37 % of the items in a box are green. Of those, 37 % are also rectangular. Of the green

Question

37 % of the items in a box are green. Of those, 37 % are also rectangular. Of the green rectangular items, 42 % are also metal. Which of the following is closest to the percentage of the items in the box that are not rectangular green metal items?

Accepted Answer

Choice C is correct. It's given that 37 % of the items in a box are green. Let x represent the total number of items in the box. It follows that 37 100 x , or 0.37 x , items in the box are green. It's also given that of those, 37 % are also rectangular. Therefore, 37 100 0.37 x , or 0.1369 x , items in the box are green rectangular items. It's also given that of the green rectangular items, 42 % are also metal. Therefore, 42 100 0.1369 x , or 0.057498 x , items in the box are rectangular green metal items. The number of the items in the box that are not rectangular green metal items is the total number of items in the box minus the number of rectangular green metal items in the box. Therefore, the number of items in the box that are not rectangular green metal items is x - 0.057498 x , or 0.942502 x . The percentage of items in the box that are not rectangular green metal items is the percentage that 0.942502 x is of x . If p % represents this percentage, the value of p is 100 0.942502 x x , or 94.2502 . Of the given choices, 94.25 % is closest to the percentage of items in the box that are not rectangular green metal items. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

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