Sample GRE Multiple Choice Math Problem – Combinations

timcurrycardinalrichelieuOn every GRE Math section, the test makers try to come up with a few extremely difficult problems that will leave even the cleverest students scratching their heads. The really evil part, though, is that even these problems can be solved in under a minute without a calculator – if you know what to do. This means that once you “figure out the trick,” these difficult problems become easy. So, while those test makers are busy cackling with sadistic glee, let’s see if we can’t beat them at their own game.

Consider the following problem:

King Louis XIII must pick a team of 5 musketeers to investigate one of Cardinal Richelieu’s nefarious schemes. If there are 10 musketeers to choose from, what is the probability that four of them (Athos, Porthos, Aramis, and d’Artangan, of course) will be selected?

A) 1/2

B) 1/10

C) 3/5

D) 1/42

E) 5/252

To solve this problem, we must first remember that the probability of any event is calculated by taking the number of desired outcomes over the number of possible outcomes. In this case, figuring out the number of desired outcomes is not too difficult. We know who four of the five musketeers should be, so the only variable is the remaining musketeer. We have already used 4 out of the 10 possible musketeers, so there are 6 possibilities left for the remaining musketeer. If we let P, Q, R, S, T, and U represent the unknown musketeers, then we could represent the desired outcomes like so:

Athos, Porthos, Aramis, d’Artangan, and P

Athos, Porthos, Aramis, d’Artangan, and Q

Athos, Porthos, Aramis, d’Artangan, and R

Athos, Porthos, Aramis, d’Artangan, and S

Athos, Porthos, Aramis, d’Artangan, and T

Athos, Porthos, Aramis, d’Artangan, and U

That leaves figuring out the total number of possible outcomes. You could try to write down all the possible combinations of five musketeers, but with 10 musketeers to choose from that’s going to take a long time, and there would be many opportunities for making mistakes. What we are trying to figure out here is how many possible combinations of 5 musketeers we could make from a group of 10. To calculate this, all we need is a little formula that you might remember from math class:

Where n is the number of items to choose from and r is the number of items to be selected. Combinations and permutations are occasionally tested on the GRE, so you would do well to memorize this formula and other relevant formulas before test day. Using the formula, we find that the total number of ways to select a group of 5 from a group of 10 is:

Thus, the number of desired outcomes over the number of possible outcomes is:

the-three-musketeers-6-1Thus 1/42, choice D, is correct. If you know what to do, it takes only about 30 seconds to solve this problem. So you see, with practice, even the hardest problems on the GRE become easy. Check back here each week for more extra hard problems and the tricks you need to solve them! Also, remember that you can find out all the tricks from experts like me with a Test Masters course or private tutoring. Until  then, keep up the good work and happy studying!

GRE Reading Comprehension Example Problem

In this passage you are presented with an unsupported hypothesis about the use of “wheeled utility vehicles” in 12th century Veracruz; namely, despite the lack of evidence, anthropologists hypothesize that the discovery of “wheeled ceramic toys” might indicate that “wheeled utility vehicles were used to carry materials needed for the monumental structures the Toltec produced.”

As you read through these potential answers, it is important that you determine what this question is actually asking. The passage says there is “no archeological evidence that the Toltec used wheels for anything but toys.” The correct answer must explain why archeologists haven’t found any non-toy wheels, or “wheeled utility vehicles.” Keep this in mind as we review the answers:

(A)   is incorrect. “Sometimes” is a weak word; “sometimes” is not enough to say that the wheel was necessarily one of tools “incorporated into (the Toltec’s) toys representations.” Additionally, this statement does not explain the lack of archaeological evidence for “wheeled utility vehicles.”

(B)   is correct because it offers a valid explanation that is consistent with the anthropologists’ hypothesis and also explains the lack of evidence for that hypothesis.

(C)   is incorrect. A discovery that the toy wheels had uses outside of being toys, such as decoration and sometimes in rituals does not “explain the lack of evidence” for wheeled utility vehicles.

(D)   is incorrect. “Areas outside of Veracruz” have nothing to do with the lack of archaeological evidence in Veracruz; this statement does not explain why no non-toy wheels have been found at Veracruz.

(E)    is incorrect. Again, this answer has nothing to do with the lack of archaeological evidence for non-toy wheels; finding toy wheels in a certain place does not explain the lack of evidence for non-toy wheels.

