In the figure shown, a square grid is superimposed on the map of a park, represented by the shaded region, in the middle

M7MBA wrote: ↑

Wed Jun 24, 2020 6:30 am

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In the figure shown, a square grid is superimposed on the map of a park, represented by the shaded region, in the middle of which is a pond, represented by the black region. If the area of the pond is 5,000 square yards, which of the following is closest to the area of the park, in square yards, including the area of the pond?

A. 30,000
B. 45,000
C. 60,000
D. 75,000
E. 90,000

[spoiler]OA=B[/spoiler]

Source: Official Guide

Solution:

We see that two squares on the grid represent 5,000 square yards, which means each square represents an area of 2,500 square yards.

We are going to assign a number between 0 and 1, inclusive, for each square, where 1 means the square is totally shaded and 0 means the square is totally unshaded. Any number between 0 and 1 means the square is partially shaded. For example, 0.5 means half of the square is shaded.

We will work each row from top to bottom and each square from left to right, with the rightmost number is the sum of the numbers we’ve assigned on that row.

0.5, 0.9, 0.9, 0.5, 0.1, 0.1 = 3

0.8, 1, 1, 1, 1, 0.9 = 5.7

0.8, 1, 1, 1, 0.9, 0.4 = 5.1

0.7, 1, 1, 0.5, 0, 0 = 3.2

0.3, 0.9, 0.4, 0, 0, 0 = 1.6

Thus the total number of shaded squares is 3 + 5.7 + 5.1 + 3.2 + 1.6 = 18.6. Since each square represents an area of 2,500 square yards, 18.6 squares represent an area of 18.6 x 2,500 = 46,500 square yards. We see that this is closest to 45,000.

Answer: B