this week's MGRE Math Beast Challenge problem

From here:




My answer will appear in the comments, but I'll tell you right now that I don't like the way this problem's been structured. As it's worded, I'd say the answer is "cannot be determined." Why? A couple reasons:

1. We can assume the figure isn't drawn to scale. The only "given" is that the round figure is indeed a circle with its center labeled. We can also safely assume that Points A, C, and D are all on the circle. It's also safe to assume that Point B is on the circle as well. Beyond that, what do we know for sure?

2. We can't assume-- since the problem doesn't specify this-- that the squarish-looking figure is indeed a square, which means we can't assume that the circle is properly inscribed within a square.

3. We also can't assume that Segment GF forms a 180-degree angle with the bottom of the putative square.

For those reasons, I think "cannot be determined" is the best answer, but I'm going to ignore the above concerns and charitably assume that the circle is inscribed in a square, thus making Point B the midpoint of that side of the square. With those assumptions in place, I believe the problem is easily soluble. Without them, however, "cannot be determined" is the only legitimate answer.

Here's how I would have presented the problem, so as to avoid any confusion about what we can and can't assume:



I'll be basing my answer off the above image, not off MGRE's.


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yes! I never tire of being right!

I always get this nerdy feeling of accomplishment when I manage to get a Manhattan GRE Math Beast Challenge problem correct. My answer to last week's challenge was 17.473 (see the comments), and that's the correct answer. MGRE's explanation:

A ratio of one value to another value should not have units (i.e. we should not need to specify a currency unit, such as dollars), as both values can be expressed in terms of dollars and the units should cancel. However, both face value and intrinsic value must be expressed in terms of the same currency; Australian dollar unit doesn’t cancel the U.S. dollar unit. We’ll use USD to signify U.S. dollars and AUD to signify Australian dollars.

Putting both values in terms of U.S. dollars:
Intrinsic value = (1 troy ounce of gold)(1775.30 USD/troy ounce of gold) = 1775.30 USD
Face Value = (100 AUD)(1.016 USD/1 AUD) = 101.60 USD
Ratio = Intrinsic/Face = 1775.30/101.60 = 17.4734252 {Use the calculator!}

Rounded to three decimal places, the correct answer is 17.473.

On any problem that requires converting from one unit of measure to another, first think about what we want to cancel. When converting from AUD to USD, we want to cancel AUD units out. Therefore, multiply by a term that has AUD in the denominator. But we must always multiply by 1, or else we’ll change the value, so the top and bottom of any fraction multipliers must be equal. We were told that 1 AUD = 1.016 USD, so (1.016 USD/1 AUD) equals 1 and also serves to cancel the AUD units in the face value calculation above.

Not to be currency biased, we could have solved in terms of AUD:
Intrinsic value = (1 troy ounce)(1775.30 USD/troy ounce)(1 AUD/1.016 USD) = 1747.34252 AUD {Use the calculator!}
Face Value = 100 AUD
Ratio = Intrinsic/Face = 1747.34252/100 = 17.4734252

Rounded to three decimal places, the correct answer is 17.473.

Woo-hoo!

You know... if you've been ignoring these math problems when I put them up every Tuesday, I really encourage you to try them. Are you afraid to be wrong? What silliness! We don't learn by avoiding risks! And hell, I'm taking as much of a risk as any of you, since I don't know the official answer to any given problem until the following week.

So what's holding you back? Give these problems a try!


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if you don't concentrate, you won't succeed

Concentration-- focus-- is one of the major themes of this blog. If you can't, don't, or won't concentrate, you won't succeed. While I'm talking primarily about test prep (because today, Monday, is test prep day), this wisdom applies to everything you do in life. Without concentration, without seriousness of mind, without earnest mental effort to avoid distraction and to narrow your focus, failure is nearly assured.

Some of you might think you can skate by on talent. I admit that that's possible: some truly talented people are lucky enough to be able to grasp new concepts and new actions with very little effort. But even such people are eventually going to hit a wall if they have any desire to better themselves. What should they do then? Rest on their laurels? Or should they push themselves even further? Meanwhile, we denizens of the fat part of the bell curve can't afford to pretend we're that talented.

Don't assume you're the noble exception. In all likelihood, you aren't. You may think you're more talented than 99% of the populace, but if I stuck you in a room with equally talented peers, you'd realize that, as special as you are, you really aren't that special. Does that depress you? Far from being discouraged, you should view that state of affairs as a challenge. Ask yourself: what can I do to make myself better? What skills do I need to hone to succeed at a given task? Instead of constantly heaping undeserved praise upon yourself for accomplishing minor tasks that everyone else accomplishes from day to day, ask yourself-- what more can I do? And remember that pushing yourself isn't merely about besting your peers: it's about setting high standards for yourself.

All of that begins with focus. Without it, we're nothing. Keep that in mind whenever you're tempted to turn aside from your studies in order to watch TV or tab over to YouTube or grab your smart phone for the hundredth time that hour.


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monkey mind and quiet mind

Chuang Tzu Story - Three in the Morning

What is this three in the morning?

It is about a monkey trainer
Who went to his monkeys and told them:
“As regards your chestnuts,
you are going to have three measures in the morning,
and four in the afternoon.”

