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Problem-Solving and Data Analysis / Percentages Difficulty: Hard

After $20 percent sign$ of the original number of marbles in a group were removed from the group, $360$ marbles remained in the group. How many marbles were removed from the group?

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Explanation

Choice B is correct. It's given that $20 percent sign$ of the original number of marbles were removed from the group. Let $x$ represent the original number of marbles in the group. It follows that $StartFraction 20 Over 100 EndFraction x$ , or $0.20 x$ , marbles were removed from the group. Therefore, $x minus 0.20 x$ marbles remained in the group. It's also given that $360$ marbles remained in the group. Thus, $x - 0.20 x = 360$ , or $0.80 x equals 360$ . Dividing both sides of this equation by $0.80$ yields $x equals 450$ . Substituting $450$ for $x$ in the expression $0.20 x$ yields $0.20 left parenthesis 450 right parenthesis$ , or $90$ . Therefore, $90$ marbles were removed from the group.

Choice A is incorrect. This is $20 percent sign$ of the remaining number of marbles.

Choice C is incorrect. This is the original number of marbles, not the number of marbles that were removed.

Choice D is incorrect and may result from conceptual or calculation errors.