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Towns A, B, and C lie in a plane but do not lie on a straigh

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Carcass
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Towns A, B, and C lie in a plane but do not lie on a straigh [#permalink] New post   01 Sep 2020, 03:46
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Towns A, B, and C lie in a plane but do not lie on a straight line. The distance between Towns A and B is 40 miles, and the distance between Towns A and C is 110 miles.

Quantity A
Quantity B
The distance between Towns B and C
60 miles



A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.


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AskMathQuestions
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Re: Towns A, B, and C lie in a plane but do not lie on a straigh [#permalink] New post   01 Sep 2020, 15:48
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Carcass wrote:
Towns A, B, and C lie in a plane but do not lie on a straight line. The distance between Towns A and B is 40 miles, and the distance between Towns A and C is 110 miles.

Quantity A
Quantity B
The distance between Towns B and C
60 miles



A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.


KUDOS for the right solution and explanation


Remind that a length of a side of a triangle is between the difference of lengths of other two sides and the sum of them.

You should consider towns \(A, B\) and \(C\) as vertices of a triangle for this question.
Let \(AB, BC\) and \(CA\) be distances between towns \(A\) and \(B\), between towns \(B\) and \(C\), and between towns \(C\) and \(A\), respectively.

Then the distance between \(B\) and \(C\), \(BC\) is between the differences of distances, \(CA - AB = 110 - 40 = 70\), and the sum of distances, \(CA + AB = 110 + 40 = 150\).
Thus we have \(70 < BC < 150\), or \(BC > 60\).

Therefore, A is the right answer.
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Re: Towns A, B, and C lie in a plane but do not lie on a straigh [#permalink] New post   01 Sep 2020, 22:13
Not sure if my approach is correct but I got the right answer

A+B=40
A+B+C=110
40+C=110
C=70

We know that A+B=40
the max distance B could have is 39 and min could be 1
and C is already 70 so distance b/w B and C has to be greater than 60
Option A is the right choice.
Prep Club for GRE Bot
gmatclubot
Re: Towns A, B, and C lie in a plane but do not lie on a straigh [#permalink]
01 Sep 2020, 22:13
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