On hearing this, all the monkeys became angry.
So the keeper said:
“All right, then--
I will change it
To four measures in the morning
and three in the afternoon.”
The animals were satisfied with this arrangement.

The two arrangements were the same--
The number of chestnuts did not change,
But in one case the monkeys were displeased,
and in the other case they were satisfied.

The keeper was willing
To change his personal arrangement
In order to meet objective conditions.
He lost nothing by it.

The truly wise man,
Considers both sides of the question
Without partiality,
Sees them both in the light of Tao.
This is called following two courses at once.

(this version of the story found here, and edited for style)


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article sur la présidentielle en France

Un article de L'Express sur la candidature de François Hollande du Parti Socialiste (PS), aussi bien que les autres candidats:

Le candidat PS à l'élection présidentielle atteint 31% des intentions de vote, contre 25% pour le président, selon une étude CSA pour BFMTV, 20 Minutes et RMC.

François Hollande recueille 31% des intentions de vote au premier tour de la présidentielle, contre 25% pour Nicolas Sarkozy, selon un sondage CSA pour BFMTV, 20 Minutes et RMC. Le candidat socialiste a gagné deux points depuis la précédente enquête des 9 et 10 janvier tandis que le chef de l'Etat sortant en cède 1.

François Bayrou est en hausse de deux points (15%) et se rapproche de Marine Le Pen, qui en perd deux (17%).

Jean-Luc Mélenchon (9%) progresse de deux points.

Loin derrière suivent Eva Joly (2%, inchangé), Dominique de Villepin (1%, -2 points), Nathalie Arthaud, Philippe Poutou, Jean-Pierre Chevènement, Corinne Lepage, Hervé Morin, Christine Boutin et Nicolas Dupont-Aignan, moins de 0,5% des voix chacun.

Au second tour, François Hollande l'emporterait par 60% des voix, en hausse de 3 points en deux semaines, contre 40% pour Nicolas Sarkozy (-3). 43% des personnes interrogées prévoient la victoire de François Hollande, 23% celle de Nicolas Sarkozy, et 22% celle d'un autre candidat. 12% ne se prononcent pas.

"Une bonne campagne" pour 60% des Français

Par ailleurs, selon ce sondage effectué au lendemain du discours du Bourget, 60% des Français jugent que le candidat socialiste fait une "bonne campagne", 32% répondant une "mauvaise campagne".

En termes de crédibilité, il est le plus convaincant quand il parle de la réduction des inégalités sociales (52%), puis l'école et l'éducation (46%), la sécurité, et les problèmes des gens (41% ex-aequo). Concernant ses propositions, le retrait des troupes d'Afghanistan d'ici fin 2012 reçoit 84% d'opinions favorables. La création d'une tranche d'impôts supplémentaire pour les plus aisés et l'obligation pour les banques de séparer opérations de crédit et spéculation sont également largement approuvées (79% d'opinions favorables chacune).

Seule l'instauration du droit de vote des étrangers aux élections locales est majoritairement refusée avec 57% d'opinions défavorables (40% de favorables).

L'intérêt pour la campagne est en hausse, 73% des Français se déclarant intéressés, en hausse de 7 points par rapport à la précédente enquête.

Questions de compréhension:

1. Selon le sondage CSA cité, les Français favorisent-ils M. Hollande ou Nicolas Sarkozy?

2. Les Français s'intéressent à la présidentielle ou non?

3. Le public n'est pas d'accord avec M. Hollande concernant quel point?

4. Sur quel sujet M. Hollande est-il le plus convaincant?


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strange sentences

What do you make of the following sentences?

1. This sentence is false.

What's the truth value of the above sentence? If the sentence is false, then it's true that the sentence is false, which makes the sentence true. But if the sentence is true, then that truth contradicts the literal import of the sentence... which makes the sentence false! You could blow your mind if you think about this too hard.


2. Police police police police police.

Yes, this is an actual sentence. Can you make sense of it? (With thanks to Malcolm.)


3. Colorless green ideas sleep furiously.

This is a classic example, often used in linguistics, of how a sentence can be grammatically correct and yet be total nonsense.


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this week's MGRE Math Beast Challenge

From here:



Go to it! My answer will appear in the comments.


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MGRE Math Beast Challenge: another one right!

You'll recall last week's MGRE Math Beast Challenge. It turns out my solution (posted in the comments last week) was indeed correct. Here's the official MGRE answer:







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SAT: tone of passage

I have some students who are occasionally confused by "tone of passage" questions in the SAT I's Critical Reading section. I've just stumbled upon a decent resource that takes you through the thinking process for one passage. Give it a look. Be careful: the article is actually four pages long, so you'll need to click the page numbers just below the first part of the article to see the rest. After you've read the article, come back here and try your hand at determining the tone of the following passages. To see the correct answer, along with an explanation, highlight the bracketed space.


Passage 1 (from here):

[NB: The UK author of this piece is examining Arnold Trehub's theory of consciousness.]