GRE reading comprehension questions will regularly feature subjects most students are not familiar with; you should expect to see questions relating to archaeology, anthropology, sociology, philosophy, theater, history, and English, as well as biology, physics, math, chemistry, economics, etc. You do not have to be an expert in these fields to answer these questions correctly! Don’t be intimidated by the verbiage or jargon used in these question types. If you feel overwhelmed by the subject matter, rest assured that the GRE is designed for you to be able to answer every question correctly based entirely on the information contained within the passage.

GRE Multiple Choice Math Problem – Speed Trap

Do you know how fast you were going on that problem?

Do you know how fast you were going on that problem?

On every GRE Math section, the test makers try to come up with a few extremely difficult problems that will leave even the cleverest students scratching their heads. The really evil part, though, is that even these problems can be solved in under a minute without a calculator – if you know what to do. This means that once you “figure out the trick,” these difficult problems become easy. So, while those test makers are busy cackling with sadistic glee, let’s see if we can’t beat them at their own game.

Consider the following problem:

If x and y are integers and y < 20, for exactly how many ordered pairs (xy) will x^2 = y?

A) 4

B) 5

C) 7

D) 8

E) 9

This one actually doesn’t seem so bad, does it?

1^2 = 1

2^2 = 4

3^2 = 9

4^2 = 16

5^2 = 25 > 20

So we’ve got (1,1), (2,4), (3,9), and (4,16). Answer choice A, right? Not so fast! You forgot that the square of a negative number is also positive, so for every y, there are two x values: one positive and one negative. So really our list should look like this:

(1,1) and (-1,1)

(2,4) and (-2,4)

(3,9) and (-3,9)

(4,16) and (-4,16)

So the answer is D, right? Wrong again! There’s one last square you forgot:

0^2 = 0

Thus, there are in fact 9 pairs: the eight already mentioned, plus (0,0). Thus, the correct answer is actually choice E.

On the GRE, sometimes slow and steady does win the race.

On the GRE, sometimes slow and steady does win the race.

Was there actually anything hard about this question? Not really. However, if you were going fast and running out of time, you might have easily made one of the careless errors above. Note that 4 and 8 are traps set for students who see this problem, think it’s easy, and then blow through it too fast without thinking carefully (if you forgot the negatives but remembered 0, there’s also choice B, 5). If you get toward the end of a math section and see a problem that looks really easy, be careful – there’s probably more to it than meets the eye. Sometimes it’s just as bad to spend too little time on a problem as it is to spend too much, so make sure you don’t go too fast through any “easy” problems at the end of a math section.

Check back here each week for more problems and the tricks you need to solve them! Also, remember that you can find out all the tricks from experts like me with a Test Masters course or private tutoring. Until  then, keep up the good work and happy studying!

GRE Vocab and the Seven Deadly Sins: Part V – Sloth

An early sixteenth century Dutch depiction of the seven deadly sins, by a follower of Heironymus Bosch.

In this, our latest post in the series GRE Vocab and the Seven Deadly Sins, we now turn to the sin of sloth and its corresponding heavenly virtue, diligence. You have probably heard of the animals known as sloths, most famously the Amazonian three-toed sloth, which moves so slowly that algae grows on its back. These creatures were actually named after the sin of sloth, which is most commonly construed as the sin of laziness; because sloths move so slowly, they were thought to be the very embodiment of this sin (even if moving is actually hard work if you’re a sloth). The word “sloth” itself derives from the Old English slowth, from which the word slow is also derived. A person guilty of the sin of sloth can be described as slothful. In Latin, however, this sin has changed names throughout its history, reflecting the changing interpretation of this sin in Catholic theology.

Originally, the sin of sloth was known as acedia and was defined as a kind of depression-like apathy that manifested itself as extreme inaction. It sometimes plagued ascetic monks and nuns, especially those who had taken vows of silence. Acedia was seen as a sin because it was believed to be a rejection of god’s gift of life and a failure to appreciate the goodness of life. In this sense, it might be appropriate to mention the word melancholy as being related to the sin of sloth. Over time, acedia was replaced by socordia, which focused more on physical and spiritual laziness, and the failure to make use of one’s god-given talents and abilities. Either way, the sin of sloth is unique among the seven deadly sins because it is the only sin defined by a lack of good actions rather than by the committing of bad actions: you can (and will) commit the sin of sloth by doing nothing at all.

