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The distance from X to Y is 20 miles, and the distance from [#permalink]

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03 May 2003, 17:49

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81% (01:00) correct
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The distance from X to Y is 20 miles, and the distance from X to Z is 12 miles. If d is the distance, in miles, between Y and Z, then d is indicated by:

A. 8 ≤ d ≤ 20 B. 8 ≤ d ≤ 32 C. 12 ≤ d ≤ 20 D. 12 ≤ d ≤ 32 E. 20 ≤ d ≤ 32

The distance from X to Y is 20 miles, and the distance from [#permalink]

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09 Oct 2008, 06:08

The distance from X to Y is 20 miles, and the distance from X to Z is 12 miles. If d is the distance, in miles, between Y and Z, then d is indicated by:

A. 8 ≤ d ≤ 20 B. 8≤ d ≤ 32 C. 12≤d ≤ 20 D. 12≤d ≤ 32 E. 20 ≤d ≤32
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

The distance from X to Y is 20 miles, and the distance from X to Z is 12 miles. If d is the distance, in miles, between Y and Z, then d is indicated by:

A. 8 ≤ d ≤ 20 B. 8≤ d ≤ 32 C. 12≤d ≤ 20 D. 12≤d ≤ 32 E. 20 ≤d ≤32

Another approach: Look at three points as forming a triangle. Third side of triangle will be >= difference between the two sides and <= sum of two sides.

Another approach: Look at three points as forming a triangle. Third side of triangle will be >= difference between the two sides and <=sum of two sides.

Hence, 20-8 <= d <= 20+12.

Caution ! Third side of the triangle will be greater than the difference between the two sides and less than the sum of two sides. (Not >= or <=) In this case, it is not mentioned that the 3 points are not on the same line. Hence the '=' scenario comes into play.

Another approach: Look at three points as forming a triangle. Third side of triangle will be >= difference between the two sides and <=sum of two sides.

Hence, 20-8 <= d <= 20+12.

Caution ! Third side of the triangle will be greater than the difference between the two sides and less than the sum of two sides. (Not >= or <=) In this case, it is not mentioned that the 3 points are not on the same line. Hence the '=' scenario comes into play.

Good point. Thanks for pointing out. When the area of triangle becomes zero, all the three vertices lie on a straight line and then only equality sign will hold true.