What about the self, then? It’s natural that given Trehub’s spatial perspective he should focus on defining the location of the self, but that only seems to be a small, almost incidental part of our sense of self. Personally, I’m inclined to put the thoughts first, and then identify myself as their origin; I identify myself not by location but by a kind of backward extrapolation to the abstract-seeming origin of my mental activity. This has nothing to do with physical space. Of course Trehub’s system has more to it than mere location, in the special tokens used to signify belonging to me and truth. But this part of the theory seems especially problematic. Why should simply flagging a spatial position and some propositions as mine endow a set of neurons with a sense of selfhood, any more than flagging them as Fred’s? I can easily imagine that location and the same set of propositions being someone else’s, or no-one’s. I think Trehub means that linking up the tokens in this way causes me to view that location as mine and those propositions as my beliefs, but notice that in saying that I’m smuggling in a self who has views about things and a capacity for ownership; I’ve inadvertently and unconsciously brought in that wretched homunculus after all. For that matter, why would flagging a proposition as a belief turn it into one? I can flag up propositions in various ways on a piece of paper without making them come to intentional life. To believe something you have to mean it, and unfortunately no-one really knows what ‘meaning it’ means – that’s one of the things to be explained by a full-blown theory of consciousness.

Moreover, the system of tokens and beliefs encoded in explicit propositions seems fatally vulnerable to the wider form of the frame problem. We actually have an infinite number of background beliefs (Julius Caesar never wore a top hat) which we’ve never stated explicitly but which we draw on readily, instantly, without having to do any thinking, when they become relevant (This play is supposed to be in authentic costume!): but even if we had a finite set of propositions to deal with the task of updating them and drawing inferences from them rapidly becomes impossible through a kind of combinatorial explosion. (If this is unfamiliar stuff, I recommend Dennett’s seminal cognitive wheels paper.) It just doesn’t seem likely nowadays that logical processing of explicit propositions is really what underlies mental activity.

Some important reservations then, but it’s important not to criticise Trehub’s approach for failing to be a panacea or providing all the answers on consciousness – that’s not really what we’re being offered. If we take consciousness to mean awareness, the retinoid system offers some elegant and plausible mechanisms. It might yet be that the theatre deserves another visit.

1. The author's tone in this passage is

a. one of enthusiastic agreement, with only a hint of doubt.
b. politely skeptical, but not entirely so.
c. angrily critical, though not about the essential points.
d. purely humorously critical.
e. respectfully objective, expressing no personal opinion.

ANSWER AND EXPLANATION (highlight the space between the brackets to see): [The answer is (B). Why? Answer (A) doesn't work because, as the last paragraph says, the author has "important reservations" regarding Trehub's theory. The author notes that elements of Trehub's theory are "elegant and plausible," which means we can eliminate answer (C). By the same token, (E) also fails, because the author obviously has an opinion about Trehub's theory, both noting its flaws and acknowledging its merits. Answer (D) fails because the passage contains no humorous elements, and is not relentlessly critical of Trehub.]


Passage 2 (from here):

[NB: The author is writing about how to approach long, involved books on history.]

But apart from this matter of personal learning style, what I’ve found is that many of my students don’t know what to do when confronted by a whole book. Some try to study it as intensively as they would try to study a chapter in a work of philosophy or political theory. They spend hours and hours on their reading, and often end up angry and unfulfilled. They’ve spent an inordinate amount of time preparing, but they rarely feel they have mastered the text. And when the discussion in class focuses on other aspects of the book in question, their frustration grows.

Others read through an assigned book the way they get through their casual reading. They read at forty to sixty pages an hour, take no notes, and give little thought to the content beyond the impressions of the moment. If they are diligent, their eyes have indeed scanned every word in the whole three hundred-page book, but anything that sticks in the student’s memory got there by chance and two days later he or she won’t be able to say anything coherent about the book’s content or point of view.

The easy thing to do for a grumpy old professor when faced with these reactions is to throw up his hands in the traditional gesture of professorial despair, and launch into one of those eloquent and ever-popular rants, ancient already in the days of Socrates, about how young people today have no attention span, don’t know anything and don’t know hard work.

It is all true, and has been true since Socrates was a sprout, but repeating traditional laments doesn’t help either students or professors wrestling with big fat books in political studies seminars. As I’ve reflected on this problem, I’m increasingly aware that reading serious books – not textbooks and not tracts of theory or philosophy – is a skill that not everybody learns. I’ve been reading dozens and even hundreds of books a year for so long that these reading skills are second nature to me; I don’t think about how to read serious books that aren’t textbooks anymore than I think about how to ride a bicycle.

As I teach, though, I see that not everybody learns how to do this in high school. Through no fault of their own, many students are raised on textbooks and treatises rather than novels and history. You aren’t born knowing how to ride a bicycle and you aren’t born knowing how to read big books effectively for seminars. On the other hand, the basic skills required, either for bike riding or book reading, aren’t all that hard to learn — and once learned, they stick.

A history book is different from a book of political theory or logical argument, and it needs to be approached in a different way. When approaching a history book, the first thing to do is to ask the Winston Churchill question. At a dinner, Churchill once criticized the dessert: “This pudding has no theme.” Most puddings and books have a theme. In the case of a book, this is a big idea or subject. Your first job as an analytical reader is to figure out what that is: you must answer the Pudding Question.