You may be familiar with the animal species known as sloths, such as this rather contented looking three-toed one.

There are many excellent potential GRE vocab words in the English language that have to do with the sin of sloth, such as indolent, lackadaisical, languid, lethargic, supine, torpid, lassitude, oscitancy, sluggard, apathy, melancholy. The word indolent, for instance, means having or showing a disposition to avoid exertion, and derives from the Latin prefix in- and the verb dolere, which means to be painful. Someone indolent, or given to indolence, would act as if even thinking about hard work were extremely painful, and would thus be very slothful..

The word lackadaisical has a rather interesting etymology; it derives from the word “lackaday,” which is a corruption of the obsolete English phrase “alack the day,” an expression of regret, sorrow, dismay, or disapproval. Alack itself is derived from the English word alas, which comes from the Latin lassus, meaning weary. Today, lackadaisical means without interest, vigor, or determination – someone lackadaisical would act as if they were too tired or weary to put much effort into anything. Another word which derives from lassus is lassitude, which means weariness of body or mind, resulting in a lack of energy. It can also refer to a condition of indolent indifference, though, and thus laziness.

A figure from the church of St. Moritz in Rottenberg.

Similarly, languid, means lacking in vigor or vitality, and a related verb, languish, means to weaken, lose vigor and vitality, or undergo neglect. Interestingly, languid and languish derive from the Latin verb languere, to be faint or weak, which is related to the Latin adjective laxus, which means loose or relaxed. Languor is a similarly derived noun meaning lack of energy or vitality; sluggishness. Languor and languish came to English from French in the late 1200s, but languid was a later addition that came straight from Latin in the 1590s.

Lethargic is the adjective form of the noun lethargy, which is the quality of being drowsy, dull, or unenergetic. Lethargy comes from the Latin noun with the same meaning lethargia, which in turns derives from the Greek words lethe and algia. You may recall that Lethe was one of the five rivers which flowed through the underworld in classical mythology. Souls that drank the waters of the Lethe were granted complete forgetfulness of their past lives, which makes sense, since the Anicent Greek word lethe itself means forgetfulness or oblivion. Algia comes from the Greek word algos, which means pain. Lethargy was thus an unpleasant or painful drowsiness or lack of energy that dulled the mind and resulted in inaction through forgetfulness.

A detail from Breugel’s 1566 painting, Harvesters.

The adjective supine commonly refers to someone or something lying on its back while prone refers to something or someone lying on its front with its back in the air. Indeed, the word supine entered the English language in the 1490s directly from Latin, deriving from the adjective supinum, which means lying on the back or facing up. However, supine can also mean exhibiting inactivity or passivity. Someone supine, or lazy, would thus often be supine, or lying on his or her back all the time.

Torpid derives from the Latin torpere, which means to numb or stiffen (perhaps like a corpse exhibiting rigor mortis). It entered English directly from Latin in the early 1600s, and came to mean inactive, sluggish, or lethargic; presumably something numb and stiff would be inactive, so the evolution in meaning makes some sense. More interesting, perhaps, is the evolution of its etymological cousin, the word torpedo. Originally, in the 1520s, natural philosophers used the Latin root to invent the word torpedo as a name for electric rays and eels, because if you grabbed one, it would shock you and leave your hand stiff and numb. During the late 18th century, and especially during the French revolution that began in 1789 and the subsequent Napoleonic wars, a new maritime weapon was invented: floating mines called “torpedoes” after the electric fishes. Over time, these weapons developed into the underwater projectile explosives that we know as torpedoes today.

The dragon Fafner from Wagner’s opera Siegfried, as imagined by Arthur Rackham.

Oscitancy, or oscitance, refers to yawning, and derives from the synonymous Latin verb oscitare, which derives from the Latin os (mouth) and citare (to move or put in motion). Oscitancy and oscitance have also come to be associated with laziness and inattentiveness, since someone who yawns a lot might be prone to laziness. The adjective form would be oscitant, as in, “The knight caught a glimpse of the dragon’s long, gleaming fangs as it closed its oscitant maw.”

