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Problem-Solving and Data Analysis Difficulty: Hard

$37 percent sign$ of the items in a box are green. Of those, $37 percent sign$ are also rectangular. Of the green rectangular items, $42 percent sign$ 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?

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Explanation

Choice C is correct. It's given that $37 percent sign$ of the items in a box are green. Let $x$ represent the total number of items in the box. It follows that $StartFraction 37 Over 100 EndFraction x$ , or $0.37 x$ , items in the box are green. It's also given that of those, $37 percent sign$ are also rectangular. Therefore, $StartFraction 37 Over 100 EndFraction left parenthesis 0.37 x right parenthesis$ , or $0.1369 x$ , items in the box are green rectangular items. It's also given that of the green rectangular items, $42 percent sign$ are also metal. Therefore, $StartFraction 42 Over 100 EndFraction left parenthesis 0.1369 x right parenthesis$ , 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 $x minus 0.057498 x$ , 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 $100 left parenthesis StartFraction 0.942502 x Over x EndFraction right parenthesis$ , or $94.2502$ . Of the given choices, $94.25 percent sign$ 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.