What does the author think is the big story the book is trying to tell – and what does the author think is the point of that story?

2. The author's tone in this passage is

a. constructively critical of his students.
b. disparaging of his students.
c. wary or suspicious of his students.
d. condescending to his students.
e. one of pity for and solidarity with his students.

ANSWER AND EXPLANATION (highlight the space between the brackets to see): [The answer is (A). Why? Answer (B) fails because the author never adopts an insulting tone about his students. To the contrary, the author notes that it would be easy to react negatively to students' inability to read a large book intelligently. He is, in fact, sympathetic to his students' plight ("through no fault of their own")-- the opposite of disparagement. Answer (C) fails for the same reason, and there is no direct evidence in the text that the author both pities his students and feels solidarity with them, thus eliminating (E) as a possibility. A test-taker might be tempted to choose (D), but there is no evidence that the author sees himself as superior to students who are obviously inferior. Besides, it's hard to be sympathetic and condescending at the same time. (A) is the best answer given the textual evidence: "repeating traditional laments doesn’t help either students or professors wrestling with big fat books in political studies seminars" and "A history book... needs to be approached in a different way" are both clear examples of a constructively critical approach: the author has perceived a problem and is offering a way to solve it.]


Passage 3 (from here):

[NB: The author, Freeman Dyson, is writing on the need for "heretics" in science in the context of discussions of global warming and climate change.]

We are lucky that we can be heretics today without any danger of being burned at the stake. But unfortunately I am an old heretic. Old heretics do not cut much ice. When you hear an old heretic talking, you can always say, “Too bad he has lost his marbles”, and pass on. What the world needs is young heretics. I am hoping that one or two of the people who read this piece may fill that role.

Two years ago, I was at Cornell University celebrating the life of Tommy Gold, a famous astronomer who died at a ripe old age. He was famous as a heretic, promoting unpopular ideas that usually turned out to be right. Long ago I was a guinea-pig in Tommy’s experiments on human hearing. He had a heretical idea that the human ear discriminates pitch by means of a set of tuned resonators with active electromechanical feedback. He published a paper explaining how the ear must work, [Gold, 1948]. He described how the vibrations of the inner ear must be converted into electrical signals which feed back into the mechanical motion, reinforcing the vibrations and increasing the sharpness of the resonance. The experts in auditory physiology ignored his work because he did not have a degree in physiology. Many years later, the experts discovered the two kinds of hair-cells in the inner ear that actually do the feedback as Tommy had predicted, one kind of hair-cell acting as electrical sensors and the other kind acting as mechanical drivers. It took the experts forty years to admit that he was right. Of course, I knew that he was right, because I had helped him do the experiments.

Later in his life, Tommy Gold promoted another heretical idea, that the oil and natural gas in the ground come up from deep in the mantle of the earth and have nothing to do with biology. Again the experts are sure that he is wrong, and he did not live long enough to change their minds. Just a few weeks before he died, some chemists at the Carnegie Institution in Washington did a beautiful experiment in a diamond anvil cell, [Scott et al., 2004]. They mixed together tiny quantities of three things that we know exist in the mantle of the earth, and observed them at the pressure and temperature appropriate to the mantle about two hundred kilometers down. The three things were calcium carbonate which is sedimentary rock, iron oxide which is a component of igneous rock, and water. These three things are certainly present when a slab of subducted ocean floor descends from a deep ocean trench into the mantle. The experiment showed that they react quickly to produce lots of methane, which is natural gas. Knowing the result of the experiment, we can be sure that big quantities of natural gas exist in the mantle two hundred kilometers down. We do not know how much of this natural gas pushes its way up through cracks and channels in the overlying rock to form the shallow reservoirs of natural gas that we are now burning. If the gas moves up rapidly enough, it will arrive intact in the cooler regions where the reservoirs are found. If it moves too slowly through the hot region, the methane may be reconverted to carbonate rock and water. The Carnegie Institute experiment shows that there is at least a possibility that Tommy Gold was right and the natural gas reservoirs are fed from deep below. The chemists sent an E-mail to Tommy Gold to tell him their result, and got back a message that he had died three days earlier. Now that he is dead, we need more heretics to take his place.

3. The author's tone in this passage is

a. intensely scolding
b. scientifically inquisitive
c. curiously frightened
d. slightly annoyed
e. drily humorous

ANSWER AND EXPLANATION (highlight the space between the brackets to see): [This question may be the most difficult for test-takers to answer, and I deliberately designed it to be that way. The correct answer is (E). Were you, perhaps, inclined to choose (B)? I don't blame you, but if you chose (B), you fell into my trap. You see, sometimes SAT questions are constructed in such a way as to mislead you by playing into your expectations and presumptions. This article is by Freeman Dyson, a well-known scientist, and we all automatically associate scientists with human qualities like curiosity and fascination with the universe. Without a doubt, Freeman Dyson is a scientifically inquisitive individual. The problem, though, is that the test question is asking you about the tone of the passage, not about the attitude of the author. That's an important difference.