Sluggard is an old English word that dates back to the 1300s, when it was spelled slogarde. Before that it probably had a Scandinavian origin, as comparisons with the Norwegian word sluggje, which means a heavy or slow person, suggest. Similarly, in modern English a sluggard is a person who is habitually inactive or lazy. Sluggard is also related to the word sluggish, which means indisposed to action or exertion or lacking energy. Both sluggard and sluggish are related to the root word slug, which describes a snail-like gastropod with no shell that moves just as slowly as its shelled counterpart.

Come on, seriously?

Apathy is the absence or suppression of feeling, emotion, or excitement, and someone experiencing apathy can be called apathetic. Apathy derives from Ancient Greek, and is composed of the prefix a-, meaning without, and pathos, meaning feeling, specifically passion and suffering. Apathy thus literally refers to a lack of feeling. The English word pathos refers to the quality of art or expression that evokes a feeling of pity or compassion. The Greek pathos, when combined with prefixes and suffixes, has many different derivatives: antipathy, which means aversion or dislike; sympathy, which is harmony or agreement in feeling, especially sorrow; pathetic, which means causing or evoking pity or feelings; empathy, the act of understanding and then vicariously  experiencing another’s emotions or feelings; pathogen, a disease-causing agent (literally from the Greek pathos and gen, meaning something that causes suffering); pathology, the study of diseases. A psychopath is a person who displays amoral and antisocial behavior, lack of ability to love or establish meaningful personal relationships, and extreme egocentricity (from Greek psyche, soul, and path, pain, literally suffering soul).

The Iron Foundry by Adolph Menzel.

Enough of all this sloth – what we need is some diligence! According to the Catholic church, diligence is the heavenly virtue meant to combat the sin of sloth, since it entails steady, productive use of one’s time. Its Latin name is industria, from which we get the English words industry and industrious, which means hard-working. The word diligence is derived from the Latin verb diligere, which is in turn derived from the prefix dis-, which means apart, and the verb legere, which means “to choose” or “to read,” so that diligere means “to choose apart” or to prefer something. This evolved into our contemporary meaning by the following logic: if you prefer something, you like it a lot; if you like it a lot, you will take great care with it; if you are careful with something, then maybe you will put steady effort into looking after it; steady effort or work then became the accepted definition and the original meaning was forgotten.

The Gleaners, by Jean Francois Millet.

Two potential GRE words that have to do with the virtue of diligence include assiduous and sedulous. Assiduous comes from the Latin verb assidere, which means “to sit down,” which was the root of the Latin word assiduus, which has the meaning of constantly working, the logic being that you were sitting down to work. After entering English direct from Latin in the 1530s, it came to mean constant in application or effort, working diligently at a task, persevering, industrious, and attentive. Sedulous also entered the English language in the 1530s direct from the Latin word sedolo, which means honest or without deception. In English, it means diligent in application or attention, persevering, and assiduous, perhaps for the same reasons we talk about “an honest day’s work.”

That’s enough for today. Next time, we move on to the sin of envy. Remember, if you want extra help getting ready for the GRE, you can study with experts like me through Test Masters. Until next time, happy studying!

Ask Test Masters – Admission to a Top 10 Graduate School

Information technology

The Information Technology logo (according to Wiki Commons).

Ask Test Masters is a free information service offered by the GRE and graduate school admission experts at Test Masters. Reader MSAspirant asks,

“Dear Test Masters, I have a score of 319 (160 Q, 159 V, 4.5 AWA) on my second attempt. On my first attempt I had a 314(159 Q, 155 V, 4.0 AWA). I have an experience of 7.5 years in Information Technology and was looking to get into a top 10 school for MS. I am a bit worried about my Quant scores. Can you please throw some light as to whether they are good enough? Should I reattempt [the] GRE or can I just focus on my SOP and Recommendation Letters.”

Dear MSAspirant,

I would first recommend consulting this article: What is a good score on the GRE? Pay close attention to the second table listed in this article. This table (reproduced below) shows the average Verbal and Quantitative scores by intended graduate school program.

Data taken from Tables 6 & 7 of GRE Snapshot Report.

Without more information, based what you’ve provided in your question, we assume that by MS you are referring to obtaining a Master of Science in Information Technology. Information Technology degrees typically include a core curriculum of business and computer science courses; however, for the purpose of answering your question (i.e. is your score good enough for a top 10 graduate school), we can categorize your intended graduate program under “engineering” (because the average scores for engineering students most closely resemble the average scores for computer science graduate students).

