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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
A cash register in a certain clothing store is at the same distance fr
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22 Apr 2022, 08:02
22 Apr 2022, 08:02
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Question Stats:
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A cash register in a certain clothing store is at the same distance from two dressing rooms in the store. The distance between the two dressing rooms is 16 feet, which of the following could be the distance between the cash register and either dressing room?
I. 6 feet
II. 12 feet
III. 24 feet
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
I. 6 feet
II. 12 feet
III. 24 feet
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Re: A cash register in a certain clothing store is at the same distance fr
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26 Apr 2022, 02:48
26 Apr 2022, 02:48
Explain this pl
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Re: A cash register in a certain clothing store is at the same distance fr
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26 Apr 2022, 02:49
26 Apr 2022, 02:49
Expert Reply
We see that we have an isosceles triangle with its base equal to 16 feet. The other two sides must be equal. We can use the triangle inequality theorem to determine the possible lengths of those two equal sides. The theorem states that the sum of the lengths of the two shortest sides is greater than the length of the longest side.
I. 6 feet
The resulting triangle would have sides of 6, 6, and 16. The two other sides cannot be 6 since 6 + 6 is not greater than 16.
II. 12 feet
The resulting triangle would have sides of 12, 12, and 16. The two other sides can be 12 since 12 + 12 is greater than 16.
III. 24 feet
The resulting triangle would have sides of 24, 24, and 16. The two other sides can be 24 feet since 16 + 24 is greater than 24. (Note in this case that the two shortest sides are 16 and 24.)
Answer: E
I. 6 feet
The resulting triangle would have sides of 6, 6, and 16. The two other sides cannot be 6 since 6 + 6 is not greater than 16.
II. 12 feet
The resulting triangle would have sides of 12, 12, and 16. The two other sides can be 12 since 12 + 12 is greater than 16.
III. 24 feet
The resulting triangle would have sides of 24, 24, and 16. The two other sides can be 24 feet since 16 + 24 is greater than 24. (Note in this case that the two shortest sides are 16 and 24.)
Answer: E
