Maximizing Tree Placement on Sidewalks: A Math Perspective

When you think about trees lining a sidewalk, you might be imagining a serene stroll surrounded by nature. But there’s a bit more math involved than you may realize! Have you ever wondered how trees can be planted efficiently along a footpath? Well, let’s take a closer look at a decent little problem that might pop up in the GMAT quant section, and how to think through it logically.

Imagine a 166-foot sidewalk boasting trees every 14 feet apart, and each tree occupying 1 foot of space—sounds simple, right? On the surface, it looks like the answer might be straightforward; however, the nuances make it rather intriguing. To tackle this, we need to break it down, keeping in mind the math behind how trees line up and claim their territory.

Understanding the Space: It’s Not Just About Distance!
Now, here’s the kicker: each tree, while occupying a lovely spot in our green paradise, also takes up a foot of space. This means that even though we're spacing them out every 14 feet, there’s a 1-foot footprint we’ve got to account for. So, when a tree is planted at the end of each segment, it effectively reduces the distance available for the next tree. Instead of 14 feet to plant the next tree, we only have 13 feet left once the first one takes its place.

Calculating the Segments
We’re going to break it down with some basic division. If we take our total length of the sidewalk—166 feet—and divide it by the 14 feet that separates the trees, we get a number that’s not quite whole:
166 feet ÷ 14 feet ≈ 11.857.

What this tells us is that we can fit a maximum of 11 complete 14-foot segments within the 166-foot sidewalk. Now, what does that mean for our trees? Let’s visualize it. Consider that the first tree gets planted at the starting point, or 0 feet. The 11th tree sits proudly at the 154-foot mark. But wait—what happened to that last jump from 154 to 168 feet? Herein lies the beauty of number calculations—the next tree would land at 168 feet, which is beyond our real estate limit!

The Final Calculation
However, many might be tempted to assume that because we reached 11 divisions, we can only place 11 trees. The catch is subtle but crucial: the very first tree was counted when we started counting from 0! So, we actually get to plant an additional tree, making it a total of 12 trees—easy math, right?

So, the answer? A maximum of 12 trees can find a home on that lovely sidewalk. Kinda makes you appreciate nature’s arrangement, doesn’t it? Whether you’re preparing for the GMAT or just sharpening your math skills for everyday problems, understanding how to look at a problem from multiple angles not only makes it easier but also a bit more fun.

In the grand scheme of things, math doesn’t always need to be dry or intimidating. Utilize these kinds of questions to connect dots between theory and practice. The beauty of quantitative reasoning is in both the challenge and the satisfaction when you find the right answer. Now go forth, calculate wisely, and maybe plant a tree or two along your way!