If you review the article linked above, there is a fairly thorough explanation as to what constitutes a “good” score on the GRE. Essentially, whether a GRE score is good or not is entirely relative to the goals of the individual. You have clear goals – be accepted into a top 10 graduate program and earn an MS; for just a moment though, let’s set your stated goals aside.

Objectively, you have an excellent GRE score. Can it be improved upon? Certainly, but it is a very good score nonetheless. For the purpose of comparison, the average GRE score is a 302.8 (152.2 Q, 150.6 V, 3.5 AWA). Your score is well above this average. Also, in case you are unaware, you may also utilize something known as ScoreSelect to ensure that the graduate institution(s) you apply to sees only the higher of your two scores, or three scores should you decide to take the GRE again.

Returning to your stated goal – admission to a top 10 university – there is no better institution to use for comparison than Harvard University. Please take a moment to review the table below, which outlines several important averages for both Master’s and PH.D. students admitted to Harvard. (Note: Data taken from Harvard Grad Data Page.)

Quant. Verbal AWA Cumulative GPA
Master’s 163 160 4.5 3.60
PH.D. 165 161 4.3 3.84

You can see that the average GRE scores for Master’s students accepted to Harvard are (163 Q, 160 V, 4.5 AWA). This puts you just at, but slightly below, the average scores of students accepted to Harvard. That is very good! Is it good enough? Maybe. Keep in mind these are average scores; some students were accepted with higher scores and others were probably accepted with lower scores.

If you really are targeting a top 10 university then you are correct to be slightly concerned with your quantitative score as it is several points below the average; however, this won’t immediately disqualify you from admission. Whether you should take the GRE again should revolve around several factors, but the two most important questions you should ask yourself are:

1)      Do I feel like I can improve my score?

2)      How would retaking the GRE fit into my current timetable?

You were able to improve your quantitative score by only one point the last time you took the GRE. Did you do any test preparation between your first exam and your second exam? If you did not, it might be worth taking the exam again as proper preparation could lead to significant score gains. If you did prepare in what you consider a sufficient amount and only achieved a marginal score increase, then it might be less worthwhile to put in the time, energy, and cost associated with preparing for and taking the GRE again.

You should also be mindful of how taking the GRE again might fit into your overall admission timetable. If you do decide to take the GRE again, you should certainly prepare for it. This means that you will have that much less time to devote towards the other aspects of your application, which (as you mentioned) include your Statement of Purpose and Letters of Recommendation, among other things. Take a look at the application deadlines of the various institutions you plan on applying to, and keep those deadlines in mind.

Your scores are good and your previous experience in the field should help as well; all of this combined should make you a competitive applicant, as is, to any university (provided you have the corresponding GPA as well). My advice is, unless you feel like you can really improve your quantitative score with preparation, to begin focusing on the other aspects of your application.

Hope this helps!

Ask-Test-Masters

Have a question? Ask the experts at Test Masters!

Have more questions? Feel free to comment below or Ask Test Masters directly! You can see previous questions here; who knows, maybe your question has already been answered.

GRE Multiple Choice Math Problem – Prime Factorization

Math problems that appear hard but are secretly easy? Most excellent!

Math problems that appear hard but are secretly easy? Most excellent!

On every GRE Math section, the test makers try to come up with a few extremely difficult problems that will leave even the cleverest students scratching their heads. The really evil part, though, is that even these problems can be solved in under a minute without a calculator – if you know what to do. This means that once you “figure out the trick,” these difficult problems become easy. So, while those test makers are busy cackling with sadistic glee, let’s see if we can’t beat them at their own game.

Consider the following brain teaser:

What is the least common multiple of 18 and 14 that is also a perfect square?

A simple enough question. But how do you figure it out? Could we just multiply 18 by 14?

18*14 = 252

That’s definitely a common multiple of 18 and 14, but is it a perfect square?

252^(1/2) = 15.87450787…

Should’ve known it wouldn’t be that easy. This IS a hard problem after all. Maybe we should multiply 18^2 by 14^2:

(18^2)*(14^2) = 63504

Well, that works, but is it the LEAST common multiple? Don’t look at me! How should I know? Hmm…something tells me it probably isn’t. Maybe we could just go through the multiples of 18 trial and error style?

