PSAT Math : PSAT Mathematics
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Example Questions
Example Question #41 : Arithmetic
Two brothers, Jake and Fred, have a pool in which 9 laps is 1 mile. Jake swims 2 laps in 1 minute, and Fred swims 4 laps in 1 minute. How far has Jake swum when Fred has finished swimming 2 miles?
3/4 miles
2 miles
9/2 miles
3/2 miles
1 mile
1 mile
We can solve this with lots of calculations and conversions of laps to miles, etc., or we can look at what the question is really asking. We want to know how far Jake swims in the time it takes Fred to swim two miles. Instead of converting Fred's miles to laps and comparing to Jake's laps, let's just look at how fast the two brothers swim in relation to one another. Fred swims twice as fast as Jake, so in the same amount of time, he will swim twice as far as Jake. Therefore if Fred swims 2 miles, Jake swims 1 mile in the same amount of time.
Example Question #21 : How To Find Rate
Every 3 minutes, 4 liters of water are poured into a 2,000-liter tank. After 4 hours, what percent of the tank is full?
60 minutes in an hour, 240 minutes in four hours. If 4 liters are poured every 3 minutes, then 4 liters are poured 80 times. That comes out to 320 liters. The tank holds 2,000 liters, so 
Example Question #41 : Proportion / Ratio / Rate
Example Question #41 : Arithmetic
Laura owns a large property. Her lawn is rectangular. It is 500 meters long, and 350 meters wide. If Laura mows the lawn at a rate of 20,000 meters squared per hour, how many hours will it take Laura to finish mowing the lawn?
The area of a rectangle is the length 
We found that Laura is mowing 175,000 meters squared at a rate of 20,000 meters squared per hour.
Plugging in 20,000 for the rate, and 175,000 for the total area gives:
Multiply both sides by the total number of hours:
Now, divide both sides by 20,000:
Example Question #1602 : Psat Mathematics
A TV show lasts 30 minutes, what fraction of the show is left after 12 minutes have passed?
1/3
4/10
3/5
2/3
12/15
3/5
After watching 12 minutes of the show 18 remain. 18 is 60% of the total 30 minutes. As a fraction it can be expressed as 3/5.
Example Question #41 : Arithmetic
A bag contains red, orange, and yellow marbles only. The marbles occur in a ratio of 5 red marbles: 4 orange marbles: 1 yellow marble. If one-third of the red marbles, one-half of the orange marbles, and one-fourth of the yellow marbles are removed, then what fraction of the remaining marbles in the bag is red?
39/73
40/73
37/77
43/75
40/43
40/73
Example Question #1 : How To Find The Ratio Of A Fraction
Marty drove 40 mi/hr for 3 hours, then 60 mi/hr for 1 hour, and finally 70 mi/hr for the last 2 hours. What was Marty's average speed?
60 mi/hr
53 mi/hr
58 mi/hr
47 mi/hr
63 mi/hr
53 mi/hr
Marty's total driving time was 3 + 1 + 2 = 6 hours. He drove 40 mi/hr for 3 hours, or 3/6 = 1/2 of the time. He drove 60 mi/hr for 1 hour, or 1/6 of the drive. Lastly, he drove 70 mi/hr for 2 hours, or 2/6 = 1/3 of the drive.
To find the average speed, we need to multiply the speeds with their corresponding weights and add them up.
Average = 1/2 * 40 + 1/6 * 60 + 1/3 * 70 = 53.33... ≈ 53 mi/hr
Example Question #51 : Arithmetic
A deck of cards has 52 cards. What is the probability of dealing a card with a face value of 4?
For this problem we need to recall that that there are 4 different suits in a deck of cards. Each suit has numbers 1 through 10, jack, queen, king, and ace. Therefore, we can write a ratio of number of 4's over total cards in the deck.
From here we can reduce the fraction and we get
Example Question #1 : How To Find The Ratio Of A Fraction
There is a 5 to 3 ratio of red marbles to green marbles in a bucket. How many red marbles can be in a bucket of 40 marbles?
In this problem, we use a proportion to solve for the number of red marbles in the bucket. Since the ratio is 5 to 3 we can set up a proportion of the red over total where the total is (red marbles + green marbles). We then set this proportion equal to 
Example Question #52 : Arithmetic
There is a 2 to 3 ratio of dogs to cats in a park. How many cats are there if there are 12 dogs?
We set up the following ratio of dogs to cats and set it equal to the new ratio we are interested in.
Then we cross multiply and divide to solve for 
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