PSAT/NMSQT Prep 2022 - Eggert M.D., Strelka A. 2022

Unit conversion
Ratios, proportions, and percents
Data analysis

LEARNING OBJECTIVE

After this lesson, you will be able to:

· Set up equivalent ratios to make units cancel

To answer a question like this:

City A and city B are 2,000 miles apart, while city C is twice as far from city A as city A is from city B. What is the approximate distance, in inches, between city A and city C? (1 mile = 5,280 feet and 1 foot = 12 inches)

A. 4.3 million

B. 52 million

C. 127 million

D. 253 million

You need to know this:

You can use ratios to perform unit conversions. This is especially useful when there are multiple conversions or when the units are unfamiliar.

For example, though these units of measurement are no longer commonly used, there are 8 furlongs in a mile and 3 miles in a league. Say you’re asked to convert 4 leagues to furlongs. A convenient way to do this is to set up the conversion ratios so that equivalent units cancel:

Notice that all the units cancel out except the furlongs, which is the one you want.

You need to do this:

Set up a series of ratios to make equivalent units cancel. (Keep track of the units by writing them down next to the numbers in the ratios.) You should be left with the units you’re converting into.

Explanation:

City C is twice as far from city A as city A is from city B, so city C is 2(2,000) = 4,000 miles away from city A. Set up a series of ratios to convert to inches (in):

Therefore, (D) is correct.

Try on Your Own

Directions: Take as much time as you need on these questions. Work carefully and methodically. There will be an opportunity for timed practice at the end of the chapter.

6. Jack is taking a road trip. If he travels 180 miles while his car uses gasoline at a rate of 40 miles per gallon and then travels another 105 miles while his car uses gasoline at a rate of 35 miles per gallon, how many gallons of fuel has his car consumed?

A. 1.5

B.3.0

C.4.5

D. 7.5

HINT: Begin Q7 by figuring out the cost per ounce of each can of pineapple.

7. If an 8-ounce can of pineapple sells for $0.72 and a 20-ounce can costs $1.10, how many more cents does the 8-ounce can cost per ounce than the 20-ounce can? (100 cents = 1 dollar)

8. An artist is creating a rectangular tile mosaic. Her desired pattern uses 5 green tiles and 3 blue tiles per square foot of mosaic. If the artist’s entire mosaic is 12 feet by 18 feet, how many more green tiles than blue tiles will she need?

HINT: Be careful to use the correct units in Q9! What units are used in the question and what units appear in the answer choices?

9. The average college student reads at a rate of about 5 words per second. If the pages of Jorge’s textbook contain an average of 500 words per page, how long will it take him to read a 45-page chapter?

A. 50 minutes

B.1 hour, 15 minutes

C.1 hour, 25 minutes

D. 1 hour, 40 minutes

10. Each MRI scan given at a hospital produces about 3.6 gigabits of data. Every night, for 8 hours, the hospital backs up the files of the scans. The hospital computers can upload the MRI scans at a rate of 2 megabits per second. What is the maximum number of MRI scans that the hospital can upload each night? (1 gigabit = 1,024 megabits)

A. 15

B.16

C.56

D. 202