Problem 19 · 2011 Math Kangaroo
Stretch
Logic & Word Problems
spatial-reasoning
Jan cannot draw very accurately, but he tried to produce a road map of his village. The relative positions of the houses and the street crossings are all correct, but three of the roads are actually straight and only the Qurwikroad is not. Who lives on the Qurwikroad?
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Answer: C — Carol
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Hint 1 of 3
The house positions and crossings are drawn correctly, so a road is really straight only if its two ends could be joined by a straight line in the picture without crossing another road.
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Hint 2 of 3
Three of the four roads can be straightened that way; the Qurwikroad is the one that cannot.
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Hint 3 of 3
Check each house's road to see which one is forced to stay curved.
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Approach: find the one road that cannot be a straight line given the fixed positions
- Since the positions of houses and crossings are accurate, a road is genuinely straight exactly when its drawn endpoints can be connected by a straight segment consistent with the other crossings.
- Three of the four roads pass that test, so they are the straight ones.
- The remaining road, the one whose endpoints cannot be joined straight without conflicting with the layout, runs to Carol's house.
- So Carol lives on the Qurwikroad, choice (C).
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