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Guide to SAT Math Problem Solving and Data Analysis + Practice Questions

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What’s Covered:

Overview of sat math problem solving and data analysis, how will the sat impact my college chances.

• Strategies for Problem Solving and Data Analysis Questions
• Practice Questions for Problem Solving and Data Analysis

Final Tips and Strategies

Problem Solving and Data Analysis questions appear on the Calculator section of the SAT Math test and involve applying mathematical knowledge to real-world contexts. These problems can be tough, so if you want to improve your math score, here are some strategies and practice problems to help you out.

The SAT Math section contributes to half of the total SAT score. This section is scored out of 800 and includes three main categories, which each have a subscore out of 15.

Here is the breakdown of each category:

• Heart of Algebra: 33%
• Problem Solving and Data Analysis: 29%
• Passport to Advanced Math: 28%

Additional Topics in Math covers the remaining 10% and consists of a variety of different mathematical topics.

The Problem Solving and Data Analysis section tests students’ ability to solve real-world problems using mathematical understanding and skills. This includes quantitative reasoning, interpreting and synthesizing data, and creating representations. These questions never appear on the SAT No Calculator section, so you’ll always be allowed a calculator for them.

Problem Solving and Data Analysis questions ask students to:

• Use ratios, rates, proportional relationships, and scale drawings to solve single- and multistep problems.
• Solve single- and multi-step problems involving percentages.
• Solve single- and multi-step problems involving measurement quantities, units, and unit conversion. 
• Given a scatterplot, use linear, quadratic, or exponential models to describe how the variables are related.
• Use the relationship between two variables to investigate key features of the graph.
• Compare linear growth with exponential growth. 
• Use two-way tables to summarize categorical data and relative frequencies, and calculate conditional probability. 
• Make inferences about population parameters based on sample data. 
• Use statistics to investigate measures of center of data and analyze shape, center, and spread. 
• Evaluate reports to make inferences, justify conclusions, and determine appropriateness of data collection methods.

Many selective colleges use a metric called the Academic Index (AI) to assess an application’s strength. The AI is calculated based on GPA and SAT/ACT scores, so you should make sure your scores are competitive to increase your chances of admission. Some colleges even automatically reject applicants with AIs that are too low.

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Strategies to Solve Problem Solving and Data Analysis Problems

Problem Solving and Data Analysis problems often involve graphs or data tables, so it’s important to pay attention to titles and labels to make sure you don’t misinterpret the information. 

As you read the question, underline or circle any important numeric information. Also, pay close attention to what exactly the question is asking for.

Because Problem Solving and Data Analysis problems vary, there is no concrete algorithm to approach them. These questions are typically more conceptual than calculation-based, so though a calculator is allowed, you probably won’t need it aside from simple arithmetic. Therefore, the key to these problems is reading carefully and knowing concepts like proportions, median, mean, percent increase, etc.

10 Difficult Problem Solving and Data Analysis Questions

Here are some sample difficult Problem Solving and Data Analysis questions and explanations of how to solve them. Remember, these questions only appear on the Calculator section of the exam, so you will have access to a calculator for all of them.

1. Measures of Central Tendency (Mean/Median/Mode)

Correct Answer: B

This problem involves computing the median. If you have a graphing calculator, this could be done via lists, but since there are only 7 data values, it might be faster to just write this one out. The median is the measure of the middle of the data set, so start by ordering the values from smallest to largest. This results in the following list: 19.5%, 21.9%, 25.9%, 27.9%, 30.1%, 35.5%, 36.4%. From here, we can clearly see that the middle value is 27.9%, so that is our median. 

However, we’re not done here. We now have to compute the difference between the median we just calculated and the median for all 50 states, 26.95%. Subtracting these two values yields 0.95%, which corresponds to answer choice B. 

2. Percent Increase

Percent increase can be a tricky concept if you don’t remember this rule of thumb: “new minus old over old.” In this case, for the percent increase from 2012 to 2013, we take the “new” value, 5,880, and subtract the “old” value, 5,600. This is 280, which we then divide by the “old” to get .05, which is 5%. 

Since the percent increase from 2012 to 2013 was 5%, and this is double the predicted increase from 2013 to 2014, we know that the percent increase from 2013 to 2014 will be half of 5%, or 2.5%.

Then, to calculate the number of subscriptions sold in 2014, we multiply the value in 2013, 5,880, by 2.5%. This yields 147, which means that in 2014, 147 additional subscriptions were sold. So, the total amount of subscriptions sold in 2014 is 5,880 + 147 = 6,027.

3. Analyzing Graphical Data

Since we are presented with a graph, let’s make note of what this graph is showing us. On the y-axis we have speed, and on the x-axis we have time. So, this graph is showing us how Theresa’s speed varies with time. 

When the graph is flat, the speed is unchanging and is therefore constant. When the graph has a positive slope, the speed is increasing, and when the graph has a negative slope, the speed is decreasing. The rates at which it increases and decreases will be constant since the graph is composed of straight lines (and a line has a constant slope, which means it changes at a constant rate).

For questions asking which statement is not true, it’s crucial to take the time to read through each answer choice. First, choice A states that Theresa ran at a constant speed for five minutes. We can see that this is true, since from 5 to 10 minutes, the graph is flat. Next, choice C says that the speed decreased at a constant rate during the last five minutes. This is also true because from 25 to 30 minutes, the graph is a line with negative slope, which indicates decreasing speed. Finally, choice D claims the maximum speed occurs during the last 10 minutes. We can see that the maximum speed (the highest point on the graph) occurs at 25 minutes, which is within the last 10 minutes, so choice D is also true.

By process of elimination, choice B should be correct, but let’s verify. Choice B states that Theresa’s speed was increasing for a longer time than it was decreasing. Speed was increasing from 0 to 5 and 20 to 25 minutes, for a total of 10 minutes. Speed was decreasing from 10 to 20 and 25 to 30 minutes, for a total of 15 minutes. So, the speed decreased for a longer time than it increased, and choice B is false, making it the correct answer.

4. Inference

Correct Answer: D

For questions involving surveys, always remember that generalizations can only be made to the specific population studied. For example, if a study is given to a select group of 5th grade math students, when analyzing the results, you can only generalize to 5th grade math students, not all math students or all 5th graders. 

In this case, the group surveyed was people who liked the book. From these people, 95% disliked the movie. So, from this survey, most people who like the book will then dislike the movie, which corresponds to choice D.

Choices A and C are incorrect since they generalize to people who see movies and people who dislike the book, which doesn’t apply to the population studied. Choice B is incorrect since it falsely generalizes to all people who read books.

5. Proportions

Proportion problems are usually fairly quick, but easy to mess up on if not read carefully. For proportions, the denominator is the total number of things in the group we’re looking at, and the numerator is the specific characteristic we want. 

This question asks for the fraction of the dogs that are fed only dry food. So, the group we’re looking at is “dogs” and the characteristic we want is that they “are fed only dry food.” 

From the table, the total number of dogs is 25. This means the denominator will be 25. Next, we must find the number of dogs which are also only fed dry food, which is 2, according to the table. So, our numerator is 2, and the answer is 2/25.

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6. Scale Factors

For this question, let’s start with what we know: the column is 8 inches tall. We know that 50 coins creates a \(3\frac{7}{8}\) inch column, which is approximately 4 inches. Since this question asks for an approximation, we know that 8 is slightly more than double \(3\frac{7}{8}\), so we’ll need slightly more than \(50\:\cdot\: 2\) pennies to create an 8-inch column. Answer B is the closest number to our approximate value.

If you wanted to be precise, you could set up an equation:

\(8 in\:\cdot\:\frac{50 coins}{3\frac{7}{8} in}\)

Because 50 coins corresponds to a column which is \(3\frac{7}{8}\) inches tall, we set those two values up in a fraction. We decide which value goes in the numerator and which in the denominator based on the units: since we started with 8 inches, we need the \(3\frac{7}{8}\) inches to be in the denominator so that the inches cancel. Then, we are left with the unit in the numerator, which is coins. The question asks for the number of coins, so this is exactly what we want.

At this point, you would use your calculator to solve the expression, and get about 103 coins. This value is closest to answer choice B.

7. Line of Best Fit/Scatterplots

Correct Answer: A

Once again, since we have a graph, let’s take a moment to read the labels. The y-axis shows density and the x-axis shows distance from the sun.

We also see that the line of best fit is sloping downwards. As the distance increases, the density seems to decrease. So, choice A is correct in that larger distances correspond to lesser densities.

Though it wasn’t explicit in this question, an important thing to note about scatterplots is that these relationships show correlation, not causation. Choice C is incorrect because it falsely implies that changes in distance cause changes in density. Choice D is incorrect since though there is no cause and effect relationship, there is a correlation between these two variables.

8. Geometric Applications of Proportions

Correct Answer: 5/18, .277, .278

This problem could be confusing in that so little information is given. However, this problem requires that you recall that the proportion of degrees is equivalent to the proportion of area. So, for this problem, all you have to do is divide 100 by 360, which is the total number of degrees in a circle.

