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The townships of Addington and Bordenview are 65 miles apart, and Clea

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The townships of Addington and Bordenview are 65 miles apart, and Clea  [#permalink]

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New post 25 Feb 2019, 01:47
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59% (01:47) correct 41% (01:48) wrong based on 39 sessions

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The townships of Addington and Bordenview are 65 miles apart, and Clearwater is 40 miles from Bordenview. If the three towns do not lie on a straight line, which of the following could be the distance from Addington to Clearwater?

A. 15
B. 25
C. 35
D. 105
E. 125

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Re: The townships of Addington and Bordenview are 65 miles apart, and Clea  [#permalink]

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New post 25 Feb 2019, 08:50
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Bunuel wrote:
The townships of Addington and Bordenview are 65 miles apart, and Clearwater is 40 miles from Bordenview. If the three towns do not lie on a straight line, which of the following could be the distance from Addington to Clearwater?

A. 15
B. 25
C. 35
D. 105
E. 125


Here's a sketch of what the map COULD look like:
Image

So, we are basically trying to find the length of the THIRD SIDE of a triangle.

We can apply this 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

We get: 65 - 40 < length of side AC < 65 + 40
Simplify to get: 25 < length of side AC < 105

Check the answer choices....
Only answer choice C is BETWEEN 25 and 105

Answer: C

Cheers,
Brent

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Re: The townships of Addington and Bordenview are 65 miles apart, and Clea  [#permalink]

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New post 26 Feb 2019, 00:49
Bunuel wrote:
The townships of Addington and Bordenview are 65 miles apart, and Clearwater is 40 miles from Bordenview. If the three towns do not lie on a straight line, which of the following could be the distance from Addington to Clearwater?

A. 15
B. 25
C. 35
D. 105
E. 125



abc all lie not on straight line so they are all present likewise triangular points
so
65+40= 105 and 65-40 ; 25
A to C will be between 105 to 25
only value 35 IMO C
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Re: The townships of Addington and Bordenview are 65 miles apart, and Clea  [#permalink]

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New post 27 Feb 2019, 10:16
Bunuel wrote:
The townships of Addington and Bordenview are 65 miles apart, and Clearwater is 40 miles from Bordenview. If the three towns do not lie on a straight line, which of the following could be the distance from Addington to Clearwater?

A. 15
B. 25
C. 35
D. 105
E. 125


We notice that since the three towns do not lie on a straight line, they form a triangle, with two sides of lengths 40 and 65 miles.

By the triangle inequality, the distance between Addington and Clearwater is no more than 65 + 40 = 105 miles and no less than 65 - 40 = 25 miles. The only choice that fits these criteria is C.

Answer: C
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Re: The townships of Addington and Bordenview are 65 miles apart, and Clea   [#permalink] 27 Feb 2019, 10:16
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