1*18 = 18. Not divisible by 14, not a perfect square.

2*18 = 36. It is a perfect square, but not divisible by 14.

3*18 = 54. Not divisible by 14, not a perfect square.

4*18 =

Time is running out, my pretty!

Time is running out, my pretty!

This is clearly going to take too long. We’re running out of time on this section – whatever shall we do? Never fear – prime factorization is here! Remember, all GRE math problems can be solved in under a minute without a calculator. If you know what to do, hard problems like this one become fast and easy. In this case, we should begin by finding the prime factors of both 18 and 14:

18 = 9*2 = 3*3*2

14 = 7*2

Remember, to find the prime factors of a number means to write out the numbers as products of only prime numbers like 2, 3, 5, 7, 11, 13, etc. In this case, the prime factors of 18 are 3, 3, and 2, and the prime factors of 14 are just 7 and 2. Now, if we just wanted to find the least common multiple of 18 and 14, we would multiply all the prime factors of 18 by all the prime factors of 14, but leave out any duplicates that appear in both lists. In this case you would multiply:

3*3*2*7 = 126

This works, because

(3*3*2)*7 = (18)*7 = 126

3*3*(2*7) = 3*3*(14) = 126

Note that you need only one 2 in 3*3*2*7, since both the prime factors of 18 (3*3*2) and 14 (7*2) include a 2. This is all well and good, except that 126 is not a perfect square:

126^(1/2) = 11.22497216…

So, what are we to do? Note that a perfect square multiplied by a perfect square is also a perfect square:

4*25 = 100

This means that we can pair up all of the unique prime factors of 126 so that we have a bunch of squares multiplied by each other. Thus,

3*3*2*7 = 126

becomes

(3*3)*(2*2)*(7*7) = 1764

We have to add an extra 2 and an extra 7 in order to make sure those numbers are part of perfect square pairs (we don’t need to add any extra 3s because there are already two of them). Sure enough, 1764 is a perfect square:

1764^(1/2) = 42

and 1764 is a multiple of both 18 and 14:

1764/18 = 98

1764/14 = 126

But, how can we be 100% sure that 1764 is the least common multiple? Well, think about it. Every perfect square that isn’t the square of a prime number will always be prime factorized into pairs like the ones above ((3*3)*(2*2)*(7*7) = 1764). Consider the following examples:

16 = 4*4 = (2*2)*(2*2)

36 = 6*6 = (3*2)*(3*2) = (3*3)*(2*2)

144 = 12*12 = (3*2*2)*(3*2*2) = (3*3)*(2*2)*(2*2)

You may have figured out this problem, but I'll get you next time! Next time!

You may have figured out this problem, but I’ll get you next time! Next time!

 

Et cetera. It’s inevitable. If the prime factors of a perfect square aren’t two prime numbers, then they will consist of multiple pairs of other prime numbers. Now, is there any way we could remove any pairs or make any of these factors smaller without breaking the conditions of finding the least common multiple of 18 and 14 that is also a perfect square?

(3*3)*(2*2)*(7*7) = 1764

I don’t think so. Remove or change one number and the product will either no longer be a perfect square or no longer be a multiple of both 18 and 14. Thus, 1764 must be the least common multiple of both 18 and 14 that is also a perfect square.

To sum up, the “trick” to solving a problem like this is to:

-find the prime factors of the two numbers in question

-pair them up

-multiply

If you know what to do, it takes about 30 seconds to solve this problem. So you see, with practice, even the hardest problems on the GRE become easy. Check back here each week for more extra hard problems and the tricks you need to solve them! Also, remember that you can find out all the tricks from experts like me with a Test Masters course or private tutoring. Until  then, keep up the good work and happy studying!

Sometimes it is GREek: Paroxysm

Paroxysms

An exploding volcano is a literal example of a paroxysm.

“Sometimes it is GREek!” is a series dedicated to examining words likely to appear on the GRE.  We aim not only to give you a new word to memorize, but also to provide you with some background and etymological history to help you remember it. At the end of the post, we will also give you a sentence with a few other new words to add to your flash cards. By following this series, you should be more prepared than ever to tackle the sentence completion, sentence equivalencies, and reading comprehension questions on test day.

