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

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

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