rate ratio speed distance psat questions

PSAT Math: Rates and Measurements

 

The PSAT Math Test contains multiple-choice and grid-in questions, as well as multi-part math question sets. These question sets have multiple parts that are based on the same scenario and may require more analysis and planning than a typical multiple-choice question. Let’s take a look at a way to help you answer these questions effectively:

Kaplan Method for Multi-Part Math Questions

Step 1: Read the first question in the set, looking for clues

Step 2: Identify and organize the information you need

Step 3: Based on what you know, plan your steps to navigate the first question

Step 4: Solve, step-by-step, checking units as you go

Step 5: Did I answer the right question?

Step 6: Repeat for remaining questions, incorporating results from the previous question if possible

Now let’s walk you through each step in more detail:

 

  • Step 1: Read the first question in the set, looking for clues

    Focus all your energy here instead of diluting it over the whole set of questions; solving a multi-part question in pieces is far simpler than trying to solve all the questions in the set at once. Further, you may be able to use the results from earlier parts to solve subsequent ones. Don’t even consider the later parts of the question set until you’ve solved the first part.

    Watch for hints about what information you’ll actually need to use to answer the questions. Underlining key quantities is often helpful to separate what’s important from extraneous information.

  • Step 2: Identify and organize the information you need

    If you think this sounds like the Kaplan Method for Math, you’re absolutely correct. You’ll use some of those same skills. The difference: A multi-part math question is just more involved with multiple pieces.

    What information am I given? Jot down key notes, and group related quantities to develop your strategy.

    What am I solving for? This is your target. As you work your way through subsequent steps, keep your target at the front of your mind. This will help you avoid unnecessary work (and subsequent time loss). You’ll sometimes need to tackle these problems from both ends, so always keep your goal in mind.

  • Step 3: Based on what you know, plan your steps to navigate the first question

    What pieces am I missing? Many students become frustrated when faced with a roadblock such as missing information, but it’s an easy fix. Sometimes you’ll need to do an intermediate calculation to reveal the missing piece or pieces of the puzzle.

  • Step 4: Solve, step-by-step, checking units as you go

    Work quickly but carefully, just as you’ve done on other PSAT math questions.

  • Step 5: Did I answer the right question?

    As is the case with the Kaplan Method for Math, make sure your final answer is the requested answer. Review the first question in the set and double-check your units and your work.

  • Step 6: Repeat for remaining questions, incorporating results from the previous question if possible

    Now take your results from the first question and think critically about whether they fit into the subsequent questions in the set. Previous results won’t always be applicable, but when they are, they often lead to huge time savings. But be careful—don’t round results from the first question in your calculations for the second question—only the final answer should be rounded.

When you’ve finished, congratulate yourself for persevering through such a challenging task. A multi-part math question is likely to be one of the toughest on the PSAT. If you can ace these questions, you’ll be poised for a great score on Test Day. Don’t worry if the Kaplan Method seems complicated; we’ll walk through an example shortly.

Expert Tip

Because these question sets take substantially more time, consider saving multi-part math questions for last. Many students freeze when they encounter a problem with multiple steps and seemingly massive amounts of information. Don’t worry! Take each piece one at a time, and you won’t be intimidated.

Rates, Measurement, and Unit Conversions

By now, you’ve become adept at using algebra to answer many PSAT math questions, which is great, because you’ll need those algebra skills to answer questions involving rates. You’re likely already familiar with many different rates—kilometers per hour, meters per second, and even miles per gallon are all considered rates.

A fundamental equation related to rates is “Distance = rate × time” (a.k.a. the DIRT equation—Distance Is Rate × Time). If you have two of the three components of the equation, you can easily find the third. An upcoming multi-part math example demonstrates this nicely.

You’ll notice units of measurement are important for rate questions (and others that require a unit conversion) and, therefore, also an opportunity to fall for trap answers if you’re not careful. How can you avoid this? Use the factor-label method (also known as dimensional analysis). The factor-label method is a simple yet powerful way to ensure you’re doing your calculations correctly and getting an answer with the requested units.

For example, suppose you’re asked to find the number of cups there are in two gallons. First, identify your starting quantity’s units (gallons) and then identify the end quantity’s units (cups). The next step is to piece together a path of relationships that will convert gallons into cups, canceling out units as you go. Keep in mind that you will often have multiple stepping stones between your starting and ending quantities, so don’t panic if you can’t get directly from gallons to cups.

The test makers won’t expect you to know English measurements by heart. Instead, they’ll provide conversion factors when needed. For example, a gallon is the same as 4 quarts, every quart contains 2 pints, and a pint equals 2 cups. And there you have it! Your map from gallons to cups is complete. The last step is to put it together as a giant multiplication problem. Each relationship, called a conversion factor, is written as a fraction. The basic rules of fraction multiplication apply, so you can cancel a unit that appears in both the numerator and denominator.

 

The PSAT will not require you to memorize conversions for conventional units. If the test asks you to convert miles into inches, for example, you will be provided with enough conversion factors to solve the problem.

Follow along as we convert from gallons to quarts to pints to cups using the factor-label method:

 

2 gallons × 4   quarts 1   gallon × 2   pints 1   quart × 2   cups 1   pint = 2 × 4 × 2 × 2   cups = 32   cups


The DIRT equation is actually a variation of this process. Suppose you travel at 60 mph for 5 hours. You would calculate the distance traveled using the equation  d = r t = 60   mi 1   h × 5   h = 300  miles. The units for hours cancel out, leaving only miles, which is precisely what you're looking for, a distance. This built-in check is a great way to ensure your path to the answer is correct. If your units are off, check your steps for mistakes along the way. The PSAT will never ask you for a quantity such as miles4 or gallons3, so if you end up with funky units like that, you’ve made an error somewhere in your work.

The following question demonstrates the factor-label method in a test-like question.

PSAT Multi-Part Math Practice Question

1. A homeowner wants to buy 81 square feet of grass for his yard, but the vendor he uses only sells grass by the square yard. How many square yards of grass does the homeowner need? (1 yard = 3 feet)

A. 9
B. 27
C. 243
D. 729



 

Work through the Kaplan Method for Math to solve this question step-by-step. The following table shows Kaplan’s strategic thinking on the left, along with suggested math scratchwork on the right.



Strategic Thinking Math Scratchwork
Step 1: Read the question, identifying and organizing important information as you go
You’re asked how many square yards of grass the homeowner needs. You know he needs 81 square feet of grass. 81 ft2 grass needed
Step 2: Choose the best strategy to answer the question

How do you convert from square feet to square yards?
Use factor-label method
What are the starting and ending quantity units? Which conversion factors are needed?


You’re starting with square feet and need to convert to square yards. You know that 1 yd = 3 ft, but be careful: 1 yd2 is not the same as 3 ft2. Consider each feet-to-yards conversion separately.
starting qty: 81 ft2
end qty: ? yd2

You’ll need to multiply by your conversion factor twice. Remember your rules for exponents: To cancel out ft2, you’ll need to divide by ft2.

81   ft 2 1 × 1   yd 3   ft × 1   yd 3   ft = 81 9   yd 2 = 9   yd 2

Step 3: Check that you answered the right question
You’ve correctly converted from square feet to square yards to get the correct answer, (A). 9 yd2