This Week’s Word: Paroxysm

From the Greek paroxysmos, meaning “irritation, or exasperation,” a paroxysm is a sudden outburst of emotion or action. Paroxysm is also used in the medical field to denote a sudden attack, recurrence, or intensification of a disease, and can also refer to a spasm or convulsion.

Paroxysm is not limited to referring solely to human emotions, actions or physiology. In fact, many authors have used paroxysm to describe turbulent or explosive occurrences in a wide range of areas, from volcanic activity and plate tectonics to corporate restructuring:

“Volcanic action is essentially paroxysmal; yet Mr. Lyell will admit no greater paroxysms than we ourselves have witnessed—no periods of feverish spasmodic energy, during which the very framework of nature has been convulsed and torn asunder.” — Adam Sedgwich, Address to the Geological Society on 2/18/1831 (quote taken from Today in Science History).

“Then, in the 1980′s, came the paroxysm of downsizing, and the very nature of the corporation was thrown into doubt. In what began almost as a fad and quickly matured into an unshakable habit, companies were ‘restructuring,’ ‘reengineering,’ and generally cutting as many jobs as possible, white collar as well as blue . . . “ – Barbara Ehreneich, Bright-Sided: How the Relentless Promotion of Positive Thinking Has Undermined America

Paroxysm is often used idiomatically; to use paroxysm idiomatically, you would say you are having a “paroxysm of [insert feeling, action or occurrence].” One example of this can be found in the Barbara Ehreneich quote above.  

It is also important to note, as is the case in the first quotation above, that when paroxysm is not being used idiomatically, it is often being used literally. So when Adam Sedgwick says “Volcanic action is essentially paroxysmal,” he means that volcanic activity literally causes the earth to shake.

Sample Sentence:

Pleasing Peter’s palate, perfect pumpkin pies prompted Peter’s passionate paroxysms.  

Miss the last “Sometimes it is Greek?” Check it out here. Want more GRE vocabulary? Click here for the free TestMasters GRE vocabulary list with over 2,000 words!

GRE Vocab and the Seven Deadly Sins: Part IV – Wrath

An early sixteenth century Dutch depiction of the seven deadly sins, by a follower of Heironymus Bosch.

This week we turn from some of the more fun sins like lust and gluttony to a more violent one: wrath. In Catholicism, wrath is defined as immoderate or uncontrolled anger or hatred. In his famous Inferno, the first part of his Divine Comedy, Dante splits wrathful sinners into two rivers: the merely angry swim about in the river Styx while being periodically poked by demons with pointy pitchforks, while the more violent ones are simmering in the river Phlegethon, which courses with boiling blood (and also has demons). There are many excellent potential GRE vocab words that have to do with the sin of wrath, including: conniption, ire, choler, irascibility, ferocity, rampant/rampage, rabid, furor, and livid.

The word conniption is something of an etymological mystery. It first emerged in American English between 1825 and 1835 (the John Quincy Adams/Andrew Jackson years), and no one is quite sure where it came from, although a number of theories have been proposed. It could be: an arbitrary pseudo-Latin sounding word meant to sound fancier than it really is; a derivative of ‘corruption,’ which was apparently used to mean anger in certain early 19th century American dialects; or, my personal favorite, a derivative of the English dialectical “canapshus,” which was probably a corruption of the word captious, which means “apt to notice and make much of trivial faults or defects; faultfinding; difficult to please” and derives from the Latin captiosus, which means sophistical. Anyway, a conniption, or a conniption fit, is a fit of hysterical excitement or anger, as in, “Don’t have a conniption fit, man! Chill out!”

One of Leonardo da Vinci’s studies for the now lost “Battle of Anghiari.”

Choler refers to irascibility, anger, wrath, or irritability in general. It can also refer to yellow bile. To find out how these two meanings are related, read my previous post on Medieval Medicine and GRE Vocab. Ferocity,  or the quality of being ferocious,  refers to “savage fierceness,” and derives from the synonymous Latin word ferocitas. It first entered the English language around 1600-1610.

