SAT Math Multiple Choice Practice Question 522: Answer and Explanation

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Question: 522

21. A cartographer is measuring the straight-line distance between five different towns. The towns are arranged in such a way that any given line connecting two of the towns will not pass through any of the other towns. How many such straight-line distances must she measure?

A. 4
B. 5
C. 7
D. 10
E. 25

Correct Answer: D


D Start by drawing out the towns. Let's call the towns V, W, X, Y, and Z. The problem states that the towns can't all be in a straight line, so draw them in a pentagon. Now connect the towns together. From the first town, V, the cartographer would have to measure 4 distances: VW, VX, VY, and VZ. From town W, she would have to measure only 3 distances, because she has already measured the distance from V to W: WX, WY, and WZ. From town X she would have to measure 2 distances: XY and XZ, and from town Y should have to measure the last distance, YZ. In total, she measured 10 distances between towns.

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