Don't be tempted to read anything into the passage: use only the textual evidence before you when answering a question. In this case, you'll observe that the passage contained not a single inquisitive-sounding sentence. This was not an exploration of the universe's mysteries; it was, instead, a fond meditation on the need for different thinkers-- "heretics"-- in scientific discourse. So (B) is wrong. Answer (A) is also wrong because Dyson's tone is gentle, not caustic. He certainly expresses no fear, so (C) is also wrong, and (D) fails because, even though Dyson makes reference to certain problems, he never expresses annoyance about them. Instead, the passage is suffused with wry humor as he chronicles the way in which Tommy Gold was repeatedly right while the rest of the scientific establishment turned out to be repeatedly wrong. The first paragraph, with its reference to being burned at the stake, is also obviously humorous in intent, as is the frequent use of the words "heretic" and "heretical," words normally employed in a religious context. None of this passage is laugh-out-loud funny, of course, which is why it qualifies as dry humor.]

I hope this little exercise in determining tone has been helpful to you. Keep on reading! There's no substitute for it. Read a lot, and read widely. Don't stick to just one genre. And as the author of Passage 2, above, recommends later on in his article: read actively. That's the best way to benefit from your studies.


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asking the cosmic questions

The Atlantic asks: What Happened Before the Big Bang?

Excerpt:

This question of accounting for what we call the "big bang state" -- the search for a physical explanation of it -- is probably the most important question within the philosophy of cosmology, and there are a couple different lines of thought about it. One that's becoming more and more prevalent in the physics community is the idea that the big bang state itself arose out of some previous condition, and that therefore there might be an explanation of it in terms of the previously existing dynamics by which it came about. There are other ideas, for instance that maybe there might be special sorts of laws, or special sorts of explanatory principles, that would apply uniquely to the initial state of the universe.

One common strategy for thinking about this is to suggest that what we used to call the whole universe is just a small part of everything there is, and that we live in a kind of bubble universe, a small region of something much larger. And the beginning of this region, what we call the big bang, came about by some physical process, from something before it, and that we happen to find ourselves in this region because this is a region that can support life. The idea being that there are lots of these bubble universes, maybe an infinite number of bubble universes, all very different from one another. Part of the explanation of what's called the anthropic principle says, "Well now, if that's the case, we as living beings will certainly find ourselves in one of those bubbles that happens to support living beings." That gives you a kind of account for why the universe we see around us has certain properties.

Fascinating and delightful. Be sure to read the whole thing.


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why learn a foreign language?

Here's a video showing plenty of celebrities speaking a wide variety of languages: Kobe Bryant speaking Italian, Will Smith speaking Spanish, Sandra Bullock speaking German, Jodie Foster speaking French, Natalie Portman speaking Hebrew, etc.

We live in a plural, diverse world, and foreign language mastery opens so many doors. The question really should be: why not learn a foreign language?


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the power of words

Prizewinning poet Taylor Mali on "What Teachers Make." I love this particular performance.


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this week's Math Beast Challenge

From here:



Go to it! My answer will eventually appear in the comments.


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got another one right!

I consider myself quite capable of teaching the Quantitative, Verbal, and Analytical Writing sections of the GRE, but I still need to keep myself on my toes. That's one reason why I do the weekly Math Beast Challenges that Manhattan GRE throws us. The challenges appear on Monday; I splash them up on this blog on Tuesday (since Tuesday is the designated math day here) and offer my own answers to the questions. When the solutions to the problems appear the following week, I recopy and display them here for your edification. This way, Dear Reader, you get to see two approaches to the problem, which allows you to decide what works best for you.

As it turns out, I got last week's problem right: the answer is, in fact, (C): the quantities are equal. Here's MGRE's explanation:

We can set up and simplify two equations, one for the calories consumed and the other for cost, using variables A and B for the number of servings of Snacks A and B, respectively.

Calories:
200A + 350B = 3250
20A + 35B = 325 {divided by 10}
4A + 7B = 65 {divided by 5}

Cost:
$1.70A + $0.60B = $11.00
17A + 6B = 110 {multiply by 10 to eliminate decimals}

So we now have a system of two equations and two variables, which could be solved for A and B. But, even in their simplified form, these two equations have awkward coefficients that will make solving messy.

Since this is a Quantitative Comparison question, it would be smarter to “cheat off of the easy statement.” That means we plug in the 4 from Quantity B as a possible number of servings of Snack A, and see what that tells us.

We’ll plug A = 4 in to each equation.

Calories: 4(4) + 7B = 65, so 7B = 65 – 16 = 49. Therefore B = 7.
Cost: 17(4) + 6B = 110, so 6B = 110 – 68 = 42. Therefore B = 7.

We have effectively shown that A = 4 and B = 7 is the solution we would have found had we solved this system of equations ourselves.

Thus, Quantity A and Quantity B are both 4.

The correct answer is C.

I'd say that's not so different from my own approach, until we get to the next-to-final step. MGRE and I certainly agreed on the fundamental issue: this was indeed a "systems of equations" problem. Where we disagreed was in how to reach the very end. I did the typical thing, and simply solved all the algebra. MGRE, by contrast, "cheated" by plugging in data from the chart to solve for one variable. This method is arguably quicker, although I think the difference between MGRE's and my respective methods amounts to just a few seconds. On the actual test, you've got a little more than a minute to solve each math problem, so there's a bit of a time buffer there, as long as you're fast on your feet.