Ire, rage, and fury are three words that are often used as synonyms, but they actually have subtle differences in meaning. According to thesaurus.com, ire  suggests greater intensity than anger, rage  suggests loss of self-control, and fury  is destructive rage verging on madness. The word ire came to English from Latin by way of Old French in the 1200s and derives from the synonymous Latin word ira, as in Dies irae, or “day of wrath,” a famous part of the requiem mass, or the Catholic mass for the dead, which describes judgement day, the climax of the apocalypse. Here’s Verdi’s famous setting:

Ira is actually the Latin word the Catholic church uses to describe the sin of wrath. Irascible, which means easily angered, and irate, which means very angry, are also derived from ira. Rage also came to English from Latin by way of French around the same time as ire. It is derived from the Latin word rabies, meaning madness or rage. As you might have guessed, rage is a paronym of rabies, the disease. While the word rabid can literally refer to someone or something who has rabies, it also retains its older meaning of furious or raging. Remember, the GRE likes to test the unfamiliar definitions of familiar words, so take note! Fury of course comes from the ancient Roman goddesses of vengeance, the Furies, or Furiae, who would punish and pursue those who committed crimes in the eyes of the gods. It came to English direct from Latin in the mid-fourteenth century. The word furor, which means fury, rage or madness, has a similar derivation and came to English about a century later.

Peter Paul Rubens’ copy of Leonardo da Vinci’s now lost “Battle of Anghiari.”

Rampage and rampant are two other related words that have to do with wrath. As you might have been able to guess from their -age and -ant endings, these words are derived from French, specifically the verb ramper, which means ‘to rear up on one’s hind legs.’ Generally, when animals rear up on their hind legs, they are not happy. Rampant can thus mean violent in action or spirit, raging, or furious, and a rampage is a state of violent anger or agitation characterized by wanton destruction. Rampant has also come to mean unchecked or widespread, as in, say, ‘rampant corruption.’

The word livid entered English around the 1620s, coming straight from the Latin word lividus, which means ‘black and blue.’ Today, livid has come to have several meanings, which I have arranged in an order that suggests how the meanings may have evolved. Livid means: dull blue or dark, grayish-blue; having a discolored, bluish appearance caused by a bruise, congestion of blood vessels, strangulation; feeling or appearing strangulated because of strong emotion (especially anger); enraged or furiously angry; reddish or flushed; or even deathly pale, pallid, or ashen. Thus, because it has developed this emotionally charged meaning, livid can now mean red, white, or blue.

An allegorical depiction of Patience by Hans Sebald Beham, 1540.

So, with all this anger in the world, what’s a poor, lost soul to do? Cultivate the heavenly virtue of patience. In Catholic theology, patience is not merely the ability to wait for something; it is the ability to restrain one’s violent impulses and to understand the point of view of others. Patience is thus seen as the ultimate weapon in the fight against wrath. The word patience is derived from the synonymous Latin word patientia. A number of good GRE vocab words relating to patience include: ataraxy/ataraxia, equanimity, clemency, and forbearance.

Ataraxy, or ataraxia, is a state of freedom from emotional disturbance and anxiety, or tranquility. It derives from the ancient Greek word ataraktos, which means untroubled (the verb tarassein means ‘to trouble,’ and the prefix a- in Greek means without). It was the goal of several ancient philosophies – Epicureanism, for instance. Attaining a state of ataraxia required great patience, since you couldn’t let the little things in life get to you. Equanimity refers to mental or emotional stability or composure, especially under tension or strain. It derives from the Latin aequanimitas, which is a combination of aequs, which means equal or even, and animus, which means spirit, soul, or mind. It entered English at the same time as ferocity, in the 1600s, and ataraxia first began showing up around five years before that.

Clemency means forgiveness or leniency, and a person who shows clemency is said to be clement. That’s why Popes sometimes like to take the name Clement – Clementine is the feminine version of the name, as in the song “Oh my darlin’ Clementine”:

Inclement weather” is thus unmerciful weather. Clemency is derived from the Latin clementia, and it entered late Middle English/Anglo-French in the late fourteenth century. Forbearance, which also refers to patient endurance or self-control, is a quality you may have needed in order to have made it this far into this post. The verb, to forbear, is a very old English word (before 900 AD – I don’t think people wrote anything in English before then), that derives from the Old English forberan, which is related to the Gothic (as in the Goths who helped destroy the Roman empire) frabairan.

That’s enough for today, I think. Always remember that if you want even more help preparing for the GRE, you can study with experts like me through Test Masters. Which sin could be next? Sloth? Envy? Pride? You’ll just have to wait and see. Until then, keep studying!