Question 37-of-

3.2 Percentages - Successive percent changes
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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?

A.

1.16 %

B.

57.50 %

C.

94.25 %

D.

98.84 %

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

Hard-difficulty · SAT Math · Percentages — Successive percent changes. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

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 37100x, or 0.37x, items in the box are green. It's also given that of those, 37% are also rectangular. Therefore, 371000.37x, or 0.1369x, items in the box are green rectangular items. It's also given that of the green rectangular items, 42% are also metal. Therefore, 421000.1369x, or 0.057498x, 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-0.057498x, or 0.942502x. The percentage of items in the box that are not rectangular green metal items is the percentage that 0.942502x is of x . If p% represents this percentage, the value of p is 1000.942502xx, 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.