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mythbusting the "smarts" issue

The Manhattan GRE blog has a very good article aimed at students who may feel they're "not smart enough" to do well on the GRE. Give it a read.


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"a beast in a gilded cage:that's all some people ever wanna be"

A passage from Patt Morrison's L.A. Times book review of Sally Bedell's Elizabeth the Queen:

Sure, why not. Let's have yet another biography of Elizabeth II, this one as she's about to mark 60 years on the throne.

So what is new to justify Sally Bedell Smith's massive "Elizabeth the Queen"? What is left to uncover, and what should be left uncovered and unknown in the life of this exemplary lady whose predetermined existence of regal obligation is yawningly unenviable, however bejeweled the box it comes in?

And this classic passage from the Chuang Tzu:

Once, when Chuang Tzu was fishing in the P'u River, the king of Ch'u sent two officials to go and announce to him: "I would like to trouble you with the administration of my realm."

Chuang Tzu held on to the fishing pole and, without turning his head, said, "I have heard that there is a sacred tortoise in Ch'u that has been dead for three thousand years. The king keeps it wrapped in cloth and boxed, and stores it in the ancestral temple. Now would this tortoise rather be dead and have its bones left behind and honored? Or would it rather be alive and dragging its tail in the mud?

"It would rather be alive and dragging its tail in the mud," said the two officials.

Chuang Tzu said, "Go away! I'll drag my tail in the mud!"

from The Complete Works of Chuang Tzu, Burton Watson, trans.

I wonder what Queen Elizabeth would say to Chuang Tzu.


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exercice de lecture et de traduction

Voici un petit extrait d'une critique du film "Mission Impossible: Protocole fantôme," avec Tom Cruise en vedette (voir ici). Lisez et traduisez.

Jusqu’ici, avec tout ce qu’on peut penser des films pris individuellement, de l’application de De Palma qui définit quelques codes toujours en vigueur dans les films d’espionnages à la révélation de J.J. Abrams qui assurait son passage du petit au grand écran sans démériter, en passant par un John Woo en plein délire, la saga Mission: Impossible est peut-être celle qui tient le mieux la route. Et ce pour une raison principale : en gardant un œil dans le rétroviseur pour perpétuer un certain esprit de l’œuvre originale (masques, trahisons, manipulations…) chaque réalisateur intervenu a réussi à imposer son univers sans jamais se renier ou se plier à quoi que ce soit. On se demandait ce qu’il allait se passer avec Brad Bird, génie de l’animation qui nous a ébloui en trois films (Le Géant de fer, Les Indestructibles et Ratatouille) et qui signe là son premier film live – qui plus est au sein d’une franchise – quelques mois seulement avant son compère de chez Pixar, Andrew Stanton. Le passage au live apporte au moins deux éléments à risque pour un habitué de l’animation : des contraintes physiques et surtout des acteurs à gérer, qui se doivent d’être aussi malléables que des personnages numériques. Dès les premières secondes, plus d’inquiétude, Brad Bird est l’homme de la situation. Mission: Impossible – Protocole fantôme trouve immédiatement sa place tout en haut dans la saga, une réussite éblouissante.

Alors la critique est-elle positive ou négative? Comment le savez-vous?


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all hail ENGRISH!

Engrish.com is a hilarious website that's been around for years. I first learned about it while I was living in Korea. The site features photos of mangled English, primarily from East Asian countries, much of which is uproariously nonsensical. Here are a few good ones, sorted by country.

China:

1. To help you rent a nice family.

2. Don't hurt me for your pretty!

3. Do not disorder rubbish here.


Japan:

1. I go down the stairs of the right side immediately and excel you.

2. Try to put on and out!

3. The wonderfully throbbing Christmas.


South Korea:

1. I do a lot of thing.

2. Crapmeat tortilla.

3. "Worm-up" clothing.



An exercise for the student of English: try to change the Engrish in the above-linked images into proper English!


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this week's MGRE Math Beast Challenge

This week's challenge:



My answer will eventually appear in the comments, but you're free to take a stab at the problem and provide your own answer. Show your work! Note to SAT students: this might be a GRE problem, but it isn't so different from the sort of problem you might see on the SAT I. Feel free to join in.


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right again!

The official answer to last week's MGRE Math Beast Challenge problem is indeed (E)!

Here is MGRE's explanation:

Interest on debt comprises 2% of total expenses for each division. So if the pharmaceutical division spends 4 times as much as the chemical division does on interest, then total expenses for the pharmaceutical division must be 4 times total expenses for the chemical division. The best thing to do is pick some smart numbers:

Total expenses for pharma = 400
Total expenses for chem= 100

{We might pause here to check our earlier logic. With these numbers, chem would spend 2 for interest on debt and pharma would spend 8. This agrees with what the problem told us about interest on debt.}

Payroll expenses for pharma = 26% of pharma total = (0.26)(400) = 104
Payroll expenses for chem = 38% of chem total = (0.38)(100) = 38

The question asks “What percent of the chemical division's payroll expense is the pharmaceutical division's payroll expense?”
With our numbers, this question is “What percent of 38 is 104?”
Rephrasing a bit: “104 is what percent of 38?”

