Graduate Management Admission Test (GMAT) Practice Test

If a 166-foot sidewalk has trees planted every 14 feet with each tree taking up 1 foot, what is the maximum number of trees that can be planted?

1. 10

2. 11

3. 12

4. 13

The correct answer is: 12

To determine the maximum number of trees that can be planted on a 166-foot sidewalk with trees spaced every 14 feet, while accounting for the space taken up by each tree, we must start by understanding how the spacing and the trees interact. Each tree occupies 1 foot of space. Therefore, if we plant a tree every 14 feet, we need to adjust the available length for planting trees accordingly. After accounting for each tree's footprint, the effective distance available for planting trees is reduced to 13 feet between each tree, since the tree at the end of that 14-foot segment occupies 1 foot of space. Next, we need to calculate how many 14-foot segments fit into the 166 feet of sidewalk. Dividing the total length of the sidewalk by the distance from one tree to the next (14 feet) gives us: 166 feet ÷ 14 feet ≈ 11.857 This result indicates that a maximum of 11 full segments of 14 feet can fit within the 166 feet. Since planting the first tree starts at the 0-foot mark, the tree planted at the 11th segment will actually occupy the 154-foot mark (0 + 14×11), with the next tree