Then, the answer is 100/360, or 5/18. If you’re faced with a similar problem on the test, where there is little to no numeric information, try to work with the numbers you do have and find helpful relationships.

9. Unit Conversions

Correct Answer: 195

Unit conversions are fairly simple once you set up the expression correctly. Start with the information given.

For this problem, the price is $62,400, so we will start with this value. Next, we will multiply this value by fractions. Each fraction will consist of a numerator and denominator which are equivalent, so multiplying by these fractions is the same as multiplying by 1. Here is what the expression would look like:

\(\$62,400\:\cdot\:\frac{1 ounce}{\$20}\:\cdot\:\frac{1 pound}{16 ounces}\)

We decide which value to put in the denominator based on the units. In this case, the dollars and the ounces cancel, leaving us with pounds, which is what the question asked for. Solving this expression results in 195 pounds, the answer to the question. 

10. Probability

Correct Answer: 5/7, .714

Probability questions are similar to proportion questions in that the denominator should be the group we’re looking at and the numerator should be the characteristic we want.

In this case, it is given that we’re looking at contestants who received a score of 5 on one of the three days, and there is a total of 7 such contestants. The characteristic we want is that the contestant received a score of 5 on Day 2 or Day 3. The number of contestants who fit this description is 2 + 3 = 5, so the probability is 5/7.

For Problem Solving and Data Analysis problems, make sure that your answer addresses what the question asked for. Wrong answer choices on the SAT often reflect common student mistakes, so take the time to read Problem Solving and Data Analysis questions carefully.

When studying for the SAT Math section, try to do plenty of practice problems. The best way to get better at math is to do more math.

Here are some other articles that will help you prepare for the SAT Math section:

• 15 Hardest SAT Math Questions
• 30 SAT Math Formulas You Need to Know
• Guide to SAT Math Heart of Algebra + Practice Questions
• 5 Common SAT Math Mistakes to Avoid
• 5 Tips to Boost Your Math SAT Score

Related CollegeVine Blog Posts

Problem Solving and Data Analysis: SAT Math Tips & Practice

When was the last time you found yourself trying to run a proper parabola in a corn field? Or when did you last get really radical four times in a row, just to make the imaginary real?

Most of the SAT math section is about stuff you’re probably not going to use outside of a formal math environment.

For example, the Heart of Algebra section makes up 30% of the section, and it’s mostly linear algebra. It’s really important for math, but you’re probably not going to use y=mx+b to understand the world around you or make daily decisions. Passport to Advanced Math is also 30% of the section, and it mostly adds an exponent to all of that algebra, hardly changing its import to the regular world.

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But what if I told you there was a secret middle child, forgotten by its parents and ignored by its peers, only to be intuitive, surprisingly practical, worth just as many points as the other sections and possibly one of the best places to pick up points on the SAT math section?

Welcome to the dark side, people. Welcome to Problem Solving and Data Analysis.

Problem Solving and Data Analysis: What’s Included?

College Board created the Problem Solving and Data Analysis questions to test your ability to use your math understanding to solve real-world problems. Your SAT score report will list this domain as one of three scored domains (along with Heart of Algebra and Passport to Advanced Math), assigning you a score of 1-15.

Fortunately, College Board has a terrible poker face, and they’ve decided to tell you which cards they’re holding right up front. Here’s what you’ll see:

• Ratios, rates and proportions
• Percentages
• Measurement quantities and units
• Scatterplots
• The relationship between variables and graphs in a data context
• Linear vs. exponential growth
• Data tables
• Sample, population, inferences and other statistical survey topics
• Mean, median, mode and other related concepts

You will see a total of 17 questions in this section, which makes it worth about 30% of your SAT math score.

And since data and calculators go together like spam and mayo, you’ll only see these questions on section four (the calculator section). They could, however, appear in either the multiple choice or the open response portions of the section.

Think about that for a moment: 17 of the 38 questions in section 4 are Problem Solving and Data Analysis questions. That’s 45% of the section!

Data Analysis: Statistics and Data Collection

Let’s talk about politics for a second. Okay, sorry, I’m not trying to be your uncle Greg at Thanksgiving. Let me rephrase: I want to talk about political surveys for a second. We are all familiar with them, regardless of which side of the aisle you sit on, so they make a familiar example.

Presidential surveys are one of the great accomplishments in the history of statistics nerds. They can describe the views of hundreds of millions of people by asking about a thousand people.

And despite some recent bad press in the last few years, they typically do a surprisingly good job. Much like Taylor Swift on even her worst day, most of them are within a few percentage points of perfection.

How do they do this, though? A lot of people instinctively want to say that a survey must include everyone if it is going to be accurate. Fortunately, that’s not true. Instead, it just needs to follow a few basic principles.

Let’s start by defining a couple of key terms:

• Sample : The group of people being surveyed. In a presidential election survey, the sample is the survey respondents.
• Population : The group of people being described. In a United States presidential election survey, the population is all American voters.

So, we ask questions of a sample in order to learn something about the population .

What’s the key to making this all work correctly? Picking your sample well. In fact, the single most important part of survey design is selecting a sample that accurately reflects the population.

A good sample has three features:

• Randomly selected: Any population has outliers in it. There are probably a thousand people in America who particularly enjoy wearing matching outfits with their dog and only talking in bark. But those people are kind of weird, and if we only asked them who they were voting for, our sample probably wouldn’t be reflective of all of America.
• Large enough to represent the population: You don’t need to get too into the details here, but you can’t accurately describe a big group by asking six people. You can, however, describe a class of 400 students by asking 80 kids, and you can describe a country of 300 million by asking a thousand. Normally, sample size issues will be glaring (if they exist).
• Part of the population: If you want to learn something about how America is going to vote, don’t poll Canadians and definitely don’t poll the French.

Those statistics nerds mentioned earlier spend a lot of their time trying to get samples that are reflective of the population. The success of a survey depends on it. But let’s say they do everything right. Their sample size is sufficiently large, they randomly selected their people and the sample is part of the population. What can they learn from the results?

There are a few caveats that should come with any survey results:

• Samples tell us what is likely, not what is necessary. I’m not going to get too into things like confidence intervals because those concepts are beyond the scope of the SAT. But surveys are ultimately just telling us what is very likely to be true, not what is guaranteed to be true. For example, every presidential election survey comes with a “margin of error” disclaimer. That is telling that the results are not a concrete number but are instead likely to fall within a certain range.
• Different samples might yield different results, even if they are both done correctly. This follows directly from the first point. If surveys are totally precise, we shouldn’t expect them to give us exactly the same results every time.
• Correlation doesn’t equal causation. For example, a recent study showed that a rooster crows every single morning. Also, get this, the sun rises every single morning, typically right after the roosters crow. Better correlation doesn’t exist. But is all of this crowing actually causing the sun to rise? Of course not. They are perfectly correlated, but that’s not the same thing as causation.

Statistics and Data Collection Practice

Let’s take a look at a practice problem:

Let’s think back through our three caveats regarding samples: they tell us what is likely to be true rather than what is necessarily true, two different samples can vary and correlation doesn’t equal causation.

The last sentence in the question is asking us what must be true rather than what is likely to be true. That creates an issue right off the bat, but let’s go through our answer choices to see what we have to work with:

• A: Can we say that the entire studenty body must have the same preference as the sample? Of course not.
• B: Must a second sample yield exactly the same results as the first? Of course not.
• C: This is just an incorrect interpretation of the survey itself. The university didn’t ask students what they use, it asked what they prefer. Those are two different things, so this can’t be the right answer.
• D : This is all we have left, so that’s our answer.

Problem Solving and Data Analysis Basics: Mean, Median and Mode

Mean, median and mode on the SAT math section tends to only require two things:

• Basic concept understanding (calculate the mean or median given a data set)
• An understanding of how mean, median and mode vary when things change

Our comprehensive guide to mean, median and mode digs into these concepts more deeply, but I want to give the most important points here.

First, the definitions:

• Mean is the average of a set of numbers. Add them up to get the sum, and then divide the sum by the number of numbers you have.
• Median is the middle number when the numbers are sorted from least to greatest. In the set 1, 2, 5, the median is 2.
• Mode is the number that occurs most frequently. In the set 1, 2, 2, 5, 6, the mode is 2.

You should be able to calculate the mean, median and mode of any data set just by knowing the definitions. But you might also see questions about how they differ as the data set changes.

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Let’s take a look at that sort of question:

For these sorts of problems, it makes sense to actually go through the motions and create your new data set with the stated changes. Our new set would be 7, 9, 12, 15 and 16+.

Running through the answer chocies:

• A: Can we calculate the mean if we don’t know exactly what the last number is? No, so this can’t be our answer.
• B: Can we calculate the median if we don’t know exactly what the last number is? Yes, we can. The median doesn’t depend on the outside numbers. In this case, our median is 12, so this is the right answer.
• C: We can’t calculate the mean, so this can’t be right.
• D: B is correct, so this is incorrect.

Visual Representations of Data

Numbers are boring, but pictures sell. This is why I’ve included pictures of a rooster, a little girl holding corn and Derek Zoolander in this post. I know your weaknesses. We humans may have opposable thumbs for smartphone use, but we have short attention spans. Just show us the pictures! And, surprisingly, College Board is sort of in on this, too. They love to figure out ways to express numbers with pretty pictures.

Okay, they aren’t pretty pictures. They are things like scatterplots, which are to great pictures like Kevin Hart is to great big people.

These questions often present a scatterplot followed by several questions. Here’s an example:

First, let’s look at the first question. The “line of best fit” is the line in the scatterplot that is shown, and it better reflects the data points than any other possible line. You can think of it as the most accurate straight line possible.

Based on this line, a price of $8.60 should result in about 110 books being sold. A price of $9.20 would result in about 70 books being sold, so the answer is 40.

On the second question, note that the text below the scatterplot tells us that we are working with twelve weeks. Data points above the scatterplot represent weeks where more books than predicted were sold, and points below the line represent weeks where fewer books than predicted were sold.

Six points are above the line, so more books were sold than predicted in 50% of weeks (6 divided by 12).

Models: The Scary Side of Problem Solving and Data Analysis

If you want to take some information that is otherwise-intuitive and easy to understand and make it such that a PhD is required to grasp it, figure out how to put it inside of a model.

Imagine you go to the fair, which costs $10 to get into, and you ride three rides at $5 each. That’s all pretty simple, right? You will spend $25 total, and if you want to ride an additional ride, that will be an extra $5. You could have understood this in elementary school.

But watch what happens when we put it into a model:

At this point, “given user” is probably giving up and going home. Sonic has corn dogs, too, you know.

But while this sounds complicated, remember that it is really the same scenario I laid out before: It’s ten bucks to get in, and five bucks per ride. If you have $30 to spend, how many rides can you ride?

It’s an easy question in a hard package. So what are we going to do? We’re going to take it out of the package.

We can do this by plugging in for the variable c and solving just as we would with any algebra problem:

The key to most model problems is to plug in values. Models can run two ways, though. They can either ask you to find a value when a model is given, or they can ask you to pick which model best describes data. Either way, plugging is your friend.

Problem Solving & Data Analysis: Final Thoughts

Problem Solving and Data Analysis is an opportunity to pick up points for many students because, unlike all of the algebra and geometry you are going to be tested on, these questions often involve some level of unfamiliarity.

Becoming familiar with an easy concept that you simply don’t know is about as easy as points gettin’ gets. And many of these concepts don’t involve much technical math; rather, they require you to understand some fundamental idea and then execute easy math.

Putting this together, you should see that this is a category where you should spend the time needed to excel. In my opinion, Problem Solving and Data Analysis is maybe the biggest opportunity for most SAT math students.

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SAT Math: Problem Solving and Data Analysis

Covering 29% of the concepts on the SAT, the Problem Solving and Data Analysis section is the second most common on SAT Math , after Heart of Algebra. Keeping in line with real-world scenarios, these SAT problems will ask you to infer information based on a study with any number of participants or interpret data from a graph. This is actually beneficial for SAT students, given that you’ll be learning lots about cause and effect and inferential statistics in college.

Now, let’s talk about how to approach the various types of Problem Solving and Data Analysis questions on the SAT, plus some practice questions to get you started! Feel free to use the Table of Contents to navigate directly to the topics you want to learn.

Table of Contents

Quick facts about sat problem solving and data analysis, ratio, proportion, units, and percentage, subjects and treatments, sat statistics (mean, median, and mode), what’s important to know about averages on the sat, sat graphs: tips and tricks.

You can expect to see about 17 Problem Solving and Data Analysis questions on the SAT Math section, although they will not be outright labeled by question type. Some answers will be single-step questions, while others will be multistep problems. If you fear mental math, there’s no need to sweat it in this section—you’ll be allowed to use a calculator. Like the other SAT Math sections, you’ll receive a Problem Solving and Data Analysis subscore on a scale of 1 to 15.

This Problem Solving and Data Analysis question type shouldn’t come as a surprise since it has probably been part of your math courses for the last five years (yep, you most likely went over this stuff, in some form, all the way back in early middle school). I’ll start with ratios.

Understanding Ratios

A good way to think of ratios is apples and oranges. Say I have two oranges and three apples, the ratio of oranges to apples is 2:3. Seems straightforward. What if I have four apples and 6 oranges? If you answered 4:6, that is not quite correct. You have to think of the ratio the way you would a fraction, in lowest terms. Both 4 and 6 can be divided by ‘2’, giving you 2:3. Notice how that is the same ratio as 2:3.

This highlights an important conceptual idea: ratio is not about total number . It is about the number of one thing, to the number of another thing, reduced, so that the ratio is expressed as two prime numbers.

One last thing about ratios. Let’s say you have a ratio of 1:2. This is not the same thing as ½. The bottom number in a fraction is always the total. The total of a ratio is always the parts of a ratio added together. In this case, 1:2 is 1 + 2 = 3. So if I have 1 apple to two oranges, 1/3 of the fruit are apples and 2/3 are oranges.

If you have more than two ratios, make sure to add up all of the ratios. For instance, if the ratio of blue marbles to red marbles to green marbles is 2 : 5: 7, red marbles account for 5/14 of the total (2 + 5 + 7 = 14).

Do you think you got that? Well, here are some practice questions to test your knowledge of Problem Solving and Data Analysis.

Understanding Percentages

Percentages can be surprisingly complicated on the SAT. Part of that is because we can’t always translate them into fractions, which are easier to work with algebraically. While it’s easy enough to think of \(50%\) as \(frac{1}{2}\), it’s rarely so easy to make the conversion on the SAT, especially when the percentages given are, say, 35% or 15%.

Finding a percent is pretty easy, as long as you have a calculator. Just divide the part by the whole and multiply the decimal that comes out by 100. So if you ate 10 out of a serving of 12 buffalo wings, then you ate (10/12)100=83.33%. Remembering that formula can save you some grief when you have to use it algebraically.

However, the SAT won’t just test you on the simple process of finding the percentage of a number (like calculating a tip). Instead, it’ll ask you to calculate in reverse (finding the whole from the part), find a combination of percentages, find a percent change, or give some other scenario-specific piece of information.

Being prepared for percent change questions, in particular, will take you far on Problem Solving and Data Analysis.

The equation for percent increase \( = frac{text{New Number – Original Number}}{text{Original Number}}*100 \).

The equation for percent decrease is \( = frac{text{Original Number – New Number}}{text{Original Number}}*100 \).

Practice Questions

Easy questions.

• The ratio of shirts to shorts to pairs of shoes in Kevin’s closet is 5 : 2 : 3. If Kevin owns 10 shirts, how many pairs of shoes does he have to give away so that he ends up having the same number of shorts as he does pairs of shoes?

A) 1 B) 2 C) 4 D) 5

Okay, this question is slightly evil, since shorts sounds like shirts and it is easy to get the two mixed up when you are reading fast. So always pay attention, even on easier questions!

Since we know that Kevin has 10 shirts and that 10, therefore, corresponds to the number ‘5’ in the ratio, that the actual number of shorts, shirts, etc., he owns is double the number in the ratio. Thus, he owns four shirts and six pairs of shoes. So he’ll have to give away two pairs of shoes so that he’ll have the same number of shoes as he does shorts. Answer: (B).

Medium Difficulty Question

• There are 200,000 eligible voters in district X, 60% of whom voted in the 2008 state election. In 2010 state election, the number of eligible voters in district X increased by 20% but if only 55% voted in this election, how many total votes were cast in the 2010 state election, assuming that no voter can cast more than one vote?

A) 12,000 B) 120,000 C) 132,000 D) 176,000

# of voters who voted in 2008 election is equal to 200,000 x 60 = 120,000

In 2010, the number of overall eligible voters increased by 20%, so 20% of 200,000 is 40,000 giving us 240,000 total voters.

Difficult Questions

We know that 7/3 of mile = one inch.

We also know that the area is 49 square miles, meaning that each side = 7: √49 = 7). To find how many inches correspond to 7 miles, we set up the following equation:

7 = 7/3x, x = 3

Another possible question type, and one that most are familiar with and probably dread, is the percent question.

To reduce something by a certain percentage, either turn that percent into a ratio over 100 or convert the percent into a decimal by moving the point back two spaces. For example, 40% equals both 40/100 and 0.40. So the answers are:

5% = .05, 5/100 or 1/20 (you don’t always have to reduce for quick calculations) 26% = .26, 26/100 or 13/50 37.5% = .375, 375/1000 or 3/8 125% = 1.25, 125/100, 5/4

• In a popular department store, a designer coat is discounted 20% off of the original price. After not selling for three months, the coat is further marked down another 20%. If the same coat sells online for 40% lower than the original department store price, what percent less would somebody pay if they were to buy the coat directly online than if they were to buy the coat after it has been discounted twice at the department store?

A) 4% B) 6.25% C) 16% D) 36%

When you are not given a specific value for a percent problem, use 100 since it is easiest to increase or decrease in terms of %.

1 st discount: 20% off of 100 = 80.

2 nd discount: 20% off of 80 = 64.

Online, the coat sells for 40% off of the original department store price, which we assumed is 100.

Online discount: 40% of 100 = 60.

This is the tricky part. We are not comparing the price difference (which would be 4 dollars) but how much percent less 60 (online price) is than 64 (department store sale price).

This is not an official title but the name I’m giving to questions that deal with studies trying to determine cause and effect .

In order to understand how to approach Subjects and Treatments questions, let’s talk about randomization. The idea of randomization is the essence, the beating heart, of determining cause and effect. It helps us more reliably answer the question of whether a certain form of treatment causes a predictable outcome in subjects.

Randomization can happen at two levels. First off, when researchers select from the population in general, they have to make sure that they are not unknowingly selecting a certain type of person. Say, for instance, that I want to know what percent of Americans use Instagram. If I walk on a college campus and ask students there, I’m not taking a randomized sample of Americans (think how different my response rate would be if I decide to poll the audience at a Rolling Stones concert).

On the other hand, if I went to a city phone directory and dropped a quarter on the page, choosing the name that the center of the quarter was closest to, I would be doing a much better job of randomizing (though, one would rightly argue, I’d still be skewing to an older age-group, assuming that most young people have only cell phones, which aren’t listed in city directories). For the sake of argument, let’s say our phone directory method is able to randomly choose for all ages.

After throwing the quarter a total of a hundred times on randomly selected pages (we wouldn’t want only people whose names begin with ‘C’, because they might share some common trait), our sample size consists of 100 subjects. If we were to ask them about their Instagram use, our findings would far more likely skew with the general population. Therefore, this method would allow us to make generalizations about the population at large.

Subjects and Treatments Practice Question

Which of the following is an appropriate conclusion?

A) The exercise bike regimen led to the reduction of the varsity runners’ time. B) The exercise bike regimen would have helped the junior varsity team become faster. C) No conclusion about cause and effect can be drawn because there might be fundamental differences between the way that varsity athletes respond to training in general and the way that junior varsity athletes respond. D) No conclusion about cause and effect can be drawn because junior varsity athletes might have decreased their speed on the 3-mile course by more than 30 seconds had they completed the biking regimen.

When dealing with cause and effect in a study, or what the SAT calls a treatment, researchers need to ensure that they randomly select amongst the participants. Imagine that we wanted to test the effects on the immune system of a new caffeinated beverage. If researchers were to break our 100 subjects into under-40 and over-40, the results would not be reliable.

First off, young people are known to generally have stronger immune systems. Therefore, once we have randomly selected a group for a study, we need to further ensure that, once in the study, researchers randomly break the subjects into two groups. In this case, those who drink the newfangled beverage and those who must make do with a placebo, or beverage that is not caffeinated.

At this point, we are likely to have a group that is both representative of the overall population and will allow us to draw reliable conclusions about cause and effect.

Another scenario and this will help us segue to the practice question above, are treatments/trials in which the subjects are not randomly chosen. For instance, in the question about the runners, clearly, they are not representative of the population as a whole (I’m sure many people would never dare peel themselves off their couches to something as daft as run three miles).

Nonetheless, we can still determine cause and effect from a non-representative population (in this case runners) as long as those runners are randomly broken into two groups, exercise bike vs. usual one hour run. The problem with the study is the runner coach did not randomly assign runners but gave the slower runners one treatment. Therefore, the observed results cannot be attributed to the bike regimen; they could likely result from the fact that the two groups are fundamentally different. Think about it: a varsity runner is already the faster runner, one who is likely to improve faster at running a three-mile course than his or her junior varsity teammate. Therefore, the answer is C).

Subjects and Treatments: A Summary

Here are the key points regarding subjects and treatments (aka cause and effect questions) on SAT Problem Solving and Data Analysis:

• Results from a study can only be generalized to the population at large if the group of subjects was randomly selected.
• Once subjects have been selected, whether or not they were randomly selected, cause and effect can only be determined if the subjects were randomly assigned to the groups within the experiment/study/treatment.
• There are three basic types of averages on the SAT that you should be pretty comfortable with at this point, and all of them start with the letter “m.” Those are the mean, the median, and the mode. In case those aren’t second nature, let’s define them, quickly.

The SAT Math test often asks you to do some statistics problems involving averages. Finding the mean is the most commonly used average and, as it so happens, the most commonly tested when it comes to SAT statistics. The formula is pretty simple:

{a+b+c+….}/n where n is the number of terms added in the numerator.  In the set of numbers {2,3,4,5}, 3.5 would be the mean, because 2+3+4+5=14, and \(14/4=3.5\)

If the numbers in a set are listed in order, the median is the middle number. In the set {1,5,130}, 5 is the median. In the set above, {2,3,4,5}, the median is 3.5, which is the mean of the middle two terms since there’s an odd number of them.

The mode is just the number that shows up the most often. It’s perfectly possible that there is no mode or that there are several modes. In the set {5,7,7,9,18,18}, both 7 and 18 are modes.

Averages come up in algebra or word problems. You’ll usually have to find some value using the formula for a mean, but it may not be as simple as finding the average of a few numbers.  Instead, you’ll have to plug some numbers into the formula and then use a bit of algebra or logic to get at what’s missing.

For example, you might see a question like this:

If the arithmetic mean of x , 2 x , and 6 x is 126, what is the value of x ?

To solve the question, you’ll need to plug it all into the formula and then do some variable manipulation.

\(frac {x+2x+6x}{3}=126\)   \({x+2x+6x}=378\)   \(9x = 378\)   \(x=42\)

Medians and modes, on the other hand, don’t show up all that often in Problem Solving and Data Analysis. Definitely be sure that you can remember which is which, but expect questions on means, most of the time. As for other types of statistical analysis, you may also be asked to solve some problems involving standard deviation .

If you’re careful to remember that the question is asking you for the sum of the sisters’ ages, you can solve this one pretty quickly. Keep in mind that we can’t find their individual ages, though. There’s not enough information for that. First we find the total combined age of the three, which must be 72, since \(24*3=72\). Careful not to fall for the trap that is (E), we take the last step and subtract 16 from that total age to find the leftover sum, which is 56, or (C).

What is a “weighted average”?

Basically, weighted means uneven, here; the numbers that you’re looking at don’t carry the same importance. For example, if I’m trying to find the average number of fleas that my pets have, and each cat has 150 while each dog has 200, then those two numbers have equal “weight” only if I have the same number of cats as dogs. Let’s say I have 1 of each.

\(frac {150+200}{2}=175\)

That’s just a normal mean, so that’s no problem. Well, the fleas are a problem, I guess. And the fact that I’m counting fleas might have my family a little worried…anyway, the math is easy. But that’s a non- weighted average.

For a weighted average, I would have a different number of cats than dogs. Let’s say I had 3 cats and 2 dogs. (And they all have fleas…things are starting to get kinda gross. Sorry.)

In order to give them the appropriate weight, we’d have to multiply each piece appropriately and change the total (denominator) to reflect it.

\(frac {3(150)+2(200)}{5}=170\)

But if you expand that, you’ll see that it’s the same as the standard mean formula.

\(frac {150+150+150+200+200}{5}=170\)

Just make sure you divide by five (because I have five pets) not two (for two types of pets).

Finding Average Rates

Average rates are a type of weighted average. Your SAT Problem Solving and Data Analysis section will include a problem or two about these, and you need to be sure not to fall for the common trap.

Maria’s drive to the supermarket takes her 20 minutes, during which she averages a speed of 21 miles per hour. She takes the same route home, but it only takes 15 minutes to cover the equal distance. What was Maria’s average speed while driving?

This is a tricky, multi-step problem, and you can’t plug in the answer choices to solve it, sadly.

Let’s first find all of our information, because the question has only given you part of it. You need to know the formula r=d/t (rate = distance/time) , also expressed as d=rt (easily remembered as the “dirt” formula). We’re going to use it both ways.

Using that formula, let’s look at the first leg of her trip. She traveled for 1/3 of an hour at 21 mph, so she must have traveled 7 miles.

That’s \(21*0.333=7\)

Using that info, we can figure out the rate of her trip back home. Going 7 miles in 1/4 of an hour on the way home, she went an average of 28 mph.

That’s \(7/0.25=28\)

So now we need to find the total average. That’s not the average of the two numbers we have! Because each mile she traveled on the way there took more time than each mile on the way home, they have different weights!

✗ \(frac{21+28}{2}=24.5\)

Instead, you need to take the total of each piece—total time and total distance—to find the total, average rate.

✓ \(frac{14 text{ miles}}{.333 text{ hours} + .25 text{ hours}}=frac{14 text{ miles}}{.5833 text{ hours}}={24 text{ mph}}\)

Average Rate Practice Question

A) 55 miles per hour B) 65 miles per hour C) 70 miles per hour D) 75 miles per hour

To figure out the average speed of the entire trip, divide the total distance by the total number of hours. The handy equation D = rt, where D is total distance, r is rate, and t is time, will make this easier.

D = 910, r = ?, t = 9 + 4 = 13 hours.

Weighted Averages That You Won’t See on Your SAT

I’ve never seen an SAT Problem Solving and Data Analysis question that asks you to find an average based on percent weights (e.g. finding a final grade in a class where quizzes count for 70%, attendance for 20%, and participation for 10%). Finding that average is a little more complicated, so it’s nice that we don’t have to worry about it.

  Simply put… if you’re finding the average of two sets of information that already are averages in their own right, as the number of fleas per cat and the number fleas per dog, you can’t just take the mean of those averages. You have to find the totals and then plug them into the formula. You should be excited about these kinds of problems, if for nothing more than having the opportunity to bust out your handy-dandy, brand-spanking’ new SAT calculator . 😛

Among the math skills that SAT Problem Solving and Data Analysis tests, reading data from tables or graphs is one of the more straightforward tasks. But there are a number of simple mistakes that might make you miss out on points if you’re not careful. The best way to avoid those totally avoidable slip-ups is to train yourself to follow a pattern.

You’ll want to read the headings, the axes, and the units of measurement, then make note of any missing information or obvious patterns.

• Add in Any Information From the Question As is often true for other types of SAT math problems, the written question might have some info in it that the figure doesn’t include. Just like you would write in angle measurements , fill in any extra info; there’s no reason to try to keep it in your head.
• Write the Math Out If you’re asked about relationships between two things, look carefully at the relationships between 4-6 pieces of information (two x s and two y s), and write out the pattern. If you’re looking for some variable, write out the equation. If it’s not clear how to go about that, maybe you should try plugging answer choices in to see if they work.

That’s all for the SAT Problem Solving and Data Analysis section! We hope this breakdown was helpful for you. To read up on the other two sections of SAT Math, check out our posts on Heart of Algebra and Passport to Advanced Math .

Chris Lele is the Principal Curriculum Manager (and vocabulary wizard ) at Magoosh. Chris graduated from UCLA with a BA in Psychology and has 20 years of experience in the test prep industry. He’s been quoted as a subject expert in many publications, including US News , GMAC , and Business Because . In his time at Magoosh, Chris has taught countless students how to tackle the GRE , GMAT, SAT, ACT, MCAT (CARS), and LSAT exams with confidence. Some of his students have even gone on to get near-perfect scores. You can find Chris on YouTube , LinkedIn , Twitter and Facebook !

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Problem Solving and Data Analysis

We have lots of free resources and videos to help you prepare for the SAT. These materials are for the redesigned SAT which is for you if you are taking the SAT in March 2016 and beyond.

Related Pages More Lessons for SAT Math More Resources for SAT

Problem Solving and Data Analysis includes questions that test your ability to

• create a representation of the problem.
• consider the units involved.
• pay attention to the meaning of quantities.
• know and use different properties of mathematical properties and representations.
• apply key principles of statistics.
• estimate the probability of a simple or compound event.

There are many ways that you can be tested and practicing different types of questions will help you to be prepared for the SAT.

The following video lessons will show you how to solve a variety of problem solving and data analysis questions in different situations.

Ratio, Proportion, Units and Percentages

There will be questions on ratios. A ratio represents the proportional relationship between quantities. Fractions can be used to represent ratios.

There will also be questions involving percentages. Percent is a type proportion that means “per 100”.

You will need to convert units when required by the question. One way to perform unit conversion is to write it out as a series of multiplication steps.

Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8

Charts, Graphs and Tables

The questions in Problem Solving and Data Analysis focus on linear, quadratic and exponential relationships which may be represented by charts, graphs or tables. A model is linear if the difference in quantity is constant. A model is exponential if the ratio in the quantity is constant.

A line of best fit is a straight line that best represents the data on a scatterplot. It is written in y = mx + c.

You need to know the formulas for simple and compound interest. Simple Interest: A = P(1 + rt) Compound Interest: A = P(1 + r/n) nt where A is the total amount, P is the principal, r is the interest rate, t is the time period and n is the number of times the interest is compounded per year.

Probability measures how likely an event is. The formula to calculate the probability of an event is: Probability = (number of favorable outcomes)/(total number of possible outcomes)

Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 Question 11 Question 12 Question 13 Question 14 Question 15

Data and Statistics

You need to know that mean, median, and mode are measures of center for a data set, while range and standard deviation are measures of spread. You will not be asked to calculate the standard deviation of a set of data, but you do need to understand that a larger standard deviation means that the values are more spread out from the mean. You may be asked to compare the standard deviation of two data sets by approximating the spread from the mean.

You do not need to calculate the margins of error or confidence level, but you do need to know what these concepts are and how to interpret them in context. Take note that the questions in the SAT will always use 95% confidence levels. Some questions may give you the confidence level and ask you to find the value for which the interval applies. When the confidence level is kept the same, the size of the margin of error is affected by the standard deviation and the sample size. The larger the standard deviation, the larger the margin of error. The larger the sample size, the smaller the margin of error. The margin of error and confidence interval are estimates for the entire population and do not apply to values of individual objects in the populations.

The results of a sample can be generalized to the entire population only if the subjects in the sample are selected randomly. Conclusions about cause and effect can appropriately be drawn only if the subjects are randomly assigned to treatment.

Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9

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Last week's blog article provided an extensive overview and look into Heart of Algebra, a major section of the SAT Math test ( it constitutes for 33% of the examination's questions! ).

If you have not yet taken a read of that piece yet, go ahead and do so before moving on with today's blog. We will be moving forward to the next section that is covered on the SAT Math, Problem Solving and Data Analysis.

The Problem Solving and Data Analysis section of SAT Math accounts for the second-largest area of the college entrance examination, roughly 29% to be exact.

As an introductory refresher, these sub-categories of SAT Math is used by the College Board in order to help break down your math score into useful subscores on your comprehensive results.

What Is Tested On The SAT Math Section?

Within the SAT Math section, you will find the format is structured by multiple-choice questions and "grid-ins." While the majority of SAT math is multiple-choice, 22% of the math examination portion will constitute grid-ins.

Grid-ins are student-produced, meaning that they require you to first solve the mathematical problem and then enter your answer into the grid provided on the answer sheet.

In total there are 58 questions, with 45 being multiple-choice and 13 as grid-ins.

The SAT Math exam is separated into four main component areas:

Heart of Algebra (19 questions)

Problem Solving and Data Analysis (17 questions)

Passport to Advanced Math (16 questions)

Additional Topics in Math (6 questions)

Need help building a study plan? Look no further, click here to read our previous blog!

Last week, we went over the first domain, Heart of Algebra. Now we will proceed towards the second-largest component of the SAT Math portion.

What Is Problem Solving And Data Analysis?

Students can anticipate working on a total of 17 Problem Solving and Data Analysis questions on the SAT Math exam. You will never be told by the College Board what type of question you are working on from the four major component areas, but you can identify them if you understand what to look for.

Problem Solving and Data Analysis problems revolve around applying your mathematical understanding beside realistic scenarios and analyzing the data rather than working through conceptual situations.

TIP: An important thing to remember for this category of SAT Math is that there will be no Problem Solving and Data Analysis questions on the no-calculator portion. This means that for every Problem Solving and Data Analysis problem you encounter, you will always be allowed to utilize an approved calculator in order to solve the question. You may not always require the aid of a calculator, but it will be permitted if you choose to use it for any Problem Solving and Data Analysis question.

Straight from the College Board , the Problem Solving and Data Analysis section test students' abilities to:

"Create a representation of a problem, consider the units involved, attend to the meaning of quantities, and know and use different properties of operations and objects. Problems in this category will require significant quantitative reasoning about ratios, rates, and proportional relationships and will place a premium on understanding and applying unit rate."

In broad terms, this category is used to illustrate a student's math comprehension and capability to solve problems that they could potentially encounter in real-life.

Struggling with reading? Get some insights on what the ACT 4 core reading passages are with our recent blog article !

You should expect that the majority of these problems will be set in either academic or career contexts and are more than likely to reference the sciences and social science.

What Will Problem Solving And Data Analysis Questions Look Like?

According to the official College Board, you can expect this sub-category to inquire about 10 major types of questions:

Use of ratios, rates, proportional relationships, and scale drawings to solve single- and multistep problems.

Solve single- and multistep problems involving percentages

Solve single- and multistep problems involving measurement quantities, units, and unit conversion

Given a scatterplot, use linear, quadratic, or exponential models to describe how the variables are related.

Use the relationship between two variables to investigate key features of the graph

Compare linear growth with exponential growth

Use two-way tables to summarize categorical data and relative frequencies, and calculate conditional probability.

Make inferences about population parameters based on sample data.

Use statistics to investigate measures of center of data and analyze shape, center, and spread.

Evaluate reports to make inferences, justify conclusions, and determine the appropriateness of data collection methods.

To condense the areas above, we will provide an overview of Problem Solving and Data Analysis three major concepts:

Ratios, units, and percentages

Relationships in Scatterplots, Graphs, Tables, and Equations

Data and Statistics Relationships

We will reference the Official College Board SAT Study Guide, Chapter 17, Problem Solving and Data Analysis .

Ratios, Units, and Percentages

A ratio is a numerical comparison that illustrates some sort of relationship between two or more values. In order to complete ratio calculations, you should increase your comfort level when it comes to multiplying and dividing fractions.

A ratio can be expressed in any of the following formats on SAT Math:

X (when Y is equal to 1)

You may see something like this:

This means that there were 5 adults for every 1 child. Of every 6 people who attended the show, 5 were adults and 1 was a child. Turning this problem into fractions, 5/6 of the 240 people that attended were adults and 1/6 were kids. 1/6 * 240 would equal 40 children attended the show, leaving you with the answer choice A.

You will encounter units in terms of oƒ unit conversion and unit rates. Unit rates express one quantity compared to another ("miles per hour", "dollars per year", etc.) Look for terms like "per" or "each." More often than not, they will require that you convert from one unit to another.

You are given that 1 mile = 1.6 kilometers. Using that information, you solve for the distance in miles. Take 1,060 kilometers and multiply it by (1 mile/1.6 kilometers) and you are left with 664.5 miles, roughly around 663 miles. The correct answer choice is C.

TIP: The College Board usually draws on both the English system of feet and inches as well as the metric system of kilometers and meters. As such, you should be well-versed and familiar with the common units for both. Practice with everyday concepts such as changing your height from inches to centimeters or concerting a car's speed from kilometers to miles.

As for percentages, students should always remember that these are relative to the number 100 and that they are a form of proportions. Given that, these questions involve usually the concepts of percentage increase and percentage decrease.

The sale price of the table is $299. Consider x as the cost from the wholesaler. Your sale price of the table is equal to the cost from the wholesaler plus 15%. Therefore, you will have $299 = 1.15x. Solve for this and the cost from the wholesaler will be $299/1.15 which equals to $260. You are told that the usual price is the cost from the wholesale (which we now know is $260) plus a percentage increase of 75%. The usual price the store charges for the table will be 1.75 * $260, which equals $455. Your answer choice is B.

TIP : In order to do well on Problem Solving and Data Analysis percentage problems, you can brush up on your practice with cross-multiplication when solving for missing values in a formula. Also, remember to work through the problems step-by-step. In the previous example, we had to solve for the cost from the wholesaler first before finally solving for the usual store price with its percentage increase.

Here is a handy list of all the important formulas given on the SAT!

Scatterplots, Graphs, Tables, and Equations

You can anticipate that questions in the Problem Solving and Data Analysis will concentrate on linear, quadratic, and exponential relationships. These are usually depicted by scatterplots, graphs, tables, or tables.

TIP: You can differentiate between linear and exponential as such,

A model is linear if the difference in quantity is constant.

A model is exponential if the ratio in the quantity is constant

The first thing you should think of when you see either a scatterplot, graph, table, or chart is how you can analyze and draw a relational conclusion between its variables.

Be knowledgable about the foundational equations and its components such as for lines ( y = mx + b ), quadratic equations ( ax² + bx + c = 0 ).

TIP : If you are unsure whether it is linear or exponential, try to follow this type of thinking.

If a quantity is increasing linearly over time, then the difference in the quantity between each time period should be the same.

If a quantity is increasing exponentially over time, then the ratio in the quantity between each time period should be the same.

Using this logic for the problem above, you see that after each hour the number of bacteria in the culture is 4 times as great as it was the prior hour. We see a constant ratio between each time period that increases the number of bacteria over time so answer choice D is the correct answer.

For the Problem Solving and Data Analysis category of SAT Math, you will most likely run into data that involves the measures of the center (the mean, average, median).

If the problem you are given does not provide enough information to calculate the for the measures of center, you may still be asked to pull a conclusion about them.

For a beginner refresher:

Mean - the average

Median - the number exactly in the middle when values are placed in order

Mode - the value that appears the most often

Range - the difference between the highest value and the lowest

If you have a strong grasp on these concepts, then it will be much easier for you to make sense and move forward with more challenging statistical concepts on the SAT Math.

The more complicated ideas revolve around terms like population parameter, standard deviation, or how far apart points in a data set are from the mean.

Let's take a look at the concept of standard deviation. It is the measure of spread and generally, the College Board will ask that you compare two sets of data to define which has a more spread out distribution (a greater standard deviation). In these particular cases, do not worry about calculating the exact value. You will need to know the foundational theory and comprehension in order to solve this type of problem.

You see that Class A has a mean score between 3 and 4. The bulk of the scores are 3 and 4, with a very few landing in 0, 1, 2, and 5. As for Class B, the mean score is 2.5 with all scores being equally distributed across all possible scores. Not many of these quiz scores are close to the mean score. Since Class A has quiz scores that are grouped closely together around the mean, the spread (or standard deviation) of the scores in Class A is smaller. The correct answer choice is A.

Covering approximately 29% of the concepts found on the SAT Math test, Problem Solving and Data Analysis assesses a student's math ability alongside real-world scenarios. You will be expected to pull information from the concepts and apply reasoning that is more practical for your future professional careers.

As for any portion of SAT Math, we recommend our students to take each step at a time to ensure that they do not make minor mistakes. One little, but crucial, error when working through a mathematical problem can result in the wrong answer choice.

Be sure to brush up on foundational concepts and equations that you should be aware of for this domain of SAT Math and start practice problems or exercises that can help you prepare.

7EDU Impact Academy offers many college preparation services including one-on-ones, counseling, and specific courses.

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Choose Your Test

Sat / act prep online guides and tips, the 4 sat sections: what they test and how to do well.

SAT General Info

Whether you're actively preparing for the SAT or simply want to learn more about the ubiquitous college entrance exam, it’s important you start with the basics: how many sections are on the SAT? W hat are the names of the SAT sections? And what kinds of skills does each section measure?

In this article, we answer all of your burning questions about the SAT sections . We'll begin by discussing how many sections are on the SAT as well as how these sections differ from one another. Then, we’ll go over the different skills on which you'll be tested, giving you our expert tips for combating each of the SAT test sections with confidence. Finally, we'll take a look at whether certain sections of the SAT are more important than others and what this means for you and your college applications.

UPDATE: SAT Essay No Longer Offered

In January 2021, the College Board announced that after June 2021, it would no longer offer the Essay portion of the SAT (except at schools who opt in during School Day Testing). It is now no longer possible to take the SAT Essay, unless your school is one of the small number who choose to offer it during SAT School Day Testing.

What does the end of the SAT Essay mean for your college applications? Check out our article on the College Board's SAT Essay decision for everything you need to know.

What Are the SAT Sections?

The SAT (which was redesigned in 2016 ) consists of  four sections: 

• Writing and Language
• Math (which consists of two subsections, No Calculator and Calculator)
• Essay (only offered during select SAT School Days)

As  the College Board  (the creator of the SAT) puts it, all sections of the SAT  work together to test “what you learn in high school” and “what you need to succeed in college.” In other words, the goal of the SAT is to ensure you possess the appropriate reading, writing, and math skills deemed necessary for success as a college student.

Each of the SAT test sections appears  only once on the exam and varies in the number of questions it contains as well as in how much time it allocates. The following table showcases some of the major features of the SAT test sections:

According to this table, the longest section (in terms of both time and number of questions) is the Math section . This is because the Math section is composed of two subsections: a No Calculator section (which always comes first) and a Calculator section. While the No Calculator section is fairly brief at only 25 minutes and 20 questions long, the Calculator section lasts for 55 minutes and contains a total of 38 questions.

You may also notice a few key similarities between the Reading and Writing and Language sections. These two sections were specifically designed to test a couple of the same skills — namely Command of Evidence and Words in Context — in different ways. The  two sections also combine for an overall Evidence-Based Reading and Writing (EBRW) score out of 800 points, so they clearly have a lot in common with each other!

Lastly, the above table highlights how all sections of the SAT (excluding the Essay) are predominantly multiple choice . Most questions on the SAT contain four answer choices from which you must select one answer. On the Math section, however, you will also face a handful of  grid-in questions  for which you must come up with your own answers and bubble them in using the numbers provided.

Now that we've covered all of the fundamentals, let’s take a closer look at each of the four sections of the SAT.

The SAT Reading Section

The Reading section focuses on  reading comprehension and understanding vocabulary in context . Each of the 52 questions in this section will be based on a passage. You'll be given five passages in total:

• 1 passage on U.S. or world literature
• 2 passages on history/social studies
• 2 passages on science (which may include graphs and/or charts)

On some areas of the Reading section, you may be given a pair of related passages instead of a single passage. You may also encounter graphs, charts, or other forms of data representation. (Note that you will not have to use any math for these questions, though you will be expected to know how to interpret the data provided.)

As illuminated in the table above, the Reading section test two primary skills:

• Command of Evidence:  your ability to find concrete evidence within the passage to support the author’s claims or answers to specific questions
• Words in Context: your ability to decipher the meanings of vocabulary words within the context of the passage, and your ability to understand how word choice influences the style and tone of a text

Big Picture

Little Picture/Function

• Vocabulary in Context
• Author Technique
• Evidence Support
• Data Interpretation

Below, I describe each of these question types and then provide you with our best tips for doing well on the SAT Reading section.

SAT Reading Question Types

Here are the different types of questions you'll encounter on the SAT Reading section.

#1: Big Picture and Little Picture / Function

These two Reading question types are opposites: Big Picture questions focus on the main point of a passage , whereas Little Picture (or Function) questions focus on the function of specific lines or sentences within a passage . Your job, then, is to use contextual evidence to decipher either the author’s overall message or the function of a selected area of the text.

#2: Inference

For this Reading question type, you must correctly  interpret the meaning of a sentence, a group of sentences, or the entire passage.

#3: Vocabulary in Context

These Reading questions ask you about the meaning of a specific word or phrase within the passage . These words and phrases may not always appear to be difficult but will usually take on lesser-known alternative meanings.

#4: Author Technique

This type of Reading question requires you to  analyze the author’s stylistic choices in regards to tone, voice, perspective, etc.

#5: Evidence Support

For Evidence Support questions, you must  locate contextual evidence for an answer to a previous question . (In other words, these questions are directly related to the questions that precede them.) To answer these questions, you must identify a particular line or group of lines from which you found the answer to a question.

#6: Data Interpretation

A Data Interpretation question requires you to interpret data (usually in the form of a table, chart, or graph) and understand how it relates to the passage.

Top 3 SAT Reading Tips

Once you've familiarized yourself with all of the Reading question types, it's time for you to employ our top three tips for the SAT Reading section!

#1: Practice Reading Passages

Because the Reading section revolves solely around passages, it's critical you dedicate the bulk of your SAT Reading prep to working with SAT-esque passages.

The best resources for passages similar to those you’ll encounter on the SAT are  official SAT practice tests . These mock SAT tests created by the College Board offer a plethora of realistic Reading passages that closely mimic the style and form of the passages you'll be given on test day.

In addition to official practice tests, you can also use unofficial SAT Reading materials — as long as they contain  high-quality Reading passages  similar to those on the SAT.

Finally, it's a smart idea to read real-life texts, such as The New York Times , The Atlantic , and Psychology Today ,   from which SAT passages are often borrowed. This way you can familiarize yourself with the type of materials you'll see on test day.

#2: Use Process of Elimination

Process of elimination is an excellent strategy (and even one recommended by a perfect scorer !) that will aid you significantly on the Reading section.

As we already know, each Reading question offers four possible answer choices of which just one is correct. This means that the other three choices must contain clear signs indicating they’re incorrect .  Some of the most common reasons answer choices are eliminated are that they're:

• Too specific
• Too loosely connected to the overall purpose or message of the passage

Remember, even a single word in an answer choice can make it incorrect , so look closely for any reason to eliminate a choice before deciding on the correct one. Be sure you avoid getting  caught up in answer choices that sort of sound correct — if a choice doesn’t 100-percent answer the question or is ambiguous in any way, chances are it's wrong!

#3: Study Vocabulary Sparingly

Unlike the old (pre-2016) SAT, which often tested obscure vocabulary words in complete isolation, the new SAT only tests vocabulary knowledge within the context of passages . Additionally,  current SAT vocabulary is only about medium difficulty , meaning many of the words tested are ones you've likely seen and may have even used before. (Woo hoo!)

The challenging part of SAT vocabulary, however, is being able to identify  lesser-known tertiary meanings of common words . What this means is, while you no longer need to dedicate hours upon hours to memorizing thousands of vocabulary words,   you do need to familiarize yourself with some of the rarer meanings of common words. Likewise, you should also know how to decipher a vocabulary word's meaning based on how it's being used in a passage.

These days, many SAT vocabulary words are similar to those on the ACT; thus, we recommend studying vocabulary for either test with both our list of SAT vocabulary words and our ACT list of 150 medium-level vocabulary words .

The SAT Writing and Language Section

The Writing and Language section (often referred to as simply the “Writing section”) may look similar to the Reading section, but instead of measuring your reading comprehension skills, this section measures your ability to identify and correct grammatical errors and stylistic weaknesses within passages . In other words, the Writing section is all about your proofreading and editing skills!

Like the Reading section, the Writing section revolves entirely around passages . These passages cover a wide array of topics, including careers, history/social studies, science, and the humanities. Unlike Reading passages, however, all Writing passages are nonfiction , taking the   form of narratives, arguments, and explanatory texts.

Your primary mission on the Writing section is to correct (or leave as is, if no errors are present) words and sentences within these passages. For science-based passages containing charts or graphs, you may be asked to replace an incorrect sentence with a new sentence that more accurately reflects the data provided.

The Writing and Language section measures the following skills:

• Command of Evidence
• Words in Context
• Expression of Ideas
• Standard English Conventions

Below, I discuss each of these four question types and what they measure on the SAT Writing section. I then provide you with our top three tips for getting a great score on SAT Writing.

SAT Writing and Language Question Types

In this section, we examine the SAT Writing question types and look at examples of how they'll appear on the SAT.

#1: Command of Evidence

These types of Writing questions focus primarily on the big picture of a passage and usually ask you to provide evidence for why you are making a particular change .

#2: Words in Context

For these questions, you must  replace a word or phrase with a more logical choice , or select “NO CHANGE” if the highlighted area is appropriate as is.

#3: Expression of Ideas

These questions require you to think about the various ways ideas can be expressed in words. More specifically, you must  rearrange, add, combine, or delete sentences to improve the overall flow of a passage.

#4: Standard English Conventions

For Standard English Conventions questions, you must correct incorrect words or phrases, so that they adhere to the basic  rules of English grammar, punctuation, spelling, and capitalization . If the highlighted word or phrase is grammatically sound, select “NO CHANGE.”

Top 3 SAT Writing and Language Tips

Here are our top tips for getting the score you want on the SAT Writing section!

#1: Master Common SAT Grammar and Punctuation Rules

Nearly half of all SAT Writing questions focus on standard English conventions, so naturally you can’t expect to do well on SAT Writing if you haven’t mastered the basic rules of English grammar and usage!

This doesn't mean you must review every single grammar rule in existence — just the ones most commonly tested on the SAT . For more details on what these rules are and how you can master them, check out our in-depth guides to  SAT grammar and SAT punctuation .

#2: Read Articles and Essays

Because none of the Writing section's passages are works of fiction, your best bet is to read real-life newspaper and magazine articles, persuasive texts, and essays . As you study, you'll use these texts to hone your editorial eye, identifying transitional words and connections in thought.

You'll also want to examine how the author builds his or her argument or main point throughout the text . What evidence does he or she provide? Is it ultimately effective? Why or why not?

There will be a wide array of topics for Writing passages, so feel free to dig into a variety of texts. I recommend starting with major publications such as The New Yorker , The New York Times , The Atlantic , Wired , and  Psychology Today .

#3: Hone Your Writing Skills

To be a sharp editor, you must understand how to write well. And to write well, you must  learn from the feedback on your own writing .

Begin by noting any red marks on essays you turn in at school, making yourself aware of any errors you continuously make on your writing. If you’re confused about a mistake you've made, ask your teacher to explain the mistake and give you tips on how you can avoid making it again.

As you write essays for school, make sure you're also  paying attention to the structure of your arguments . Consider the simple "hamburger" structure of essays: you've got your introduction (top bun), your evidence and supporting details (lettuce, tomato, and meat), and your conclusion (bottom bun). Knowing how to effectively structure your own essays should over time allow you to develop a keener understanding of how SAT passages are organized.

The SAT Math Section

Onto the world of numbers! Unlike the English-centered Reading and Writing sections, the SAT Math section consists of  practical, real-world math and measures the problem-solving abilities most useful for college-level coursework and future employment.

The Math section comprises two subsections:

• Math No Calculator , for which you are not permitted to use a calculator
• Math Calculator , for which you may (but aren't required to) use a calculator

The Math section is the only section on the SAT (excluding the Essay) to contain a non-multiple-choice question format called the grid-in . 22 percent of Math questions are grid-ins , so although it’s not the main question format on SAT Math, it’s crucial you understand how it works.

The Math section tests you on the following concepts:

• Heart of Algebra
• Problem Solving and Data Analysis
• Passport to Advanced Math
• Additional Topics in Math

Below, I describe each of these Math question types and give you expert tips for securing an excellent SAT Math score.

SAT Math Question Types

Here are the four types of Math questions you'll see on the SAT.

#1:  Heart of Algebra

This content area constitutes the  largest focus of the SAT Math section , accounting for approximately one-third of all Math questions. Heart of Algebra questions focus on (you guessed it!) algebra — primarily linear equations, systems of equations, inequalities, and absolute values.

#2:  Problem Solving and Data Analysis

There are 17 Problem Solving and Data Analysis questions on the SAT. All of these questions are on the Math Calculator subsection (meaning you'll see none of these on the No Calculator subsection). These questions focus on data interpretation (i.e., how to read charts, graphs, tables, etc.) as well as rates, ratios, percentages, linear and exponential relationships, and probability.

#3:  Passport to Advanced Math

There are 16 Passport to Advanced Math questions on the SAT. These advanced questions test your understanding of the structure of equations and expressions , including your ability to   rearrange and rewrite them. For these questions, you may be asked to solve a quadratic equation, create an exponential function, or manipulate polynomials.

#4: Additional Topics in Math

While 90 percent of the Math section deals with the three topics listed above, the last 10 percent targets what the College Board calls "Additional Topics in Math." This question type is basically a catch-all for any math concept that doesn’t fit neatly into the other three categories. Such topics predominantly deal with  geometry , trigonometry , and complex numbers.

Top 3 SAT Math Tips

Use our top tips below to get your best score ever on SAT Math!

#1: Review Basic Math Concepts

You can’t expect to score highly on the Math section if you’re not familiar with most or all of the basic math concepts being tested on the SAT.

To get started, take a look at our  giant stockpile of SAT Math resources you can use (for free!). This guide contains links to several Math guides offering a solid overview of critical math concepts you should know for the SAT, including algebra, numbers, coordinate geometry, and plane and solid geometry.

You can also check out our guide to the best SAT Math prep books  and browse your options for high-quality Math content review and practice.

#2: Memorize Common Formulas

Another tip is to memorize all  critical SAT Math formulas you’ll need for test day. Doing this will allow you to solve many math problems that you can't solve without knowledge of a particular formula.

But what about the reference diagram on the test? Do you really need to memorize formulas if you'll be given a list of them on the SAT? Although you may think memorizing these formulas is a waste of time, in reality  memorizing them will actually  save you time on test day . Here are the formulas exactly as you'll see them on the SAT:

By memorizing the formulas above, you won't need to constantly flip back to the diagram and will therefore be able to solve math problems more quickly. This will effectively give you  more time to put toward other math problems that are more challenging .

However, there is one caveat: the 12 formulas on this reference diagram deal specifically with geometry, a topic which makes up a significantly small portion of the new SAT. So while it’s crucial you memorize these formulas, it’ll be far more advantageous for you to prioritize other major laws and formulas that will not be given to you on test day and are more likely to come up on the SAT.

#3: Plug In Answers and Numbers

Our final tip for SAT Math is a popular test-taking strategy: plugging in answers and numbers . In this strategy, if you’re faced with a math problem you’re unsure how to solve, you can attempt to solve it by either plugging in random numbers or plugging in answer choices one by one. Doing this will reveal which answer choice yields the correct result.

Use the plug-in answer strategy for multiple-choice math questions that ask you to solve for a specific value. Always start with answer choice B or C , so you can determine whether to work your way up or down to get a higher or lower answer.

For multiple-choice and grid-in questions you don’t understand, try plugging in your own numbers (or sets of numbers) to see whether equations and inequalities hold true  for various values.

Note that these strategies, though helpful, should generally only be used if you’re unsure how to solve a math problem using other methods, such as simplification and algebra. Ultimately, though, the SAT doesn’t care how you get an answer — just that it’s the correct one! So if you don't know what to do, get in there and plug away.

The SAT Essay (Optional)

NOTE: As we mentioned above, now that the Essay is only offered during select SAT School Days , very few students will take it. Additionally, no colleges still require the Essay, so even if you do take it, your score will not impact your college applications.

The SAT Essay is an entirely writing-based section for which you must read a 650-750-word passage and then  write an essay analyzing how the author constructs his or her argument as well as how persuasive the argument is .

Note that you are not being asked whether you agree or disagree with the argument. You are also not expected to write about your personal experiences (like how test takers were prompted to do on the old SAT).

The Essay also uses a unique scoring system compared to those of the other SAT test sections. There are three components to the SAT Essay grade :

For each of these components, two graders will assign you a score on a scale of 1-4. These two scores are then added together to give you total scores for each component (on a scale of 2-8). Thus, a perfect SAT Essay grade would be 8|8|8 (4s from both graders for each of the three rubrics).

But what exactly do these three components measure? Below, I describe each of the SAT Essay grades and introduce to you our top three tips for ensuring a high Essay score on test day.

Skills Tested on the SAT Essay

The three components of the SAT Essay grading rubric each measure a different skill in regards to your writing ability.

The Reading score highlights your overall  understanding of the passage and how well you use appropriate textual evidence from the passage to construct your essay.

The Analysis score shows how well you understand the construction of the author's argument  in terms of reasoning, style, and evidence. It also measures your ability to choose the most effective evidence from the passage to support your evaluation.

The Writing score revolves entirely around your ability to write . You will be given a grade based on the strength of your thesis and on your essay's organization, focus, tone, style, and adherence to standard written English conventions.

Top 3 SAT Essay Tips

And now here are our expert SAT Essay tips to help you get the high score you deserve!

#1: Learn the Types of Examples to Look for in Passages

Before you take the exam, make sure you know all of the major types of examples you can look for in passages to use as support in your essay. The six types of evidence to be aware of are:

• Facts and statistics
• Counterarguments and counterclaims
• Explanation of evidence
• Vivid language
• Direct appeals to the reader

For more information, check out our detailed guide on how to look for and use these pieces of evidence . As you write, be  sure you’re using the most relevant and effective support; you don’t need to use every example you find!

#2: Read the Prompt First

Although you'll likely be tempted to get through the passage before attacking the prompt, reading the prompt first can lend you a big hand as it directly states what the author’s central claim is . Once you know what kind of argument you'll be dealing with, you can then read the entire passage, keeping an eye out for any evidence that supports this central claim and thinking of ways you can effectively incorporate these pieces of evidence into your essay.

As a reminder, your essay should focus on what techniques and evidence the authors uses to set up his or her argument  as well as how effective these techniques are.

#3: Write More Than 1 Page

Though not explicitly stated on the SAT Essay rubric, your essay must be of a reasonable length (1+ pages) in order to merit a high score . This means anything less than a page is bound to guarantee you a low essay score, as the essay will very likely lack sufficient detail, evidence, and analysis.

On test day, you’ll get four pages for writing (and one additional piece of scratch paper for planning and outlining your essay). Aim to use at least two pages for your essay.  Anything longer is perfectly fine; however, just remember it's ultimately better to produce a succinct and focused essay instead of a verbose or tangential one.

Ready to go beyond just reading about the SAT? Then you'll love the free five-day trial for our SAT Complete Prep program . Designed and written by PrepScholar SAT experts , our SAT program customizes to your skill level in over 40 subskills so that you can focus your studying on what will get you the biggest score gains.

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Are Certain SAT Sections More Important Than Others?

Because the SAT has several sections, you may be wondering which (if any) are the most important in regards to scores.

To start, the essay is, by far, the least important of all SAT sections . With the College Board no longer offering the essay during regular SAT administrations, nearly no students will now take it, and no colleges require essay scores. Basically, if you're one of the few people who do still take the essay (because your school required it for an SAT School Day), your score won't impact your college applications, although your high school might use the essay score for its own purposes.

But what about the SAT Reading, Writing, and Math sections? Which of these is the most important? Or are they all equally important?

Generally speaking, the SAT Reading, Writing, and Math sections are all of fairly equal importance . Most schools report SAT scores using the total score (a combination of the EBRW and Math scores), implying there is equal consideration of the Reading, Writing, and Math sections. Furthermore, any school requiring the SAT will always require scores from the Reading, Writing, and Math sections, so all three of these sections are evidently essential for college admission (unlike the optional Essay).

In spite of these trends,  there may be cases in which one of the two scores (EBRW or Math) will hold slightly more weight than the other . For example, if you are applying to an engineering school like MIT, admissions committees may pay a little extra attention to your SAT Math score — the more relevant score to your program — and less to your EBRW score.

In the end, it's best to think of both your EBRW and Math scores as being equally important, and your Essay score (if you took the essay) as being the least important.

Key Takeaways for the SAT Sections

The SAT is composed of four sections: Reading, Writing and Language, Math, and Essay (optional). These sections target an array of academic skills deemed necessary for college, from reading comprehension to proofreading to problem solving.

To ultimately do well on the SAT, you must understand what each of the SAT sections measures, what each sections tests you on, and what approaches you can use to get the scores you want.

Although the Essay isn’t a requirement for any colleges anymore, those requiring SAT scores will often prefer applicants who have a strong set of EBRW (Reading and Writing) and Math scores, so always try to aim for a high total score !

What’s Next?

Want to learn more about the SAT? Take a look at our complete guide to what the SAT is and get tips on when to start studying and what resources you can use to get the scores you need for college!

Thinking of taking the ACT, too? Start with our introduction to the ACT sections and then check out our guide to what a good ACT score is to learn how you can get a great ACT score.

Disappointed with your scores? Want to improve your SAT score by 160 points? We've written a guide about the top 5 strategies you must be using to have a shot at improving your score. Download it for free now:

Hannah received her MA in Japanese Studies from the University of Michigan and holds a bachelor's degree from the University of Southern California. From 2013 to 2015, she taught English in Japan via the JET Program. She is passionate about education, writing, and travel.

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