We can see that 104 is more than 100% of 38, so (A) and (B) can be eliminated.
Actually, 104 is more than twice 38 (i.e. 104 > 76), so (C) and (D) can also be eliminated.

We can solve to prove that (E) is the answer by translating the percent question into an equation:
104 is what percent of 38?
104 = (x/100)(38), where x is the answer.
x = (104)(100)/38
x = 273.6842....

To the nearest whole percent, 104 is 274% of 38.

The correct answer is E.

I like MGRE's explanation, which involves, arguably, a little less math than my own explanation does. Many math problems on both the SAT and the GRE can be solved in this way: through logical deduction instead of hardcore algebra. Remember to eliminate possibilities as you work: by narrowing the number of plausible answers, you increase your chances of guessing correctly-- if you find yourself needing to make a guess. Of course, if you're able to use deduction to eliminate four out of five possibilities, then you're golden!


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if you prefer impersonal videos

The Khan Academy, essentially a cyberspace school, offers all students free(!) instruction in a variety of subjects ranging from math to lab science to history. Salman Khan started making YouTube videos a few years ago-- originally to help his cousins, but then as part of a larger educational project that has taken much of the country by storm.

If you're looking for Khan's SAT prep videos, click here. If you have the College Board's official guide to the SAT I, you can follow along with Khan on his videos.


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gi-il (忌日, 기일)

My mother died of brain cancer two years ago today. I chronicled much of this ordeal at my blog, Kevin's Walk. Since today is Friday, a day I've designated for religion-related discussion, I thought I'd pass along a famous story about the Chinese Taoist philosopher Chuang-tzu, who is said to have acted strangely when his wife died:

When Chuang Tzu’s wife died, his friend Hui Tzu came to offer his condolences and found Chuang Tzu hunkered down, drumming on a potter pan and singing.

Hui Tzu said, “You lived with her, raised children with her, and grew old together. Even weeping is not enough, but now you are drumming and singing. Is it a bit too much?”

Chuang Tzu said, “That is not how it is. When she just died, how could I not feel grief? But I looked deeply into it and saw that she was lifeless before she was born. She was also formless and there was not any energy. Somewhere in the vast imperceptible universe there was a change, an infusion of energy, and then she was born into form, and into life. Now the form has changed again, and she is dead. Such death and life are like the natural cycle of the four seasons. My dead wife is now resting between heaven and earth. If I wail at the top of my voice to express my grief, it would certainly show a failure to understand what is fated. Therefore I stopped.” (Chapter 18)

This version of the story is taken from here.

Different cultures develop different ways of dealing with death and mourning. In Korea, which carries on the old Chinese tradition of venerating one's ancestors, people typically have a jaesa (제사), a ceremony for previous generations. While it may sound morbid, I suppose this day could be described as a "death day," the closed-parenthesis counterpart of a birthday. But is it really all that morbid to celebrate the transition from life to death? Far from being morbid, the day could be seen as a kind of ritualized symmetry.

Today, then, I and my family commemorate my mother's death. While it pains me that I can no longer hug her or hold her hand, I'm grateful for the care and wisdom she imparted.

I love you and miss you, Mom.










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"regular" verbs that behave a bit strangely

In French, there are some verbs that are conjugated almost like good old regular verbs, but with some slight alterations. I want to talk about two major types of "almost-regular" verbs: (1) the -eCer verbs and the (2) -cer/-ger verbs.

1. -eCer verbs

This type of verb has an infinitive form that ends in "e," plus a single consonant, plus "er." Examples:

s'appeler (to be named/called)
jeter (to throw)
amener (to bring)
péter (to burst, fart)
se promener (to walk/go walking)

Watch how each of the above verbs behaves when each is conjugated in the present indicative (l'indicatif du présent):

s'appeler
je m'appelle
tu t'appelles
il s'appelle
nous nous appelons
vous vous appelez
ils s'appellent

jeter
je jette
tu jettes
elle jette
nous jetons
vous jetez
elles jettent

amener
j'amène
tu amènes
il amène
nous amenons
vous amenez
ils amènent

péter
je pète
tu pètes
elle pète
nous pétons
vous pétez
elles pètent

se promener
je me promène
tu te promènes
il se promène
nous nous promenons
vous vous promenez
ils se promènent

Notice anything in common about the ways in which the above verbs "twist" themselves away from the regular "-er" form? Perhaps the first thing to note is that the first, second, and third-person singular conjugations are all spelled differently from the infinitive: s'appeler gets a double "l"; jeter gets a double "t"; amener gets a grave accent (un accent grave); péter does, too; and so does se promener. There's no rule governing what -eCer verb gets which type of conjugation; as with all irregular verbs, these "almost-regular" verbs will simply need to be memorized.

Note, too, that the first- and second-person plural forms (nous et vous) are conjugated normally, i.e., in the manner of regular "-er" verbs. Finally, note that the third-person plural forms (ils, elles) go back to being slightly irregular.

