Percentages SAT question

Math · Problem-Solving and Data Analysis · Medium · Answer it here, explanation included.

In a group, $40$ % of the items are red. Of all the red items in the group, $30$ % also have stripes. What percentage of the items in the group are red with stripes?

ExplanationShow

Choice B is correct. It’s given that in a group, $40%$ of the items are red. It follows that the number of red items in the group can be represented by $0.4 x$ , where $x$ represents the total number of items in the group. It’s also given that of all the red items in the group, $30%$ also have stripes. It follows that the number of items in the group that are red and have stripes can be represented by $0.3 (0.4 x)$ , or $0.12 x$ . The expression $0.12 x$ represents $12%$ of $x$ . Since $x$ represents the total number of items in the group, it follows that $12%$ of the items in the group are red and have stripes.

Choice A is incorrect and may result from subtracting $30%$ from $40%$ rather than calculating $30%$ of $40%$ .

Choice C is incorrect and may result from adding $30%$ and $40%$ rather than calculating $30%$ of $40%$ .

Choice D is incorrect and may result from calculating the percentage that $30%$ is of $40%$ rather than calculating $30%$ of $40%$ .

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