37\% \text{ of the items in a box are green. Of those, } 37\% \text{ are also rectangular. Of the green rectangular items, } 42\% \text{ 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?}

C. 94.25\%. 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 $\frac{37}{100}x$, or $0.37x$, items in the box are green. It's also given that of those, 37\% are also rectangular. Therefore, $\frac{37}{100}(0.37x)$, 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, $\frac{42}{100}(0.1369x)$, 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 $100\left(\frac{0.942502x}{x}\right)$, 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.

SAT Math skill page

SAT Percentages Practice

Turn SAT percent problems into multipliers, equations, and clean comparisons instead of guessing from answer choices.

Practice percentages in Dolphin Practice questions

10-15 min practice time3 questions on pageProblem Solving and Data Analysis

Practice time10-15 min

Question bank3 questions

Best forProblem Solving and Data Analysis

What this tests

What to know for this SAT skill

Find a percent of a quantity
Use percent increase and decrease multipliers
Solve reverse percentage questions
Translate discounts, tax, and growth into equations

Dolphin question bank

Practice your skill

Question 1 of 3Hard

The number a is 190% greater than the number b. The number b is 80% less than 24. What is the value of a?

9.12
13.92
26.40
36.48

Show answer and solution

Correct answerB. 13.92

Solution walkthrough

It's given that the number $b$ is 80% less than 24. It follows that $b$ is equal to 24 minus 80% of 24, which can be written as $b = 24 - \frac{80}{100} \times 24$ .
This is equivalent to $b = 24 - 0.8 \times 24$ , or $b = 4.8$ . It's also given that the number $a$ is 190% greater than the number $b$ .
It follows that $a$ is equal to $b$ plus 190% of $b$ . Since $b = 4.8$ , this can be written as $a = 4.8 + \frac{190}{100} \times 4.8$ .
This is equivalent to $a = 4.8 + 1.9 \times 4.8$ , or $a = 13.92$ .

Question 2 of 3Hard

After 20% 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?

72
90
450
1,800

Show answer and solution

Correct answerB. 90

Solution walkthrough

It's given that 20% 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 $\frac{20}{100} x$ , or $0.20 x$ , marbles were removed from the group. Therefore, $x - 0.20 x$ marbles remained in the group.
It's also given that 360 marbles remained in the group. Thus, $x - 0.20 x = 360$ , or $0.80 x = 360$ .
Dividing both sides of this equation by 0.80 yields $x = 450$ . Substituting 450 for $x$ in the expression $0.20 x$ yields $0.20 (450)$ , or 90.
Therefore, 90 marbles were removed from the group.

Question 3 of 3Hard

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?

1.16%
57.50%
94.25%
98.84%

Show answer and solution

Correct answerC. 94.25%

Solution walkthrough

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 $\frac{37}{100} x$ , or $0.37 x$ , items in the box are green.
It's also given that of those, 37% are also rectangular. Therefore, $\frac{37}{100} (0.37 x)$ , 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, $\frac{42}{100} (0.1369 x)$ , 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 $100 (\frac{0.942502 x}{x})$ , 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.

Avoid these traps

Common mistakes on this skill

Adding instead of multiplying

Percent change is multiplicative. A 20% increase means multiply by 1.20, not just add 20.

Using the final value as the original

Reverse percent questions require solving from the final amount back to the starting amount.

Confusing percent with decimal form

Convert 15% to 0.15 and 85% to 0.85 before writing the equation.

Study plan

How to practice this skill in Dolphin

Convert every percent into a decimal or fraction before calculating.
Use 1 plus the rate for increases and 1 minus the rate for decreases.
For reverse percentages, write an equation using the final value.
Check whether the answer should be larger or smaller than the given value.

Practice percentages in Dolphin

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FAQ

Questions about SAT Percentages Practice

Are percentages common on SAT Math?

Yes. Percent questions appear in discounts, growth, data comparisons, and real-world word problems.

What is the fastest way to solve percent change?

Use a multiplier. For example, a 12% increase is multiplication by 1.12, and a 12% decrease is multiplication by 0.88.

Why do reverse percent questions feel harder?

They start with the final value, so you have to divide by the percent multiplier instead of multiplying forward.