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Sub 505 (Easy)|   Geometry|               
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Which of the following gives all possible values of x in the figure ab 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


PS05602.01
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B
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Which of the following gives all possible values of x in the figure ab Updated on: 25 Apr 2021, 13:05
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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Bunuel

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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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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Which of the following gives all possible values of x in the figure ab 26 Apr 2019, 20:04
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Sum of the two sides should always be greater than the third side
only B satisfy this condition



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Which of the following gives all possible values of x in the figure ab 28 Apr 2019, 03:50
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third side rule simple
sum <7 and >1
IMO B

Bunuel

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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Which of the following gives all possible values of x in the figure ab 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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Which of the following gives all possible values of x in the figure ab 27 May 2019, 19:17
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Bunuel

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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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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Which of the following gives all possible values of x in the figure ab 19 Nov 2020, 09:50
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Bunuel

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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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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Which of the following gives all possible values of x in the figure ab 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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Which of the following gives all possible values of x in the figure ab 06 Aug 2025, 22:18
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