Keep this irregularity in mind whenever you see any -eCer verbs.



2. -cer/-ger verbs

This type of "-er" verb ends in -cer or -ger. Examples:

lancer (to throw, launch)
annoncer (to announce)
commencer (to begin, start, commence)
manger (to eat)
plonger (to dive, plunge)
voyager (to travel)

Watch what happens when we conjugate the "-cer" verbs.

lancer
je lance
tu lances
il lance
nous lançons
vous lancez
ils lancent

annoncer
j'annonce
tu annonces
elle annonce
nous annonçons
vous annoncez
elles annoncent

commencer
je commence
tu commences
on commence
nous commençons
vous commencez
ils commencent


And now, the "-ger" verbs:

manger
je mange
tu manges
il mange
nous mangeons
vous mangez
ils mangent

plonger
je plonge
tu plonges
elle plonge
nous plongeons
vous plongez
elles plongent

voyager
je voyage
tu voyages
on voyage
nous voyageons
vous voyagez
ils voyagent


What rule do you see at work here? In truth, the rule is as much about pronunciation as it is about conjugation: in French, it's often the case that the pronunciation of the letters "c" and "g" will change in front of the vowels "a" and "o." This rule operates in nouns just as it does in verbs:

le français (not le francais)

So you have to understand that, if you want your "c" to sound like an "s" in front of "a" and "o," you need to add the cedilla (la cédille), that little diacritical mark that dangles under the "c." If you forget the cedilla and mistakenly write "le francais," a Frenchman will read that and mentally hear "le franké." Not pleasant.

For a "g" to be a soft "g" in front of "a" and "o," you need to add an "e." Hence: nous voyageons.

As with any language, French is full of irregularities. These can drive a beginning student crazy, but it's best to learn them well now; otherwise, you may form bad habits in your writing and speech later on. Strive for perfection as you learn the language so that you don't doom yourself to speaking it with a laughable accent. Bad habits, once formed, are very hard to unlearn.


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jealousy vs. envy, personality vs. character

"You got a new car? I'm so jealous!"

Not so fast: I'm inclined to say that you're actually envious. What's the difference between jealousy and envy? Well, these two words are often used interchangeably, but a more proper reckoning of their respective definitions would be that envy refers to coveting what one doesn't have, whereas jealousy refers more to a greedy possessiveness about what one already has.

In simple terms: you're envious of what you don't have; you're jealous of what you do have.

Examples:

1. A jealous husband won't let his wife talk with other men.

2. The dragon jealously guards its treasure.

3. When Martha saw her friend's new car, she became envious and wanted one of her own.

4. Brian envied his best friend's successful acting career.

Standard dictionaries don't necessarily support the above distinction, which is why I noted that the words and concepts are often used interchangeably. But see this entry for some philosophical support for the distinction I make. I think I'm on solid ground.

Two other words that are often used interchangeably are personality and character. I tend to think of personality as superficial and external, whereas character refers to something more profound and internal. A smiling politician might have a very pleasant personality, yet be of bad character. Conversely, an army drill sergeant might have a nasty personality, yet be of sterling character. There's certainly some overlap between these two words; to call someone "nice," for example, may be to say something about that person's personality (s/he appears kind) or about his/her character (s/he actually is kind). but you can't go wrong if you think of character as deeper than personality.

Other words to think about:

stingy vs. greedy

frugal vs. stingy

injure vs. harm vs. hurt

See whether you can tease out the differences between and among the above words.


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this week's MGRE Math Beast Challenge

My answer to last week's challenge, regarding the honeycombed hexagons, was indeed correct: Quantity A is greater. MGRE says:

Regular hexagons are very special—divide the hexagon with three diagonals (running through the center) and you will get six equilateral triangles. Why are the triangles equilateral? Since the sum of the angles in any polygon is (n – 2)(180), the sum for a hexagon is 720. Divide by 6 to get that each angle is 120. When you divide the hexagon into triangles, you split each 120 to make two 60 degree angles for each triangle. Any triangle that has two angles of 60 must have a third angle of 60 as well, since triangles always sum to 180.

Since the triangles are equilateral, we know that all of them have all sides equal to 2√3. For each triangle, we know that the height will always equal half the side times √3. (This is a good fact to simply memorize; however, had you not memorized this, you could divide each equilateral into two 30–60–90 triangles and use the side ratios of 1 : √3 : 2 for a 30–60–90 triangle.)

Therefore, the height of each triangle is simply √3 * √3 = 3.

Since the area of a triangle is [(1/2)bh], the area of each equilateral triangle is: (1/2)*(2√3)*3 = 3√3.

Since there are six such equilateral triangles in each hexagon, the area of each hexagon is 18.

Since there are six hexagons in the honeycomb, the total area of the figure is 108√3 = 187.061487....

The correct answer is A.

This week, we've got another Data Interpretation challenge:




Go to it! My own answer will eventually appear in the comments.


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Happy New Year!

It's 2012! If you're taking the SAT in late January, good luck to you! I've already written a great deal about handling the SAT Critical Reading section; click on the relevant labels (see the tag cloud in my blog's left-hand margin).


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