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Problem Solving And Data Analysis · Percentages And Unit Conversions

SAT Percentages And Unit Conversions Practice Questions (Free + Explanations) | Quiz 9

Question 12345 of 5

Question 1 of 5

The table shows values of a quantity measured in both meters and feet.

A student uses the table to estimate the percent error made by using feet for every meter instead of the actual conversion shown in the table. Based on the table, what is that percent error, to the nearest tenth of a percent?

Explanation

From the table, the conversion rate is constant, so divide feet by meters using any row:

So the actual conversion is about feet per meter.

The student's estimate is feet per meter. Percent error is

Compute the difference:

Then

Rounded to the nearest tenth of a percent, this is .

Therefore, the correct answer is .

Concept summary

To find percent error, first determine the actual unit rate from the table, then use .

Question 2 of 5

A laboratory reports the concentration of a liquid additive as a percent by volume. A technician mixes 300 milliliters of a solution that is additive with 500 milliliters of a solution that is additive. The resulting 800-milliliter mixture is then diluted by adding 200 milliliters of pure water, and the final concentration is additive. Which statement must be true?

Explanation

Let the amount of additive in the 300-milliliter solution be milliliters. Let the amount of additive in the 500-milliliter solution be milliliters. Before dilution, the 800-milliliter mixture contains milliliters of additive. Then 200 milliliters of pure water are added, so the total volume becomes 1,000 milliliters, but the amount of additive stays the same. Since the final concentration is , the final amount of additive must be milliliters. So

Solving gives

and

Therefore, must be true.

Concept summary

Track the amount of the substance separately from total volume. When water is added, the amount of additive stays constant while the total volume changes, so percent concentration must be modeled with additive amount divided by total volume.

Question 3 of 5

A rectangular garden is 30 feet long and 20 feet wide. A uniform walkway is built around the outside of the garden. The area of the walkway alone is 60% of the area of the original garden. What is the width of the walkway, in feet?

Explanation

The area of the original garden is square feet. The walkway's area is 60% of this, so the walkway has area square feet.

Let the width of the walkway be feet. Since the walkway goes around the entire outside, the outer dimensions are by . The total outer area is therefore .

Because the walkway alone has area 360,

So,

Expand:

Divide by 4:

Factor:

So or . A width cannot be negative, so .

The width of the walkway is 3 feet.

Concept summary

For a uniform border around a rectangle, increase each dimension by twice the border width, then compare the new total area to the original area. Percent statements about area must be applied to area, not to side lengths.

Question 4 of 5

A lab orders a chemical that is shipped in bottles labeled 500 milliliters each. Because of evaporation during handling, each bottle contains 4% less than its labeled amount when it is used. A technician needs to prepare 7.2 liters of a diluted solution that is 25% chemical by volume, using only the chemical from these bottles and water. If every bottle used has the same reduced amount, what is the least number of bottles the technician must open?

Explanation

The final solution must be 25% chemical, and the total volume is 7.2 liters. So the amount of chemical needed is liters. Each bottle is labeled 500 milliliters, but each actually contains 4% less, so each bottle has milliliters of chemical. Converting to liters, each bottle contains liter. Now divide the required chemical amount by the amount per bottle: . Since 3.75 bottles are needed, the technician must open 4 whole bottles. Therefore, the least number of bottles is 4.

Concept summary

Solve percentage-and-conversion word problems by finding the required part of the total, adjusting the unit amount by the given percent change, converting units consistently, and then rounding up when a whole number of items is needed.

Question 5 of 5

A quantity is changed by two successive percent adjustments: first it is increased by , and then the result is decreased by . If the final value is greater than the original value, what is the value of ?

Explanation

Let the original value be . After an increase of , the value becomes . Then decreasing that result by multiplies it by , so the final value is

We are told this final value is greater than the original, so it also equals . Set the expressions equal:

Since , divide both sides by :

Now divide by :

Subtract 1:

Multiply by 100:

Therefore, the correct answer is .

Concept summary

Successive percent changes are modeled by multiplying decimal factors. An increase of is a factor of , and a decrease of is a factor of .

Your results

0of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

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Your results

1of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

2of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

3of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

4of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

5of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice