Miller Analogies Test (MAT)

Preparing to take the Miller Analogies Test (MAT)?


You’ve found the right page. We will answer every question you have and tell you exactly what you need to study to pass the MAT.

Quick Facts

Get the “need to know” information at a quick glance.


The Miller’s Analogies Test is taken by students who are seeking admittance to graduate school programs. The test, which contains 120 analogy questions, must be completed within 1 hour.


Let’s look at an overview of what you can expect on test day.


The cost of the Miller Analogies Test varies by testing location. Check with your local testing center for the exact cost of the exam. The typical exam fee is $70 – $100. If you are unsure of how to register for the MAT exam, contact your local testing center.

The cost includes sending your score to up to three schools. It will cost an extra $25.00 per school if you would like your score sent to additional schools.


Here’s the MAT score breakdown:

MAT scores range from 200 to 600 and the average MAT score is about 400.

The percentile ranks included on your Official Score Report will indicate the percentage of recent test-takers who received scores lower than yours. Percentile ranks range from 1 to 99, with 99 being the best.

Immediately after you complete the test, you will see a “No Score Option” on your screen. If you choose this option, your score will not be sent to any of the schools you chose. Your testing fee will not be refunded if you choose this option, and you will not receive a Preliminary Score Report.

Pass rate

There is no passing score for this exam. Graduate admissions offices consider MAT scores as well as MAT percentile rankings, but they also consider other factors, such as grade point average.

Study Time

The time which you will need to spend preparing for the exam depends upon your content knowledge, your ability to understand analogies, and your general comfort level in testing situations.

Most students need to spend about 1-2 months studying for the MAT. You can use the resources on our site to determine your areas of weakness and spend the majority of your study time focusing on those areas.

What test takers wish they would’ve known:

  • Theoretically, you may take the MAT as frequently as you would like, but beware of retaking the exam! Many test-takers are surprised to learn that schools can see how many times you have retaken the MAT and if you increase your score by more than 50 points within 12 months, your scores are automatically cancelled. It is better to score well on the exam the first time.
  • Being a reader will improve your chances of scoring well. This habit means that you will frequently consider words and their relationships and you will be exposed to an array of concepts. If this is not already a habit of yours, get into a habit of reading as soon as you can!
  • Since test performance depends greatly on language concepts, non-native English speakers may especially benefit from additional study time. 
  • It’s important to assess your weaknesses before creating a study plan. Otherwise, you may spend too much time focusing on the wrong concepts.
  • Study a little bit each day. Many students who try to cram before the exam regret the choice.
  • Answer every question on the exam. You are not penalized for incorrect responses. It is better to guess than to leave a choice blank. If you are able to, eliminate some answer choices before you guess.
  • Do not make any plans the night before your test. Take the time to relax and get plenty of sleep. Make sure that your identification, directions to the testing center, and any other materials that you need are together the night before the exam. You don’t want to be hurried and distressed right before you take the test!
  • Eat a good breakfast before the test.
  • Plan to arrive at the testing center a few minutes early.
  • Wear layers. You can remove or put on a light jacket or sweater in order to be more comfortable in the testing center, which could be warm or cool

Test details obtained from the Pearson Assessments site. Pearson Assessments is the creator and owner of the MAT.

Content Objectives

The MAT has 120 questions. You will have 60 minutes to complete this content area.

The analogies on the test can be neatly divided into five content objectives:

  • Words and Language
  • Humanities
  • Natural Sciences
  • Social Sciences
  • Mathematics

So, let’s talk about them.

Words and Language

This content objective is designed to test your knowledge of English grammar and language by asking you to recognize the relationships between words.

Let’s look at some concepts for this content objective.


Denotation is the dictionary definition of a word. In other words, it is what a word literally means. It’s a good idea to brush up on your vocabulary before the test, but how can you remember so many new words?

The answer is to use mnemonic devices. A mnemonic device is a memory technique which involves association. Let’s look at some examples of how to use mnemonic devices to remember words.

These examples focus on using rhymes, but there are other ways to make mnemonic devices work for you – any association will do!


Now you know that a word’s denotation is what it literally means. A word’s connotation refers to the thoughts, feelings, and ideas associated with a word. 

For example, skinny has a negative connotation. Thin can mean the same thing as skinny, but its connotation is more positive.

Review the examples below.

Try completing the following analogy:

Miserly : Frugal :: Boisterous : a. Inexpensive b. Rowdy c. Energetic d. Euphemistic

This analogy tests your knowledge of denotation and connotation. Miserly and frugal mean nearly the same thing, but miserly has a more negative connotation. The word which means nearly the same thing as boisterous, but has a more positive connotation is energetic. C is the correct answer. While rowdy is also similar in meaning, rowdy has a negative connotation.


On the MAT, you are likely to be presented with analogies that test your knowledge of grammar. Let’s review a few terms and concepts associated with grammar.

Try completing the following analogy:

Adjective : Noun :: Adverb : a. Pronoun b. Verb c. Antecedent d. Phrase

An adjective describes a noun. An adverb describes a verb. The correct answer is B.

Word Parts

Being able to identify word parts is a very important skill for students who take the MAT. Sometimes, you will be given analogies in which you must identify a word part. However, you can benefit from your knowledge of word parts on almost every analogy on the exam.

Why are word parts so important?

Words can be reduced to their word parts. Every question on the exam tests your knowledge of words in some way. If you do not understand what a word means, you cannot complete an analogy correctly unless, of course, you happen to make a lucky guess.

If you understand the meaning of common word parts, you can use that knowledge to make meaning of unfamiliar words on the exam. 

Review the chart below. The example word parts may be very helpful to know on the actual exam.

Try completing this analogy:

Gaseous : Aero- :: Aqueous : a. Des- b. Emb- c. Osteo- d. Hydro-

Aqueous means “having the quality of water” and gaseous means “having the qualities of gas.” “Aero-” is a root word that means air, which is gaseous. So, which answer is a root word which refers to an aqueous substance? D, Hydro- is correct.


MAT questions regarding pronunciation test your knowledge of how to correctly say words. Try the following example:

Worcester : Versailles :: Gloucester : a. Illinois b. Connecticut d. Montenegro d. Jalisco

This analogy refers to places, but it is not asking for your knowledge of geography. Worcester and Gloucester are rhyming words; they have a similar pronunciation. The correct answer to the analogy is Illinois

Why? Both Versailles and Illinois end with a silent “s.”

Try another analogy:

Tangelo : Acaí :: Window : a. Façade b. Foyer c. Chimney d. Balustrade

The first two words are types of fruit. A window is part of an architectural feature of a home, but how do you choose the correct word?

The answer, again, is pronunciation. Tangelo rhymes with window and acaí rhymes with chimney.

If you aren’t able to find the answer from the meanings of the words alone, consider how they are pronounced!


Questions relating to the Humanities Content Objective on the MAT usually relate to the arts, religions, history, philosophy, and languages. We’ll explore some of these concepts now.

Art History

Let’s take a look at art history, a category that often appears as an MAT humanities analogy. If you don’t know Michelangelo from Dalí, don’t worry–we’ll review these artists and others right now.

Try to commit some of the following table to memory; you will be asked a follow-up question.

Now, try this analogy:

Munch : Norway :: Matisse : a. France b. Spain c. Denmark d. Painter

Munch was a Norwegian painter and Matisse was a French painter. The correct choice is A.

So, will arts that are not visual appear on the MAT? Often, other arts make an appearance as well. The image below provides a timeline of major artistic periods in history as well as various types of artists associated with those periods.

Comparative Religion and Mythology

Versions of the MAT often include some analogies about religions or mythology. You are less likely to see these types of analogies than other Humanities analogies though, so let’s just cover the basics.

Use the following chart to review some concepts and terms associated with religion.

Now that we’ve compared some of today’s religions, let’s take a look at ancient mythology. While many cultures have their own mythologies, you are most likely to encounter Greek gods and their Roman counterparts:

Now, try this analogy without referring to the table:

Romance: Aphrodite :: War : a. Mars b. Ares c. Artemis d. Neptune

In ancient Greece, romance was associated with Aphrodite. So, who’s associated with war? Both Ares and Mars, but Mars was a Roman god, so B is the correct answer.


So, what do you need to know about literature to perform well on the Humanities analogies? Well, you might be asked about a type of literature, a broad literary term, or a specific author.

Let’s review some basic literary terms:

  • Antihero: A flawed, unlikely main character
  • Alliteration: Repetition of consonant sounds
  • Assonance: Repetition of vowel sounds 
  • Ballad: Poem that is meant to be sung, tells a story
  • Bildungsroman: “Coming of age” novel
  • Climax: Point at which the action of a work peaks
  • Couplet: Two consecutive lines that rhyme with each other 
  • Denouement: End of a work, when the action winds down
  • Epic: Long heroic poem 
  • Hyperbole: Extreme exaggeration 
  • Idiom: Saying with a figurative meaning 
  • Imagery: Language that appeals to the five senses
  • Metaphor: Comparison that does not use “like” or “as”
  • Onomatopoeia: Words that imitate sounds
  • Personification: Human attributes are given to a non-human
  • Plot: Events of a work 
  • Prose: A work which is not poetry
  • Simile: Comparison using “like” or “as”
  • Sonnet: Poem of 14 lines 
  • Stanza: Section of a poem; formatted like a paragraph

Try out this analogy:

Sonnet : Poetry :: Bildungsroman a. Couplet b. Stanza c. Autobiography d. Prose

A sonnet is a type of poetry. A bildungsroman is an example of prose. D is the correct answer.

Now, think about all of the famous authors, poets, and literary works created over centuries–that’s a lot of literature! That’s also one reason why readers tend to have an advantage over non-readers on the MAT.

Let’s review a few of the most renowned writers. The list below includes poets and authors. One of the most famous works by each author is listed by his or her name.

  • Alcott, Louisa May: Little Women 
  • Alighieri, Dante: The Divine Comedy
  • Angelou, Maya: The Color Purple 
  • Austen, Jane: Pride and Prejudice 
  • Brontë, Charlotte: Jane Eyre 
  • Brontë, Emily: Wuthering Heights 
  • Caroll, Lewis: Alice in Wonderland 
  • Chaucer, Geoffrey: The Canterbury Tales 
  • Defoe, Daniel: Robinson Crusoe 
  • Dickens, Charles: Oliver Twist
  • Hawthorne, Nathaniel: The Scarlet Letter 
  • Hemingway, Ernest: The Old Man and the Sea 
  • Homer: The Odyssey 
  • Hugo, Victor: Les Misérables 
  • Kafka, Franz: The Metamorphosis 
  • Kipling, Rudyard: The Jungle Book
  • Melville, Herman: Moby Dick Miller
  • Milton, John: Paradise Lost 
  • Morrison, Toni: Beloved 
  • Nabokov, Vladimir: Lolita 
  • Orwell, George: Animal Farm 
  • Plath, Sylvia: The Bell Jar 
  • Poe, Edgar Allan: “The Raven” 
  • Seuss, Dr.: The Cat in the Hat 
  • Shelley, Mary: Frankenstein 
  • Sinclair, Upton: The Jungle 
  • Stevenson, Robert Louis: Treasure Island 
  • Stowe, Harriet Beecher: Uncle Tom’s Cabin 
  • Swift, Jonathan: Gulliver’s Travels 
  • Thoreau, Henry David: Walden 
  • Tolkien, J. R. R.: The Lord of the Rings 
  • Tolstoy, Leo: Anna Karenina 
  • Twain, Mark: The Adventures of Huckleberry Finn

Whitman, Walt: Leaves of Grass

Natural Sciences

Now that we’ve reviewed some Humanities Content Objectives, let’s take a look at the Natural Sciences. We’ll start with astronomy.


Astronomy is a branch of science which focuses on space, celestial bodies, and the universe. Here are some key terms to know:

  • Asteroid: A body of metal and rock that orbits the sun
  • Black Hole: A body of mass so dense that nothing, including not light, can escape once it has entered its gravitational field
  • Comet: A mass of ice and rocky debris that orbits the Sun in an ellipse
  • Constellation: A distinctive grouping of stars
  • Earthshine: Sunlight reflected by Earth that makes Earth’s moon “glow” 
  • Eclipse: When the shadow of a planet or moon falls upon another celestial body
  • Galaxy: A group of stars, gas, and dust that is about 10,000-100,000 light-years in diameter
  • Light-year: The distance that light travels in a year, approximately 6 trillion miles
  • Magnitude: Describes the brightness of a star or other celestial object
  • Meteor: The visible path of a meteoroid in the atmosphere 
  • Meteorite: A meteoroid that is at least partially intact after hitting a celestial body
  • Meteoroid: Smaller pieces which have broken off from asteroids.
  • Orbit: The curved path of an object around another object 
  • Sunspot: Dark areas on the sun’s surface which are relatively cool.

Next, we’ll review biology.


In case you haven’t taken a biology course lately, it might be useful to remember that biology is the study of living organisms. The word biology means the study of life. The suffix –ology means “the study of,” and -ologies, including those that are related to biology, and those that are not, are very frequently included on versions of the MAT.

Here are a few other -ologies which are encompassed by biology.

Ready to test your knowledge? Try completing this analogy: 

Algology : Phycology :: Malacology : a. Zoology b. Mycology c. Ornithology d. Conchology

Algology and phycology are synonyms; they both refer to the study of algae. Malacology and conchology both refer to the study of mollusks, so D is correct. How can you remember conchology? 

Easy, use a mnemonic device – think of a conch, which is a mollusk!

Now that you’ve reviewed various biological pursuits, let’s zoom in with a microscope. The following terms are helpful to remember when thinking of the building blocks of life:

  • Cell membrane: Acts as a wall between a cell the outside environment
  • Chloroplast: Plant organelles in which photosynthesis occurs
  • Chromosome: Made of DNAs, contains genes
  • Cytoplasm: The liquid inside of a cell  which surrounds organelles
  • DNA: Deoxyribonucleic acid, contains genetic information
  • Gene: A unit of heredity
  • Meiosis: Cell division process in sexual reproduction
  • Mitosis: When chromosomes split into two identical sets
  • Organelle: A tiny “organ” within a cell
  • Nucleus: Organelle containing genetic information, a cell’s “brain” 
  • Transcription: The act of copying of DNA to RNA 
  • Vacuole: An organelle found in all plant cells

Before we move onto another science objective, let’s look at one more concept which related to biology: animal names. This topic appears frequently on the MAT. 

The list below is organized as follows:

Animal: Male, Female, Offspring, Group, Adjective

  • Bear: Boar, sow, cub, sleuth, ursine 
  • Bee: Drone, queen, larva, swarm, apian 
  • Cat: Tom, queen, kitten, clowder, feline 
  • Cattle: Bull, cow, calf, herd, bovine 
  • Crow: Crow, crow, chick, murder, corvine
  • Deer: Buck, doe, fawn, herd, corvine 
  • Ferret: Hob, jill, kit, business, ferrety
  • Fox: Dog, vixen, kit, skulk, vulpine 
  • Goat: Billy, nanny, kid, tribe, hircine
  • Horse: Stallion, mare, foal, herd, equine 
  • Lion: Lion, lioness, cub, pride, leonine 
  • Pig: Boar, sow, piglet, sounder, porcine 
  • Rat: Buck, doe, kitten, mischief; murine 
  • Sheep: Ram, ewe, lamb, flock, ovine 
  • Snake: Snake, snake, snakelet, pit, serpentine
  • Swan: Cob, pen, cygnet, wedge, swanlike

Other interesting collective nouns include a parliament of owls, romp of otters, fluffle of rabbits, and a prickle of porcupines. Some might also call a group of snakes a nightmare, but it’s best to stick with pit on the exam!


Don’t worry, you won’t be asked to balance any chemical equations on the Miller’s Analogy Test!

However, it is a good idea to know some basic chemistry terms and to understand what they mean. Chemistry is yet another science which test-takers should not be surprised to encounter on the exam.

As a reminder, chemistry is the science of substances that make up matter. So let’s review some basic concepts.

  1. Are atoms and molecules the same thing? No. An atom is smaller than a molecule. Atoms are made up of protons, neutrons, and electrons. Molecules are a group of atoms that are bonded together?
  2. How do atoms bond together? Three types of bonds can bind atoms: ionic bonds, covalent bonds, and metallic bonds.
    • Ionic bonds: electrons transfer from one atom to another, creating oppositely charged ions that attract each other.
    • Covalent bonds: atoms share electron pairs between themselves. (Think: covalent – coworker. You share with your coworkers.)
    • Metallic bonds: if you’ve ever gathered static and been slightly shocked by touching a metal doorknob, you know that metal is a great conductor of electricity. That’s because the electrons of a metal can easily become detached or mobile. The attraction of these mobile electrons to their stationary cation forms a metallic bond.
  3. So, what’s an element? An element is a substance made entirely from the same type of atoms. All of the atoms making up an element have the same number of protons.
  4. What’s the difference between protons, neutrons, and electrons? Protons have a positive charge, neutrons have no charge, and electrons have a negative charge. (Think proton – positive, neutron – neutral, electron – being electrocuted would be a negative experience!)

Here are a handful of other helpful chemistry terms:

  • Acid: Reacts with a base, has a pH less than 7 
  • Anion: A negatively charged ion 
  • Base: Reacts with an acid, has a pH greater than 7 
  • Cation: A positively charged ion 
  • Electrolyte: Chemical compound that conducts electricity
  • pH: Measurement of acidity 
  • Solute: Put into a solvent to form a solution
  • Solvent: Dissolves a solute to form a solution
  • Valence electrons: An atom’s outermost electrons 


Geology is about more than just rocks! The field of geology covers the processes which act on the physical structure of the earth as well as the substances that make up the earth. Geologists are also concerned with the history of the earth itself.

Let’s review the earth’s time periods and eras. The numbers in the chart below reflect millions of years ago. The chart is organized from most recent to earliest.

Now, let’s look at some key terms related to geology:

  • Cementation: Process by which minerals “glue” sediments together to from rocks 
  • Clay: Mineral grains formed chemical weathering
  • Coal: Rock made of compressed and carbonized plant matter
  • Crystal: A geometric solid minerals with regular structures
  • Deposition: Process of sediment settling from water or wind
  • Faults: Cracks caused by rock movement during earthquakes
  • Lava: Molten rock that erupts from a volcano
  • Mineral: A natural chemical compound
  • Strata: Layers of rock formed by deposition
  • Tectonic plates: Portions of the lithosphere that move and affect the Earth’s crust
  • Volcanic ash: Small fragments of rock that spew from volcanoes
  • Weathering: Breakdown of surface rock; can be physical, biological, or chemical

Social Sciences

You can expect to complete to encounter the Social Sciences Content Objective as you complete analogies on the MAT. Let’s explore some branches of the social sciences which are often encountered on the exam.


Anthropology is the study of humans. There are four main subfields of anthropology: cultural anthropology, linguistic anthropology, biological anthropology, and archeology. Anthropologists explore our species as a whole, across various cultures across the world, and across multiple time periods.

Together, we’ll review, compare, and contrast some anthropological concepts.

Now that you have reviewed some terms, quiz yourself by completing this analogy:

Matriarchy : Materteral :: Patriarchy :: _______ a. Fraternal b. Sororal c. Avuncular d: Levirate

Matriarchy describes a social structure in which females are in power. Patriarchy describes a social structure in which males are in power. Materteral also relates to women; it refers to one’s aunt. So, what word refers to one’s uncle, the male equivalent of an aunt? Avuncular (C) is the correct answer.


Criminology is the study of crime. You just reviewed some anthropological terms, such as maternal, which describe the relationship to a certain family member. Did you know that there are also some terms which refer to crimes committed against certain family members?

There are terms for these crimes, especially when it comes to murder. There are other words used to describe particular murders as well. While murder is not a light topic, it can be interesting to learn about the different terms which relate to murder and other crimes.

Since criminology terms often appear in analogies classified as part of the Social Sciences Content Object, let’s review some of those words now:


Next, we’ll explore some concepts related to geography, another category that is often included on the MAT.

First, let’s look at some key geographical terms.

Now that you’ve reviewed some basic terms, let’s look at some specific locations around the world.

Are you ready to test your knowledge? Try completing the following analogy:

Longest : Missouri  :: Tallest : a. Everest b. Himalayas c. Denali d. Kilimanjaro

So, if the Missouri is the longest river in North America, you are looking for the answer choice (all of which are mountains) that describes the tallest mountain in North America. Choice C, Denali, is correct.

Political Science

It’s time to get political! Analogies related to political science are often included on the MAT as part of the Social Sciences Content Objective. 

Remember all of the -ologies that you encountered while reviewing other objectives? There are a several -acracies which are related to political science. Take a look:

  • Aristocracy: Government ruled by a few elite members (ex. patricians of Rome)
  • Autocracy: Government is ruled by one person (ex. Nazi Germany)
  • Democracy: All citizens have some influence (ex. U.S., ancient Athens)
  • Ethnocracy: Government in which one ethnic group rules over another (ex. pre-civil war southern U.S.)
  • Gerontocracy: Government ruled by elder members of population (ex. Sparta)
  • Meritocracy: Government in which those deemed to possess talent rule (ex. imperial China)
  • Mobocracy: Government ruled by the mob (ex. French Revolution)
  • Plutocracy: Government ruled by the wealthy (ex. pre-WWII Japan)
  • Ptochocracy: Government ruled by the poor (ex. Cultural Revolution in China)
  • Theocracy: Government driven by a religious institution (ex. The Vatican; fictional dystopian society in Atwood’s The Handmaid’s Tale)
  • Timocracy: Government ruled by property owners (ex. feudalism in medieval Europe)

You have already reviewed the term oligarchy. Notice that many of the terms you just read are types of oligarchies (rule by a few members). Here are a few other terms to know:

  • Capitalism: Trade and industry are controlled by private owners
  • Communism: Property is shared by the public
  • Constitutionalism: Government limited by fundamental laws
  • Socialism: Seeks to reject social classes
  • Totalitarianism: Government has complete control

So, let’s test your knowledge. Try to complete the following analogy.

Beloved : Ethnocracy :: 1984 : a. Timocracy b. Totalitarianism c. Constitutionalism d. 2019

Beloved is a novel by Toni Morrison. It is about an escaped slave in the late 18th century U.S. who flees from the South; the South was an ethnocracy during that time. George Orwell’s 1984 is a dystopian novel characterized by a totalitarian government. Choice B is the correct answer.


Now, let’s get psyched for psychology! You don’t need to prepare to become a licensed therapist in order to perform well on the MAT, but some basic psychological principles and ideas often appear on the exam.

Do you remember the guy with the big white beard? No, not Santa Claus, Sigmund Freud. Freud is often considered to be the father of psychoanalysis and a lot of modern psychology has its roots in his work.

According to Freud, everyone has an ego, an id, and a super-ego.

  • Ego: The part of an individual’s personality that is shown to the world. The ego helps an individual make sense of real life and is practical.
  • Id: The id is governed by pleasure and instinct. Freud did not believe one’s id to be freely accessible to an individual.
  • Super-ego: The super-ego is mainly unconscious and drives a person to feel guilt and to gravitate toward morality. This unconscious part of the super-ego is called the ego ideal, or the ideal self. The conscious part of the ego makes decisions.

Now that we’ve reviewed those terms, let’s talk a little bit about abnormal psychology. Abnormal psychology basically refers to concepts relating to how an individual is atypical or needs treatment for a problem. Most people find abnormal psychology to be fascinating because it describes conditions which are a bit out of the ordinary.

You have probably heard most of the following terms before, but you may be a little unsure of what they each mean. 

Let’s review:

Try out this analogy:

ADHD: Attention :: GAD : a. Depression b. Aggression c. Self-aggrandizement d. Anxiety

People suffering from ADHD struggle with attention and people with GAD struggle with anxiety; D is correct. 

Next, let’s talk about conditioning, a process during which organisms (including humans) learn. 

In classical conditioning, a stimulus is introduced and the subject learns to respond a stimulus introduced to the environment. Pavlov’s dogs are a famous example. Psychologist Ivan Pavlov performed an experiment in which whenever he fed a group of dogs, the food was accompanied by the sound of a bell.

After a time, the dogs would drool in anticipation of food whenever they heard the bell–even if no food was presented to them.

In operant conditioning, the subject has a greater role to play. The subject is responsible for changes in its environment. B.F. Skinner is the psychologist which most people associate with operant conditioning. Skinner performed an experiment in which rats who accidentally pulled a lever were rewarded with food. Soon, they were conditioned to pull the lever in order to receive food. This is an example of positive reinforcement.

Refer to the table below:


Next, let’s sharpen up your sociology skills. Sociology is the study of how people act in groups or societies. Let’s look at some key terms.

As you may notice, sociological content is very similar to anthropological content. Now that we’ve brushed up on the Social Sciences Content Objectives, let’s move onto another area.


If math isn’t your forte, you’ll probably appreciate that only about 14% of the content on the MAT is mathematical. Furthermore, you won’t have to perform any calculations on the exam. However, it is important that you understand some mathematical principles and terms related to math in order to score well on the exam.

Let’s look at some topics which are commonly included in the Mathematics Content Objectives.

Algebra and Arithmetic

The following table gives you some terms which you may encounter on the exam, as well as definitions and examples. Pay special attention to the bold text in the examples.

Try this example analogy:

Multiplication : Product :: Division :  a. Dividend b. Divisor c. Quotient d. Numerator

The product is the answer to a multiplication problem. The quotient is the answer to a division problem. C is correct.


Next, let’s review some geometric terms.

Now, let’s look at some specific types of shapes. Pay attention to their prefixes; a prefix tells you how many sides a shape has.

  • Triangle: Three sides
  • Quadrilateral: Four sides (in a square, all four sides are equal and all angles equal 90°)
  • Pentagon: Five sides
  • Hexagon: Six sides 
  • Heptagon: Seven sides
  • Octagon: Eight sides
  • Nonagon: Nine sides
  • Decagon: Ten sides
  • Hendecagon: Eleven sides
  • Dodecagon: Twelve sides

Now, try to complete this example analogy:

Triangle : Equilateral :: Quadrilateral :  a. Rectangle b. Polygon c. Square d. Scalene

An equilateral triangle is a triangle in which the sides are all equal and the angles are all equal. A square is a quadrilateral in which the sides are all equal and the angles are all equal. C is the correct answer.

Roman Numerals

Although we rarely encounter Roman numerals in our daily lives, they have a tendency to show up on the MAT. Remember: when a smaller value precedes a larger values, you should subtract the smaller value from the larger value. 

  • I: 1 
  • V: 5 
  • X: 10 
  • L: 50 
  • C: 100 
  • D: 500 
  • M: 1,000

Example: MCMLXXXIV = 1984.

And that’s a basic overview of the content objectives on the MAT!

Analogy Types

The Miller Analogies Test features analogies that fall into four major classifications:

  • Semantic 
  • Classification
  • Association
  • Non-semantic

We will look closer at these analogy types now.


Semantic analogies deal with the meanings of words. Let’s look at some types of semantic analogies.

Synonyms and Antonyms

Synonyms are two words that are basically the same in meaning, such as small and little. Practice with the following analogy:

METICULOUS : EXACTING :: CURRENCY _________________ 

  1. denomination 
  2. fiscal
  3. financial
  4. accepting

This is a synonym analogy, albeit in disguise. Meticulous and exacting can be synonyms. The word you are looking for is a synonym for currency. Choices A – C are not synonyms for currency. These choices are misleading because, like currency, they can relate to money.

However, currency can mean accepting. D is the correct answer. Be sure to consider all meanings of a word when completing an analogy, especially if none of the answers feel right at first.

Antonyms are two words that are opposite in meaning, such as wet and dry. Try the following analogy:


  1. Xenocentrism
  2. Xenophobia
  3. Assimilation
  4. Anthropocentrism

Dubious and indisputable are antonyms. Choice A, which means “preference for another culture” is an antonym for ethnocentrism. Choice A is correct.


Analogies which deal with intensity will include a term which is similar to another term, but to a greater or lesser degree. For example, hate is much stronger than dislike.

Take a look at the following analogy and pay attention to the intensity of the words:

STREAMING : TORRENTIAL :: TIRE :  _________________ 

  1. incapacitate
  2. bore
  3. doldrum
  4. tread

The correct answer is A. Picture torrential rain; it is more intense than streaming rain. To incapacitate someone can mean to completely wear them out to the point that they are not functioning; this is more intense than to tire someone.

Try another analogy:

VITRIOLIC : SATIRICAL :: EXTIRPATE :  _________________ 

  1. raze
  2. subdue
  3. mollify
  4. confound

B is the correct answer. This time, the words are ordered from mild to strong. Subdue is less intense than extirpate.


Next, let’s look at some classification analogies.


Some analogies deal with categories. You may need to classify a member of a class or to determine a subordinate or superordinate relationship by classifying the terms. 

Try this analogy:

KILIMANJARO : MOUNTAIN :: VOLGA :  _________________

  1. lake
  2. gulf
  3. river
  4. range

Kilimanjaro is classified as a mountain and the Volga is a river. Choice C is correct.

Try this analogy:

BISHOP : CARDINAL :: CORPORAL :  _________________

  1. Robin
  2. Sergeant
  3. Diocesan
  4. Private

This is an analogy that follows a superordinate : subordinate structure. In the order of Catholic officials, a bishop ranks higher than a cardinal. In the U.S. Marine Corps and the U.S. Army, a corporal ranks higher than a private. D is the correct answer.

Parts and Whole

Some analogies on the MAT are formatted as part : whole, whole : part, or part : part (wherein both parts help to make up the same whole).

See if you can complete this analogy:

SODA : BREAD :: MOZZARELLA :  _________________

  1. caprese
  2. toast
  3. Italian
  4. basil

Don’t let this analogy trick you; soda bread is a type of bread. However, soda (also called baking soda or bread soda) is also an ingredient found in bread. How do you know that the term soda is being used as an ingredient, not a category of bread? 

The answer is in the answers. Since cheese is not an answer, you can rule out that relationship.

Mozzarella (along with basil and tomatoes) is an ingredient used to make a Caprese salad. A is correct.


Next, let’s look at analogies which require you to consider some different types of associations.

Object and Characteristic

Some of the analogies on the exam will ask you to think about the characteristics of an object or person. You might need to think about an attribute an object or individual possesses or lacks or the setting in which an object or individual may be found.

Try this analogy, thinking about the characteristics associated with the terms.

HERO : SLAVE :: TIMIDITY :  _________________

  1. heroine
  2. freedom
  3. capture
  4. rescue

So, hero and slave are not really related; think about the relationship between hero and timidity instead. A hero does not have timidity (cowardice). What does a slave lack? B, freedom, is correct.


Some analogies may require you to think of the order of events or the sequence of a transformation. For example, caterpillar : butterfly shows a clear sequence, or order.

Try this analogy:

IV : V :: V :  _________________

  1. VI
  2. IV
  3. X
  4. IX

Answer A is correct. Four (IV) comes before five (V). Five comes before six (VI).

Agent and Object

Agent and object analogies require you to think about cause and effect relationships, the relationships between creators and creations, and the relationships between tools and their use. 

Practice by completing this analogy:

STICKS : DRUMMER :: BOW : ________

  1. archery
  2. cellist
  3. performance
  4. violin

This analogy follows the pattern of tool : user. Choice B is correct.

Try another agent and object analogy:


  1. gravity
  2. verticality
  3. tenacity
  4. pitch

A barometer measures pressure and a plumb measures verticality. Choice B is correct.


Non-semantic analogies do not deal with the meanings of words. So, what could they possibly address? Logic and phonetics are the areas they address the most frequently. Let’s practice.


Equality analogies typically ask you to evaluate two values which are equal or unequal. You might also need to evaluate words which are equivalent to part of other words.

Here is an example:

RETALIATE : ATE :: SPRUNG : _________

  1. spring
  2. sprint
  3. run
  4. grunt

Choice C is correct. “Ate” is part of retaliate. “Run” is part of sprung. Notice that the analogy is not semantic; the meanings of the words are unimportant.

Try this analogy next:


  1. deserter
  2. stressed
  3. asserts
  4. distressed

The word semordnilap is actually a semordnilap of palindromes; but that’s not important here. All you need to know is the pattern word : (word spelled backwards). Stressed is desserts spelled backwards! B is the correct answer.

Try one more equality analogy:

4 : 16 :: 8 : _____

  1. 12
  2. 2
  3. 64
  4. 32

Since 16 is 4 squared, 8 squared is the answer. C is correct.

Letter and Sound

Some non-semantic analogies deal with letter patterns, sound patterns, rhymes, homophones, and words with similar sounds. We’ll complete a couple of example analogies.

EIFFEL : FIZZ :: WAFFLE : ______

  1. pizzaz
  2. fluffle
  3. raffle 
  4. froze

In this analogy, you are looking for double letters. Eiffel and waffle contain double fs. Fizz and pizzaz contain double zs. A is correct. 

By the way, fluffle is a real word; you may recall from before that it refers to a group of rabbits.

Here is another practice analogy:


  1. bang
  2. frantic
  3. crush
  4. dial

This analogy deals with sounds. Specifically, it deals with alliteration, words which begin with the same consonant sounds. Crash and kerchief begin with the same sound, as do phone and frantic. B is correct.

And that’s some basic info about the analogies on the MAT!

Section III: Quantitative Reasoning Assessment

The Quantitative Reasoning Assessment includes 31 questions. You will be given 62 minutes, about one-third of your total testing time, to answer the questions on this section.

This part has five main objectives:

  • Problem Solving
  • Data Sufficiency and Analysis
  • Number Forms, Relationships, and Sets
  • Number Theory and Algebra
  • Geometry


So, let’s start with Problem Solving.

Sub-area I: Problem Solving

This objective tests your knowledge of the fundamental rules of arithmetic and algebra. In order to perform well in this section of the test, you should able to work quickly and decisively in order to answer questions as efficiently as possible. However, you should always check your answer by plugging it into the original problem whenever possible!

Take a look at some concepts that may appear on the test.

Fractions and Decimals

Some questions on the test will challenge your ability to work with fractions.

Remember that when multiplying fractions, you should multiply the numerators by each other and the denominators by each other. In order to divide two fractions, flip one of the fractions and multiply the new numerators by each other and the new denominators by each other. When adding or subtracting fractions, don’t forget to start by making the denominators equivalent.

Remember that you can always turn a fraction into a decimal or mixed number by making the denominator 100. For example, 1/5 = 20/100 or .20.

Let’s take a look at an example problem.

Let’s take a closer look at what the question is really asking: if you can buy an eraser for a dollar, how many erasers can you buy for a cent?

Now, the answer choices are presented as fractions, but we need to remember that 1 dollar is 100 cents. In other words, 1 cent is equal to .01 dollars or 1c is 1/100 dollars.

Therefore, we know we are looking for a fraction with a number larger than 100 in the denominator. B can only be the correct answer choice.


You already know that a percent is just a converted fraction. For example, .30 = 30%. Some of the questions on the test will require you to use that knowledge to find out what percent of one quantity is to another.

You may also need to find out the percent change, which could be a percent increase or a percent decrease. Here’s a sample problem which requires you to calculate the percent decrease:

If Joe drinks 10% of the coffee from a 16-ounce cup before breakfast and 20% of the remaining amount with breakfast, approximately how many ounces of coffee are left after breakfast?

A. 5.3 ounces
B. 6.2 ounces
C. 11.2 ounces
D. 11.5 ounces
E. 13 ounces

In order to solve this problem, we will need to perform two separate steps. It would be a mistake to add 10% and 20% and calculate 30% of 16. Remember, there is less coffee in the cup the second time that Joe drinks from it.

First, we need to find 10% of 16 and subtract that amount from 16 to get our first solution. Then, we need to find 20% of our first solution and subtract that amount from the first solution in order to reach our final solution:

16 × 0.1 = 1.6
16 – 1.6 = 14.4 (first solution)
14.4 × 0.2 = 2.88
14.4 – 2.88 = 11.52 (final solution)

Therefore, the correct answer is B. Sometimes, as in this example, it is necessary to round off to a value. Choice B is the closest in value to our final solution.

Order of Operations

If you have not taken a math course recently, it may be helpful for you to remember “PEMDAS” while working on problem-solving questions.

This acronym stands for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. The mnemonic phrase, “Please Excuse My Dear Aunt Sally” can help you to remember PEMDAS.

Let’s practice with a sample equation and solve it step by step:

8 + (2 x 5) x 3⁴ ÷ 9

  1. Parentheses: 8 + (10) x 3⁴ ÷ 9
  2. Exponents: 8 + (10) x 81 ÷ 9
  3. Multiplication/Division: 8 + 810 ÷ 9
           = 8 + 90
  4. Addition/Subtraction: 98

While working with the order of operations, solve problems left to right. Notice that in the multiplication/division step, we applied multiplication (left) before the division (right).

If you are a little out of practice with order of operations, it’s very important to hone your skills – you will need to use the order of operations on other subsections of the test, as well!

Defined Operations

Defined operations are very different from the order of operations. In a defined operations question, the test makers will tell you how to plug in numbers in order to solve an equation. You must follow their instructions to get the correct answer.

Defined operations questions can look a little funny. Here’s an example of one:

In defining the figure as “ac – bd,” the test makers are giving you instructions for how to apply numbers and variables whenever you see them in the diamond arrangement.

First, we should determine the value of x. Based on the last figure, a = 5, b = 4, c = 2, and d = 1. Let’s plug those numbers into the equation we have been given:

x = (5 × 2) – (4 × 1)
x = 10 – 4
x = 6

Now, we must solve the same equation using x = 6. Based on our answer and the second figure, which we must solve to find the final answer, a = 6, b = 10, c = 2, and d = 1.

(6 × 2) – (10 × 1)
= 12 – 10
= 2

Therefore, our final answer is 2. Defined operations questions may look tricky, but you are being given the instructions to solve them. All you need to do is to make sure that you pay attention to what the instructions are.

Sub-area II: Data Sufficiency and Analysis

This area tests your ability to determine whether or not an answer can be found based upon given information. Data sufficiency and analysis questions have prompts which contain two pieces of information.

The answer options will appear in the following format:

A. (1) ALONE is sufficient to answer the question. (2) ALONE is NOT sufficient to answer the question.
B. (2) ALONE is sufficient to answer the question. (1) ALONE is NOT sufficient to answer the question.
C. BOTH (1) and (2) are needed to answer the question.
D. BOTH (1) and (2) are sufficient to answer the question independently.
E. The question cannot be answered based on the information given.

Take a look at some concepts that may appear on the test.

Three-Step Elimination

In order to answer data sufficiency and analysis questions, it is best to have a plan to tackle them. Use the following plan to eliminate answer choices:

Step 1: Size up the prompt.

Step 2: Consider information (1) thoroughly.

Step 3: Consider information (2) thoroughly.

Step 1: Size up the prompt.

Determine what is being asked. Gather a general idea of the information that (1) and (2) are giving.

If (1) and (2) are essentially giving the same information, you can eliminate choices A – C. If the information is basically the same, (1) and (2) do not need to work together; one would not add any more information to the other. Furthermore, if one of them is not sufficient, the other will not be either.

If the information is the same, choose either (1) or (2) and decide whether it is sufficient or insufficient to answer the question. If it is sufficient, choose D. If not, choose E.

Step 2: Consider information (1) thoroughly.

If (1) and (2) appear to be giving different information, you will need to move on to the second step. Consider the information in (1) a little more deeply.

If (1) is sufficient to answer the question, either A or D is the correct answer.

If (1) is NOT sufficient to answer the question, you know that either:

  • You will need (2), with or without (1), to answer the question.
  • The question cannot be answered.

At this point, based on how much time you have spent on the question and the test in general, make a judgment call on whether or not to invest further time on the question.

To save time but possibly lose a point, choose A or D. Otherwise, move on to the final step.

Step 3: Consider information (2) thoroughly.

Answer the question does (2) prove to be sufficient alone?

Yes, (2) is sufficient alone:

  • If (1) was ALSO sufficient alone, the answer is D.
  • If (1) was NOT sufficient alone, the answer is B.

No, (2) is NOT sufficient alone.

  • Eliminate D and B.
  • If (1) was sufficient to answer the question, choose A.
  • If (1) was NOT sufficient to answer the question alone, can you figure out the answer by using both (1) and (2)? If so, the answer is C. If you still cannot figure out the answer, E is correct.

Now that you’ve developed a strategy, let’s try it out on a sample question:

A. (1) ALONE is sufficient to answer the question. (2) ALONE is NOT sufficient to answer the question.
B. (2) ALONE is sufficient to answer the question. (1) ALONE is NOT sufficient to answer the question.
C. BOTH (1) and (2) are needed to answer the question.
D. BOTH (1) and (2) are sufficient to answer the question independently.
E. The question cannot be answered based on the information given.

Now, let’s use our plan to come to a solution.

Step 1: Size up the prompt.

This is a percent increase question; Ted paid more than the dealer, but we don’t know by how much. The information given is similar, but not the same.

Step 2: Consider information (1) thoroughly.

We can determine how much Ted paid by calculating the profit (50%) the dealer made on his $10,000 purchase.

$10,000 + 0.5($10,000) = Amount paid by Ted

Since (1) is sufficient to answer the question, we can eliminate all choices EXCEPT A and D.

Step 3: Consider information (2) thoroughly.

Based on (2), we can determine how much Ted paid for the wardrobe with the following equation:

$10,000 x 3/2 = Amount paid by Ted

Without performing any actual calculations, we can determine that both (1) or (2) can answer the question independently. Choice D is correct.

Sub-area III: Number Forms, Relationships, and Sets

This objective tests your knowledge of ratios and standard deviation, as well as your ability to determine rates, such as production rates and speed.

Take a look at some concepts that may appear on the test.


A ratio is a part compared to a whole. For example, if 5:6 represents the ratio of oranges in a bowl to all of the fruit in the bowl, 5 oranges + 1 additional fruit = 11 pieces of fruit. 5/11 pieces of fruit in the bowl are oranges.

Here’s an example problem that is similar to what you may see on the test:

A basket contains only pens and pencils. If 18 of the items are pens, and if the ratio of the number of pencils to the number of pens in the basket is 5:3, how many items are in the basket?

A. 34
B. 36
C. 44
D. 48
E. 52

First, let’s look at the ratio.

5 pencils + 3 pens = 8 items
(Remember, this is the ratio, not the answer to the question.)

If 18 of the items are pens, then 18 = 3 parts of the whole. If we divide by 3, we find that each part is equal to 6 items.

6 (1 part) x 8 = 48 items

Choice D is the correct answer.

Rate of Production

The rate describes the relationship between a quantity and an amount of time. We can determine the rate of production by using the following formula:

Rate = Quantity ÷ Time

Here’s an example scenario:

If an editor can edit 5 pages per hour, how many pages can she edit in 150 minutes?


It is likely that you will see several problems on the test which will require you to perform computations that include different monetary values. Let’s look an example problem now.

Mrs. Jones has $2.05 in dimes and quarters. If she has four more quarters than dimes, how much money does she have in dimes?

A. 30 cents
B. 70 cents
C. 20 cents
D. 80 cents
E. 60 cents

If we use Z to represent the total number of dimes, Z + 4 must be the total number of quarters. Since the value of a dime is 10 cents, we will use 10Z to represent the total value of the dimes and 25(Z + 4) to represent the total value of the quarters:

10Z + 25(Z + 4) = 205
10Z + 25Z + 100 = 205
35Z + 100 = 205
35Z = 105
Z = 3

3 x 10 = 30 cents

The correct answer to this question is A.

Time, Speed, and Distance

Calculating the rate of speed is very similar to calculating the rate of production, which we recently reviewed. The following formula may be used to calculate the rate of speed:

Speed = Distance ÷ Time

Using the formula, we can determine that if a car travels 110 miles in 2 hours, the car is going 55 miles per hour (given that no one needs to make a rest stop!):

Speed = 110 ÷ 2
55 = 110 ÷ 2

We can adjust the same formula to determine the two other variables:

Distance = Speed x Time
Time = Speed x Distance

Sub-area IV: Number Theory and Algebra

This objective tests your algebra skills and your ability to work with linear and nonlinear equations, inequalities, and distance and midpoint formulas.

Take a look at some concepts that may appear on the test.


Some of the questions on the test may require you to calculate the root of a number. A root is simply the inverse of an exponent. Remember “root” means “reverse”!

You are most likely to encounter square roots and cube roots on the test.

A square root indicates a number multiplied by itself. For example, the square root of 9 is 3.

√9 = 3
9 = 3 x 3

A cube root indicates a number multiplied by itself 3 times. For example, the cube root of 27 is 3.

³√27 = 3
27 = 3 x 3 x 3

Linear Equations with Two Variables

We’ve already practiced solving some equations to find out the value of a variable (such as when we reviewed time, speed, and distance).

Sometimes, you will need to solve equations which contain more than one variable, or unknown value. In these equations, the value of one variable depends upon the value of another. Consider the following equation:

3x + 4y = – 8 and x – 2y = ½
Determine the value of each x and y.

We can work to solve one variable at a time. First, let’s find the value of x by eliminating y. We need to multiply the terms in the second equation by 2 to get 2x – 4y = 1.

Now, we can add our equations:

3x + 4y = – 8
2x – 4y = 1
5x + 0y = -7
x = -7/5

We have found the value of x. Next, we can find the value of y by multiplying the second equation by 3 (to get 3x – 6y = 3/2) and subtracting it from the first equation.

3x + 4y = – 8 
3x – 6y = 3/2
10y = -9½
y = – 19/20

Quadratic Equations

A quadratic equation contains variables that are squared. These equations can be identified in the following format:

ax² + bx + c = 0

These equations create a parabola (which looks like a smile or a frown) when graphed. Sometimes, quadratic equations are disguised. Take a look at the following example, which is not in the traditional form:

2a² = 16

There appears to be no b value in that equation, but we can rearrange it to get:

2a² – 16 = 0

Let’s practice solving a quadratic equation. In order to do so, we will need to use the quadratic formula:

+ 4x – 14 = 0
Solve for x.

In order to find the solution or the value of x, we need to plug the given values into the formula:

Algebraic Inequalities

On the test, you will likely need to solve inequalities, as well as equations. In order to do so, you will need to isolate a variable, just as you do when you solve equations.

It is important to keep in mind that when you divide or multiply by a negative number, you must reverse the greater than (>) or less than (﹤) symbol. Let’s take a look at an example inequality which requires us to reverse the sign:

12 – 4x < 8 (subtract 12 from each side)
–4x < –4 (divide each side by -4)
x 1 (flip the less than sign)

The same rule for flipping less than and greater than signs holds true for less than or equal to ( ≤ ) and greater than or equal to ( ≥ ) signs; we must reverse them when we multiply or divide by a negative number.

Let’s try something a little more challenging and solve two inequalities at the same time:

-2  ≤ 6 – 2x   ≤ 4

Multiply each part by 3 to get:

-6  ≤ 6 – 2x   ≤ 12

Next, subtract the 6:

-12  ≤ -2x   ≤ 6

Finally, isolate the x:

6    x  -3


-3  ≤ x   ≤ 6

Overlapping Sets

Sometimes, you may be presented with sets of data that overlap, or contain the same numbers. Overlapping sets may not be immediately recognizable because they may be described in word problems.

Let’s look at an example question containing an overlapping set:

A closet contains 24 shirts. Each shirt has either a collar, long sleeves, or both a collar and long sleeves. If 10 of the shirts have collars and 19 of the shirts have long sleeves, how many of the shirts have long sleeves but no collars?

The question includes three mutually exclusive sets: (1) collared shirts without long sleeves (2) long-sleeved shirts without collars (3) shirts with both collars and long sleeves. The total number of people in these three sets is 24.

If we use s to represent the number of shirts with both long sleeves and collars, we can create the following equation:

(10 – s) + n(19 – s) = 24
29 – s = 24
s = 5

Now that we have found the number of shirts with both long sleeves and collars, we can subtract that number from the total number of shirts with long sleeves:

19 – 5 = 14

Sub-area V: Geometry

This objective tests your knowledge of concepts such as lines, angles, shapes, and coordinate planes. If you haven’t had a geometry class in a while, don’t worry – we will review some basic concepts right now.

Lines and Angles

The concept of lines and their intersections is a basic building block for many geometry problems. Remember that if lines are perpendicular, they create right angles. If lines are parallel, they never intersect.

A transversal is a line which crosses two parallel lines. The following diagram is an example of two parallel lines crossed by a transversal:

Using the diagram, review the following types of angles:

  1. Exterior angles: ∠A∠F∠G∠D
  2. Interior angles: ∠B∠E∠H∠C
  3. Consecutive interior angle pairs: [∠B and∠E] [∠H and∠C]
  4. Alternate exterior angle pairs: [∠A and∠G] [∠Fand∠D]
  5. Alternate interior angle pairs: [∠E and∠C] [∠H and∠B]
  6. Corresponding angle pairs: [∠A and∠E] [∠C and∠G] [∠D and∠H] [∠F and∠B]

Since we know that lines equal 180°, we can use that information to find the unknown values of angles.

For example, if ∠A in the previous figure is equal to 141°, you know that ∠E is also equal to 141° and that ∠B and ∠F are equal to 39°.

When it comes to intersecting lines, often you only need to know the value of one angle to solve the rest of the “puzzle!”

The Pythagorean Theorem

Some questions on the test will evaluate your ability to work with triangles, which are three-sided geometric shapes with three angles. The three angles of any triangle add up to 180°.

The most important type of triangle to know is the right triangle, a triangle with an angle which measures 90°. A right angle of a right triangle may be identified by a small box in the corner of the triangle:

When working with right triangles, you will often need to apply the Pythagorean Theorem by using the Pythagorean equation a² + b² = c².

According to this theorem, side c is the side of the triangle opposite the right angle; side a and side b are the other two sides of the right triangle. Here’s a simple example of how the Pythagorean equation can be used.

If side a of a triangle is 4 inches and side b is 3 inches and side c is the hypotenuse, what is the length of side c?

To solve this problem, just plug the numbers into the Pythagorean equation:

4² + 3² = c²

Apply the exponents:

16 + 9 = c²

Add the values on the left:

25 = c²

And find the square root of c:

c = 5

Pythagorean Triplets

A Pythagorean triplet is a ratio which describes each of the three sides of a right triangle. The first two numbers refer to the shorter legs of the triangle and the final number refers to the hypotenuse. Here are some common Pythagorean triplets:

Since you are working with ratios, you know that a triangle measuring 3:4:5 has the same proportions as a triangle measuring 6:8:10 or 15:20:25.

The first two Pythagorean triplets (1:1:√2 and 1:√3:2) also have Pythagorean angle triplets. The angles of these two types of right angles respectively measure 45°/45°/90° and 30°/60°/90°.

Let’s look at an example problem:

The following diagram contains two right triangles. How long is line BD?

Before we worry about BD, we need to find the value of AD. Since triangle ADC is a 30°/60°/90° triangle, its ratio must be 1:√3:2.

Using the ratio 1:√3:2, and considering that 10 is the value of the hypotenuse, side AD should be 5 inches because the ratio 5:10 is the ratio 1:2.

If side AD is 5 inches, then side BD is also 5 inches because triangle ADB is a 45°/45°/90° with a ratio of 1:1:√2. In other words, the two shorter legs of triangle ADB are exactly the same length!


On the test, you’ll work with circles and calculate their circumferences and surface area. To calculate the circumference of a circle, use the formula C = 2πr. The “r” represents the radius, a segment that connects the center of the circle to the edge of the circle.

For example, imagine that you have a circle with a radius of 4 feet.

In order to determine the circumference, just plug 4 into the C = 2πr formula. When you do this, you will find that the circumference of the circle is 25.23.

Remember that the radius is half of the diameter. If we had been given the diameter of the circle instead of the radius, we could easily reach the same conclusion by dividing the diameter in half and plugging that answer into the same formula.

C = 2πr is the same as C = πd

In order to determine the surface area of a circle, we would use the formula A = πr² . The area of the same circle (with a radius of 4 feet) would be 50.27 square feet.


Any geometric figure which contains only straight lines is an example of a polygon. Triangles, rectangles, octagons, and parallelograms are all examples of polygons.

Using the following formula, in which n represents the number of sides, we can find the sum of the interior angles of a polygon:

(n – 2)(180°) = sum of interior angles

Here are a few examples of how this formula may be applied:

Triangle (3 sides): (3 – 2)(180°) = 180° ÷ 3 = 60°
Quadrilateral (4 sides): (4 – 2)(180°) = 360° ÷ 4 = 90°
Pentagon (5 sides): (5 – 2)(180°) = 540° ÷ 5 = 108°
Hexagon (6 sides): (6 – 2)(180°) = 720° ÷ 6 = 120°
Heptagon (7 sides): (7 – 2)(180°) = 900° ÷ 7 = 129°
Octagon (8 sides): (8 – 2)(180°) = 1080° ÷ 8 = 135°

Notice the underlined text above. It reflects the measure of each angle in a regular polygon. A regular polygon is a polygon which contains only angles which are equal in measure.

Now, let’s use the formula for interior angles to solve an actual problem.

A hexagon has six internal angles with the following measurements: 124°, 122°, 54°, x°, x°, ⅘x°. What is the least possible sum of any two of the hexagon’s internal angles?

First, let’s apply our formula:

(6 – 2)(180°) = 720°

Subtract the known angles from 720°.

720°- (124° + 122° + 54°) = 420°

The three remaining angles must add up to 420°. Let’s set up an equation to determine their values:

x + x + ⅘x = 420°
14/5x = 420°
x = (420)5/14 = (30)(5) = 150

Therefore, two of the angles are equal to 150° and one of the angles is equal to 120° (⅘ of 150°).

Now that we know the measures of all of the angles, we know that the smallest angles measure 120° and 54°.

Therefore, the smallest possible sum of any two of the angles is 174°.

Coordinate Planes

A coordinate plane is a two-dimensional number line. On a coordinate plane, the vertical line is called the y-axis and the horizontal line is called the x-axis. The lines on a coordinate plane are perpendicular and intersect at the zero point. This point is called the origin.

Let’s look at an example of how to graph a point on a coordinate plane. To graph the point (2, 4), you need to know that the first number is always x and the second number is always y (x, y).

Start at the origin (0,0). Now, count over to the “2” on the x-axis and up to the “4” on the y-axis. You’ll end up with this answer:

You can use y = mx + b to describe any line on a coordinate plane. In this equation, the x and y values of any point on the line may be used. We use m to represent the slope and b to represent the y-intercept. The y-intercept is where the line crosses the y-axis.

In order to determine the slope of a line, you simply need to find two points on the line. We subtract the y value of the first point from the y value of the second point. Underneath, we subtract the x value of the first point from the x value of the second point.

You can also do this in reverse and subtract the first point from the first if you wish. Just remember to keep the y values on top!

As an example, let’s calculate the slope of two points, A and B, on the same line.

Let’s look at an example question which requires us to work with two points on a line:

On a coordinate plane, at what point along the y-axis does a line passing through point E (5, –2) and point J (3, 4) intersect that axis?

This question is asking us to find the y-intercept (b) of a line. We already know the values of two points, so let’s start with finding the slope (m) using the method you just learned.

Now that we have the slope, let’s go back to the formula y = mx + b. We can use either point E (5, –2) or point J (3, 4) to find the answer. Let’s plug in the values from point J:

y = mx + b
4 = (-3)3 + b
4 = -9 + b
13 = b

The y-intercept of our line is 13!

Section IV: Verbal Reasoning Assessment

The Verbal Reasoning Assessment includes 36 questions. You will be given 65 minutes, about one-third of your total testing time, to answer the questions on this section.

This part has three main objectives:

  • Critical Reasoning
  • Sentence Correction
  • Reading Comprehension


So, let’s start with Critical Reasoning.

Sub-area I: Critical Reasoning

This objective tests your ability to make logical inferences about arguments and conclusions without being distracted by irrelevant statements or assumptions. You should also be able to locate conclusions within prompts and to understand how arguments are strengthened or weakened.

Take a look at some concepts that may appear on the test.

Making Inferences

An inference is a reasonable conclusion made by examining incomplete information. Inference questions usually include words such as “conclude,” “conclusion,” and “infer.” When given an inference question, avoid assumptions and making great leaps; the answer will be a conclusion that does not go far beyond the given information in the prompt.

Let’s look at an example question:

The New Hanover County government promised its citizens that the new state highway will not pass through existing sites in which Species B, a protected species of waterfowl breeds, lives, including Zone Z. However, the new highway will pass within a mile of Site Z, which is the center of several important breeding sites for members of Species B, though this has not been discovered yet. Which of the following inferences is best supported by the statements made above?

A. The government has broken its promise to the citizens of New Hanover County.
B. The citizens of New Hanover County are worried that the noise the new highway will create might disturb the Species B individuals which breed in Zone Z.
C. Because the government is committed to preserving the breeding sites of Species B, there is no threat to Zone Z, nor any undiscovered nearby breeding sites.
D. It does not matter whether breeding sites around Zone Z are damaged by the highway since New Hanover County needs the new highway in order to bring in more tourists, and this factor is more important than the thrival of Species B.
E. Unless the state highway plan changes, undiscovered breeding sites will likely be threatened during the construction of the road.

Let’s consider each of the answers together:

Choice A contradicts the premise that the county government promised that the state highway will not pass through the existing breeding sites of Species B. Although the state highway will pass through undiscovered breeding sites, it is incorrect to determine that the government has broken its promise; the government does not plan to pass through Zone Z, only near that site.

Choice B presents a new challenge regarding another concern of the citizens. There is no information in the existing premises to support the statement about noise, so this cannot be the correct answer.

Choice C addresses the premise that the government has promised to preserve the breeding sites of Species B. However, consider the premise that the highway will pass near Zone Z, which is the center of several breeding sites. This fact reveals that other breeding sites could be threatened. Therefore, choice C is incorrect.

Choice D may be ruled out almost automatically because it is based on assumptions and is only loosely linked to the information given. Remember, avoid making great leaps; use what you know to be true to make an inference!

Choice E is the most logical choice because it reflects a probable conclusion to the given premises. You know that the area around Zone Z includes several undiscovered breeding sites. You know that the highway will be built near Zone Z – in other words, it will be built in the area around Zone Z. Therefore, you can conclude that undiscovered breeding sites may be threatened unless construction plans change.


When answering assumption questions, you will be given a prompt which includes premises, a conclusion, and a list of assumptions.

The correct answer contains an assumption that would logically make the conclusion in the prompt true. The incorrect answers contain assumptions that do not make the conclusion in the prompt correction.

Most assumption questions will actually contain the word “assumption.” This is good news for you because this will make this type of task easier to identify.

Let’s look at an example question:

For many consecutive years, the price of avocados at each of four statewide grocery store chains has been about 50% higher than the national average price. Furthermore, the per-pound difference in avocado prices among the four stores were never more than five cents. Among grocery stores in other states, the price of avocados reflected as much as a dollar difference per pound during the same time period. The four grocery store chains must have made arrangements in order to not compete among themselves and to agree to fixed levels at which to set their avocado prices.

The claim that the four grocery store chains fixed avocado prices rests on which of the following assumptions?

A. No other grocery store sold avocados at a higher price than the four chains.
B. The average price of avocados in all grocery stores in the state where the four chains operated greatly exceeded the national average.
C. Consumers in the same state as the four chains also purchased avocados from many other grocery stores in the state.
D. Grocery shoppers in the state where the four chains conduct business generally prefer avocados over other product options, even if avocados are more expensive than the other product options.
E. The wholesale price that grocery stores paid for avocados varied significantly between states during the time period of interest.

Now, we can consider each of the five assumptions and decide which assumption makes the most sense with respect to the prompt.

Choice A might give some credibility to the conclusion that the four chains agreed to fix the price of avocados. However, the assumption is vague. We do not know whether to consider stores across the nation or only stores which compete in the same state as the four chains. Also, just one store charging consumers a higher or lower price would not create a statistically significant impact.

Choice B does not support the argument that the four stores held a monopoly and fixed prices. Rather, it would support the idea that the four stores only charged high prices for avocados out of necessity.

Choice C weakens the argument that the four chains held a monopoly on avocados and agreed upon fixed prices because the presence of more competitors would make a monopoly less likely.

Choice D is not relevant to the argument, which is concerned with the cost of avocados only, not the cost of avocados in comparison with other produce options.

Choice E is the best answer because it eliminates a factor (wholesale pricing) that would logically impact the prices which consumers paid for avocados. With this factor eliminated, we can make a better argument for the conclusion that the four chains agreed to fix prices.

Weakening Evidence

Just like the assumption questions, weakening evidence questions will present you with an argument in which premises and assumptions are used to reach a conclusion. However, you will identify which of the answer choices weakens the argument the most.

Weakening evidence questions will include phrases such as “weaken the argument,” “damage the argument,” and “flawed reasoning.”

Let’s look at an example question together and find the correct answer:

An undocumented painting, supposedly Italian and from the 15th century, has been offered to an art museum. The painting may be genuine because it comes from a private collection. However, yellow hues in 15th-century paintings tend to look dull, whereas this painting has comparatively very bright yellow tones. Therefore, the painting has more than likely been forged.

Which of the following options, if correct, most seriously weakens the argument?

A. The art museum has a policy in place to accept only international pieces which are accompanied by completed and valid export forms.
B. The landscape in the background of the painting is very similar to other landscapes depicted in the background of paintings which were completed in Italy during the 15th century.
C. Recently, a similar painting with bright yellow hues was revealed to be forged by a modern artist and fraudulently sold to a museum as a historical piece.
D. Expert art appraisers believe that foragers cannot convincingly reproduce the wooden panels which were typically used as canvases by painters in the 15th century.
E. Some solutions which art restorers and collectors use to clean very old paintings can make the hues of the paintings appear brighter.

Now, before we begin looking at the answer choices, remember: we want to find the choice which weakens the argument that the painting is probably a forgery.

Choice A does not address forgery, and therefore it does not weaken the argument.

Choice B somewhat weakens the argument that the painting is a forgery. If the background of the painting in question looks similar to the backgrounds of legitimate paintings, it may seem less likely that the painting was forged. However, a convincing forgerist would have knowledge of the appearance of legitimate paintings from the same area and era, and he would probably try to emulate the same style.

Choice C strengthens rather than weakens the argument that the painting is a forgery, so it is not the correct answer.

Choice D addresses the forgery of paintings, but it brings up a new topic, wooden panels, which were never addressed in the prompt.

Choice E is the correct answer because it gives a possible legitimate reason why a 15th century painting might display bright yellow hues.

Supporting Evidence

Think of a supporting evidence question as the opposite of a weakening evidence question. Once again, you will be given a prompt which uses premises to support a conclusion. However, you will identify which of the answer choices strengthens the argument the most.

Look for phrases such as “best supports,” “most strongly supports,” and “effectively strengthens” in order to identify a supporting evidence question.

Let’s look at an example of a supporting evidence question:

In a blind study of individuals suffering from dust mite allergies, each subject was administered AllerCalm or a placebo. Six months later, fewer than 25% of the individuals who were administered AllerCalm continued to experience allergy symptoms, in comparison with about 75% of the subjects who were given the placebo. This confirms that AllerCalm is effective in curing allergies to dust mites.

Which of the following statements, if correct, most strongly supports the argument?

A. None of the participants who received AllerCalm reported any negative side effects to the medication.
B. Proven research indicates that if a study is blind to the researchers, but not the experimenters, the researchers may treat the control group differently than the group receiving the actual treatment.
C. During the six months of the experiment, some of the subjects took other allergy medications to help control their symptoms.
D. Six months after the experiment, the total number of subjects who reported allergy symptoms were fewer than at the beginning of the experiment, when all subjects reported allergy symptoms.
E. During the six months of the experiment, researchers frequently monitored the subjects’ homes and reported no significant change with regard to evidence of dust mites.

Let’s think about which of the choices provides evidence to support the idea that AllerCalm cures dust mite allergies:

Choice A is irrelevant because it shows that AllerCalm is probably safe, but it does not support the argument that AllerCalm is effective.

Choice B is incorrect because it actually weakens the argument. If researchers knew which subjects were receiving AllerCalm, they may have been more likely to suggest to these individuals that their symptoms were improving, thus altering the results reported by the subjects.

Choice C could also be used to weaken the argument. If all or even some of the subjects who received AllerCalm took other allergy medications, the other medications could account for why these subjects were less likely to report allergy symptoms.

Choice D is incorrect because it neither provides new information, nor distinguishes between the control group and the group receiving AllerCalm.

Choice E is the correct answer because it supports the idea that there was no significant change to the subjects’ environment, thus lending credibility to the study.

Sub-area II: Sentence Correction

This objective tests your knowledge of English grammar and sentence structure by presenting you with sentences in need of correction. You will evaluate a sentence which contains errors, as well as a list of different versions of the original sentence.

After reading the revised sentences in the list, you will select the best version of the sentence. When selecting your answer, choose the version of the sentence which is concise and best conveys the meaning of the sentence.

Always read the original sentence before selecting your answer. As you do so, ask yourself if something about the sentence seems awkward.

Take a look at some concepts that may appear on the test.

Adjectives and Adverbs

Some sentences will show an error in the choice between an adjective and an adverb. Remember, adjectives describe nouns and adverbs describe verbs and adjectives. Generally, adverbs end in -ly.

Take a look at the chart below to review the examples of these two types of words:

Now, let’s look at an example sentence and choose the appropriate correction:

The data suggests that over the next decade, demand for the product will increase at an unexpectedly fast rate, and greatly surpasses the previous predictions of most economists.

A. increase at an unexpected fast rate, and greatly surpasses
B. be at an unexpected increased rate and will greatly surpass
C. increase at an unexpectedly fast rate, and even surpasses
D. increase at an unexpected fast rate, greatly surpassing
E. increase at an unexpectedly fast rate, greatly surpassing

In this example, E is the correct answer. This is because the adverb “unexpectedly,” instead of the adjective “unexpected,” should be used to describe the word “fast.” We can rule out A, B, and D because they both use the verb “unexpected.”

We can rule out C because of the use of “surpasses;” the sentence clearly refers to a future event, not a current trend. The use of “surpasses” indicates that the demand is currently increasing at an unexpected rate.

Personal Pronouns

Sometimes, you will be presented with a sentence which incorrectly uses a personal pronoun. Personal pronouns, such as “itself,” “his,” and “they” refer to specific nouns.

Now, let’s look at a GMAT-type sentence which contains an error with a personal pronoun:

Those of the lawmakers opposing the woodland protection bill have only theirselves to blame for the outrage in the local community.

A. Those of the lawmakers opposing the woodland protection bill have only theirselves to blame
B. Those lawmakers, who opposed the woodland protection bill, have only themselves to blame
C. Those of the lawmakers who are opposing the woodland protection bill have only theirselves to blame
D. Those of the lawmakers who are opposing the woodland protection bill have only themself to blame
E. Those lawmakers who opposed the woodland protection bill have only themselves to blame

In this example, answer choice E is correct. The nonword “theirselves” should be replaced with the pronoun “themselves.” Furthermore, choice D uses a more concise phrase to replace the refusing phrase “those of the lawmakers opposing.”

Choices A and C may automatically be ruled out because they contain the nonword “theirselves.” Choice B contains superfluous commas which indicate that the reader should pause at awkward moments. Choice D is incorrect because it uses the singular pronoun “themself” to refer to the plural noun “lawmakers.”

Pronoun-Antecedent Agreement

An antecedent is simply the noun to which a pronoun refers to. As we saw in incorrect answer choice D in the previous section, pronouns should agree with their antecedents. For example, if an antecedent is singular, the pronoun should be singular.

Let’s take a look at a question similar to what you will encounter on the test:

Many successful entrepreneurs throughout history, such as Steve Jobs, are still recognized for his own achievements.

A. Many successful entrepreneurs throughout history, such as Steve Jobs, are still recognized for his own achievements.
B. Many a successful entrepreneur throughout history, such as Steve Jobs, are still recognized for their own achievements.
C. Many successful entrepreneurs throughout history, such as Steve Jobs, is still recognized for his own achievements.
D. Many successful entrepreneurs throughout history, such as Steve Jobs, is still recognized for their own achievements.
E. Many successful entrepreneurs throughout history, such as Steve Jobs, are still recognized for their own achievements.

In this example, choice E is correct because the pronoun “their” appropriately addresses the plural antecedent “entrepreneurs” and well as the singular antecedent “Steve Jobs.”

Choices A and C are incorrect because the pronoun “his” only addresses Steve Jobs.

Choice B is incorrect because “entrepreneurs” becomes singular. Therefore, the plural pronoun “their” is not the correct match.

Choice D would be correct, except that “is” is singular instead of plural and does not agree with the plural antecedents. The error involving “is” also appears in choice C.

Subject-Verb Agreement

Just as pronouns and antecedents should agree, verbs and subjects should agree, too. When a subject is plural, the verb describing its action should also be plural. If a subject is singular, the corresponding verb should also be singular.

Let’s look at some examples in which the subjects and verbs are underlined:

Incorrect: The Senior Vice President, along with a few other executives, were in a meeting on Tuesday.
Correct: The Senior Vice President, along with a few other executives, was in a meeting on Tuesday.

Incorrect: Professionalism, particularly with respect to timeliness and communication, are necessary in order to complete the task.
Correct: Professionalism, particularly with respect to timeliness and communication, is necessary in order to complete the task.

When completing this portion of the test, remember to carefully look for the subject of the sentence. Do not be confused by other nouns in the sentence which may not agree with the actual subject. Identifying the subject first is a great strategy for success!

Misplaced and Dangling Modifiers

A modifier is a word, phrase, or clause that describes another word. Usually, modifiers are adjectives, like “conscientious” or “personable.” Sometimes, a modifier is included in the wrong part of a sentence. Consider this example:

“The live bowl of fish looks great in her office.”

Since the fish are alive and the bowl is not, “live” is a misplaced modifier. You could revise the sentence by moving the modifier:

“The bowl of live fish looks great in her office.”

A dangling modifier is a modifier which does not clearly refer to another word in a sentence. The word that a dangling modifier is meant to describe is missing. Consider this example:

“Set by an arsonist, the firefighters were able to save the burning store.”

We can assume that a fire is what the arsonist set, but let’s try clarifying the sentence:

“The firefighters were able to save the burning store from the fire set by an arsonist.”

Sub-area III: Reading Comprehension

This objective tests your ability to determine the main idea of a passage, to find supporting ideas and details, and to recognize when you are asked for information which is “out of context” and does not resonate with the passage. You should also be able to recognize and describe an author’s tone and viewpoint.

Take a look at some concepts that may appear on the test.


One excellent way to read passages strategically is to make notes as you move through them. Creating this “map” will help you to guide yourself through the passage.

While mapping, note the purpose of each paragraph. Remember to look for major themes. You should record the overall function of the paragraph, not minor details. If you need to refer to details later, you may use your map to find them.

Here is an example of what a passage map might look like. Notice that it is divided into paragraphs and gives only the overarching ideas in each.

¶1 Introduction – zoning conflict
¶2 Argument for new zoning
¶3 Argument against new zoning
¶4 Solutions/compromises
Purpose – Offers solutions related to zoning conflict, compromises suggest favoritism towards individuals against zoning

Note that the map also includes a final section, “Purpose,” which should include the author’s overall message. If you are asked a question about the main idea of the passage, you would refer to your notes for this part of the map.

If you were asked a question about why individuals were against the new zoning, you could refer to your map and immediately know to go to the third paragraph for more details.

Main Idea

Finding the main idea of a text is a crucial skill when reading. You can expect nearly every passage on the Reading Comprehension section of the exam to be accompanied by a question which requires you to identify the main idea.

Finding a central idea or theme in a text is all about getting to the point. As you read, think about the “big picture” created by the details in the text in order to determine the overall message. Is the author trying to make a general statement about life, to explain a major concept, or to argue a point? Before reading the answer choices, summarize the text in your own words. This is also an excellent time to refer back to the passage map you created!

Let’s take a look at an example main idea question. The following passage is an excerpt from Crime: Its Cause and Treatment by Clarence Darrow:

The question of capital punishment has been the subject of endless discussion and will probably never be settled so long as men believe in punishment. Some states have abolished and then reinstated it; some have enjoyed capital punishment for long periods of time and finally prohibited the use of it. The reasons why it cannot be settled are plain. There is first of all no agreement as to the objects of punishment. Next there is no way to determine the results of punishment. If the object is assumed it is a matter of conjecture as to what will be most likely to bring the result. If it could be shown that any form of punishment would bring the immediate result, it would be impossible to show its indirect result although indirect results are as certain as direct ones. Even if all of this could be clearly proven, the world would be no nearer the solution. Questions of this sort, or perhaps of any sort, are not settled by reason; they are settled by prejudices and sentiments or by emotion. When they are settled they do not stay settled, for the emotions change as new stimuli are applied to the machine.

A state may provide for life imprisonment in place of death. Some especially atrocious murder may occur and be fully exploited in the press. Public feeling will be fanned to a flame. Bitter hatred will be aroused against the murderer. It is perfectly obvious to the multitude that if other men had been hanged for murder, this victim would not have been killed. A legislature meets before the hatred has had time to cool and the law is changed. Again, a community may have capital punishment and nothing notable happens. Now and then hangings occur. Juries acquit because of the severity of the penalty. A feeling of shame or some bungling execution may arouse a community against it. A deep-seated doubt may arise as to the guilt of a man who has been put to death. The sentimental people triumph. The law is changed. Nothing has been found out; no question has been settled; science has made no contribution; the public has changed its mind, or, speaking more correctly, has had another emotion and passed another law.

Which of the following options best summarizes the content of the passage?

A. Decisions regarding the punishment of criminals are often based on emotional reactions and punishments often generate further emotional reactions.
B. The criminals responsible for atrocious crimes often elicit intense emotional responses from communities.
C. Members of the public may feel a sense of shame and guilt after severe punishments are inflicted upon criminals.
D. Although laws regarding capital punishment vary by government, people generally feel the same emotional response when presented with the topic.
E. With respect to financial consequences, the execution of a criminal is a lesser burden on a community than the confinement of the individual to lifelong imprisonment.

In this case, options B and C are ideas which may be gathered by the passage. However, they both support a larger idea – the idea which is presented in option A, the correct answer.

Option D is incorrect because it actually states the opposite of the ideas presented in the first four sentences.

Option E is incorrect because it is completely off topic; financial consequences are never addressed in the passage.

When searching for the correct answer choice for a main idea question, seek to eliminate any choices which fall within the following four categories:

  1. Too broad – expands beyond the scope of the passage
  2. Too narrow – focuses on a particular detail or point
  3. Distorted – shows a misunderstanding of the main idea
  4. Irrelevant – indicates ideas which are not addressed in the passage

Supporting Ideas and Details

Supporting ideas and details questions are related to the main idea question type. The main idea drives the whole passage. Therefore, the details mentioned in the passage support its main idea in some form.

Correctly answering a detail question requires you to build upon the skills you need to answer a main idea question; first, you must identify the main idea. Afterwards, you may need to reread part of the passage to identify how the details relate to the main idea. Once again, remember to use your passage map for help!

You can identify detail questions by phrases such as “the role of the third paragraph is…” or “the life cycle of grasshoppers is mentioned because…” Basically, keep an eye out for when you are asked about the purpose of a specific idea or paragraph.

When searching for the correct answer choice for a main idea question, seek to eliminate any choices which fall within the following three categories:

  1. Inference – not directly stated in the passage
  2. Distorted – shows a misunderstanding of the detail or its purpose
  3. Extreme Language – simplified statement about a detail which includes words like “never,” “none,” or “always”


As you reviewed when reading about the Analytical Writing portion of the exam, tone is the author’s attitude towards a subject. The passages on the Reading Comprehension section will not contain, obviously show, or openly state how an author feels.

However, you will still need to identify the authors’ tones on this section of the exam even though the authors’ attitudes will be very subtly expressed.

To discover an author’s tone, you will need to pay careful attention to word choice. This means being aware of the connotation of words.

The denotation of a word is its dictionary definition. Connotation refers to the overtones or associations of a word. To understand connotation, think about how words are often connected with certain emotions.

Let’s look at some examples of specific words which have different connotations though they may share the same denotation.

Evaluating the author’s word choice will help you to answer tone questions such as the following example questions:

The author’s attitude toward capitalism would best be described as which of the following?

Which of the following options best describes the tone of the passage?

Based on the statements in the second paragraph, which of the following could be inferred about the author’s attitude toward the use of fossil fuels?


You can expect to encounter two types of out-of-context questions on the test. Both types of questions will require you to select the answer which best resonates with the author’s main idea.

Let’s take a look at each of the two types of out-of-context questions:

  1. Author’s perspective

These questions will present an idea which is not included in the passage and ask what the author would think about the idea. When answering this question type, you will need to use your skills of determining an author’s perspective.

How would the author of the passage most likely respond to (new theory or assertion)?

Based on the passage, which of the following statements describes how the author would react to (new idea or assertion)?

Which of the following options best describes how the author would most likely respond if presented with (new situation or concept)?

  1. Unrelated situation

Some out-of-context questions will ask you to compare an idea in the passage to a completely different idea or situation. This type of question will be similar to one of the following examples:

Which of the following situations is most similar to the situation described in the passage?

Identify the hypothetical situation that is most comparable to a situation presented in the passage.

Which example is most similar to the example provided in the passage?

Out-of-context questions test your ability to recognize an argument or an idea, and then recognize a similar idea in a different context. The correct answer will be the answer which most clearly resonates with the author’s ideas. Basically, you will make the most logical inference possible in order to come to a conclusion.

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