink] New post   09 Dec 2023, 03:26
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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 figure ab [#permalink] New post   26 Apr 2019, 20:04
Sum of the two sides should always be greater than the third side
only B satisfy this condition



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Re: Which of the following gives all possible values of x in the figure ab [#permalink] New post   28 Apr 2019, 03:50
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


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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] New post   23 May 2019, 05:20
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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] New post   19 Nov 2020, 09:50
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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


Show Spoiler
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, \(4 - 3 < x < 4 + 3\) \(= 1 < x < 7\)

The Answer is B
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Re: Which of the following gives all possible values of x in the figure ab [#permalink]
19 Nov 2020, 09:50
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