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Problem Solving And Data Analysis · Percentages And Unit Conversions

SAT Percentages And Unit Conversions Practice Questions (Free + Explanations) | Quiz 7

Question 12345 of 5

Question 1 of 5

A square has side length centimeters. Its side length is increased by , and then the area of the larger square is converted from square centimeters to square meters. Which expression represents the area of the larger square in square meters?

Explanation

If the original side length is , then increasing it by gives a new side length of . The area of the larger square is therefore square centimeters. Since meter centimeters, square meter square centimeters. So to convert from square centimeters to square meters, divide by . The area in square meters is , which is choice C.

Concept summary

When a length is multiplied by a factor, area is multiplied by the square of that factor. Also, converting square units requires squaring the linear conversion factor.

Question 2 of 5

A delivery company charges a fuel surcharge based on the total distance of a route. Last month, a route was 120 miles long. This month, the route was changed so that its length increased by 15%, and the company reports distance in kilometers, using mile kilometers. Approximately how many more kilometers is the route this month than it was last month?

Explanation

First find the increase in miles: of is miles. Then convert that increase to kilometers: kilometers. Therefore, the route is approximately kilometers longer this month.

Concept summary

To solve percentage-and-conversion problems, first identify whether the question asks for the total amount or the change, then apply the percent and convert units in the correct order.

Question 3 of 5

A recipe uses ounces of dried fruit. A larger batch uses more dried fruit, and the amount for the larger batch is to be written in pounds. Which expression is equivalent to the number of pounds of dried fruit needed for the larger batch?

Explanation

A increase means multiply the original amount by . Starting with ounces, the larger batch uses ounces. Since ounces equals pound, convert ounces to pounds by dividing by . So an equivalent expression is , which matches choice A.

Concept summary

To increase a quantity by a percent, multiply by the percent written as a decimal. To convert ounces to pounds, divide by .

Question 4 of 5

A graph shows the relationship between distance, in kilometers, and distance, in miles, for several road routes. The points , , and lie on the graph, where the first coordinate is kilometers and the second coordinate is miles. Based on this graph, about what percent of a distance measured in kilometers is the same distance measured in miles?

Explanation

To find what percent of the kilometers value is equal to the miles value, use the ratio . From any point on the graph, such as , this ratio is . Converting to a percent gives . Since the question asks for about what percent, the best answer is .

Concept summary

When interpreting a coordinate graph for unit conversions, use the ratio of the output value to the input value, then multiply by 100 to express that ratio as a percent.

Question 5 of 5

A laboratory recorded the amount of a liquid sample in two units, as shown in the table.

| Sample | Volume (milliliters) | Volume (liters) |
|---|---:|---:|
| 1 | 250 | 0.25 |
| 2 | 600 | 0.60 |
| 3 | 1,200 | 1.20 |
| 4 | 850 | ? |

The laboratory then increased the volume of Sample 4 by . Based on the table, what is the new volume of Sample 4 in liters?

Explanation

From the table, milliliters equals liter, so milliliters is liter. Increasing by means multiply by :

So the new volume is liters.

Concept summary

Use the table to convert between milliliters and liters, then apply a percent increase by multiplying by the percent written as a decimal.

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