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In a desert, X and Y are two spots that are separated by 100 km. At point X, are placed two pillars, one black and one white. Along the line joining X and Y, a white pillar is placed for every 180 m and a black pillar is placed for every 350 m. How many times can one find black and white pillars together while traveling from X to Y ?
14
15
16
17
- You start at point X, where one black and one white pillar are already placed.
- Every subsequent white pillar is placed every 180 meters.
- Every subsequent black pillar is placed every 350 meters.
- To find how often black and white pillars coincide, calculate the least common multiple (LCM) of 180 and 350.
- The LCM of 180 and 350 is 630 meters.
- The distance from X to Y is 100,000 meters (100 km).
- Dividing 100,000 meters by 630 meters, you get about 158.73.
- This means black and white pillars coincide at least 158 times along the way.
- Including the starting point at X, the total becomes 159.
Correct Answer: 15
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