PSAT Math Quiz: Rates, Ratios, Proportions & Percents

PSAT Math Quiz: Rates, Ratios, Proportions, and Percents

Content Review:

Test your PSAT readiness by taking this PSAT math quiz!

Question 1

During fairly heavy traffic, the number of cars that can safely pass through a stoplight during a left turn signal is directly proportional to the length of time in seconds that the signal is green. If 9 cars can safely pass through a light that lasts 36 seconds, how many cars can safely pass through a light that lasts 24 seconds?

A. 4
B. 6
C. 7
D. 8

B: To answer a question that says “directly proportional,” set two ratios equal to each other and solve for the missing amount. Don’t forget–match the units in the numerators and in the denominators on both sides.

Let c equal the number of cars that can safely pass through a light that lasts 24 seconds. Set up the proportion and solve, to find that (B) is correct.

(9 cars / 36 seconds) = (c cars / 24 seconds)
9 x 24 = 36 x c
216 = 36c
6 = c

Question 2

According to data provided by The College Board, the cost of tuition and fees for a private nonprofit four-year college in 1988 was approximately $15,800 (in 2013 dollars.)

In 2013, the cost of tuition and fees at the same type of college was approximately $30,100.  If the cost of education experiences the same total percent increase over the next 25 years, approximately how much will tuition and fees at a private non profit four-year college cost (in 2013 dollars)?

A. $44,400
B. $45,800
C. $57,300
D. $66,200

Find the percent increase using the formula: percent change = amount of change divided by original amount. Then apply the same percent increase to the amount for 2013. The amount of increase is 30,100 – 15,800 = 14,300, so the percent increase is 14,300 ÷ 15,800 = 0.905 = 90.5% over 25 years.

If the total percent increase over the next 25 years is the same, the average cost of tuition and fees will be 30,100 x 1.905 = 57,340.50, or about $57,300, which is (C).

Question 3

A chef is preparing ingredients to make a large quiche. The recipe calls for 5 cups of milk and 2 eggs. There is also a lower-fat option that calls for 4 cups of water and 3 eggs. The caterer wants to see what happens when he uses both milk and water. To keep the same ratio of liquid to eggs, what ratio of milk to water should he use?

A. 1:1
B. 5:4
C. 8:15
D. 15:8

D: You need to find the ratio of milk to water. You’re given two ratios: milk to eggs and water to eggs. Both of the given ratios contain eggs, but the egg amounts (2 and 3) are not identical.

To directly compare them, find a common multiple (6). Multiply each ratio by the factor that will make the number of eggs equal to 6:

Milk to Eggs: (5:2) x (3:3) = 15:6
Water to Eggs: (4:3) x (2:2) = 8:6

Now that the number of eggs needed is the same in both ratios, you can merge the two ratios to compare milk to water directly: 15:6:8. Therefore, the proper ratio of milk to water is 15:8, (D).

Question 4

A cybercafé is a place that provides internet access to the public, usually for a fee, along with snacks and drinks. Suppose a cybercafé charges a base rate of $25 to join for a year, an additional $0.30 per visit for the first 50 visits, and $0.10 for every visit after that. How much does the cybercafé charge for a year in which 72 visits are made?

A. $32.30
B. $36.60
C. $42.20
D. $46.60

C: When a question involves several rates, break the situation into separate, manageable pieces and deal with each in turn. Visitors must pay the cafe a flat $25.00 fee to join regardless of the number of visits. The first 50 visits cost $0.30 each, or 50($0.30) = $15.00.

The remaining 72 – 50 = 22 visits cost $0.10 each, or 22($0.10) = $2.20. The total cost for 72 visits is therefore $25.00 + $15.00 + $2.20 = $42.20, which is (C).

Question 5
Engine oil often contains additives that are designed to prevent certain common engine problems. One such additive is zinc, which reduces engine wear. Company A’s oil contains 4% zinc, and Company B’s oil contains 9%. Suppose a car uses 8 pints of Company B’s oil and a truck uses 6 quarts of Company A’s oil.

How many times more zinc is in the car’s oil pan than in the truck’s? (1 quart = 2 pints)

A. 0.34
B. 0.67
C. 1.5
D. 3

C: It’s easiest to compare two amounts when they are written in the same units, so start by converting the car’s pints to quarts and then go from there. The conversion from pints to quarts is straightforward.

8 pt x (1 qt / 2 pt) = 4 qt

Next, find the amount of zinc in each car using the percent formula: percent x whole = part. Write the percents as decimals and multiply:

Car: 0.09 x 4 quarts = 0.36 quarts of zinc
Truck: 0.04 x 6 quarts = 0.24 quarts of zinc

Finally, compare the amount in the car to the amount in the truck:

(0.36 / 0.24) = 1.5. The car has 1.5 times as much zinc in the oil pan as the truck, which is (C).

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