Monday, June 25, 2012

answer to last week's MGRE Math Beast Challenge

MGRE has this to say about last week's Math Beast Challenge:

We are told that the 11th grade girls at Stumpville High School have an average GPA of 3.1, and the overall 11th grade average GPA is 3.05. Fortunately, the 11th grade has the same number of boys and girls, so rather than using the weighted average formula, we can simply conclude that the boys’ average GPA must be 3.0. Write on your paper something like:

11th grade boys average GPA = 3.0

(If you’re not sure about our quick inference, try this example: If a dozen people in a room each have an average of \$10 and another dozen people each have an average of \$20, then the average amount of money each person has is exactly \$15, since the \$10 group and the \$20 group are the same size. Similarly, if this example had told you that a dozen people have an average of \$10, another dozen people have x dollars, and the overall average is \$15, then – since 15 is exactly halfway between 10 and 20 – you could confidently conclude that the other dozen people have an average of \$20.)

We are told that all of the boys enrolled in Honors Chemistry are in 11th grade. From the first chart, add up the total number of boys: 46 + 52 + 52 + 50 = 200. From the bottom chart, we can see that 6% of boys take Honors Chemistry. 6% of 200 is 12, so write on your paper something like:

11th grade boys in Honors Chem = 12

We are told that these 12 boys have an average GPA of 3.8. And yet the average GPA for boys in 11th grade is only 3.0 – thus, we are expecting the rest of the boys’ GPAs to be much lower than the Honors Chemistry boys’ GPAs.

However, we CANNOT do the kind of “quick logic” we did above and assume that, since the Honors Chem 11th grade boys have an average GPA of 3.8 and the 11th grade boys in general have an average GPA of 3.0, therefore the rest of the boys have an average GPA of 2.2 (since 3.0 is exactly in the middle of 2.2 and 3.8). THIS IS A TRAP! We cannot conclude that the answer is 2.2, because the number of Honors Chem 11th grade boys and the number of other 11th grade boys are NOT THE SAME.

We must calculate a weighted average (to review Weighted Averages, see Manhattan Prep’s GRE Word Problems Strategy Guide). Remember that there are 12 boys in the 11th grade who are in Honors Chem and 40 who are not in Honors Chem:

[12(3.8) + 40(x)]/52 = 3.0

12(3.8) + 40x = 156

45.6 + 40x = 156

40x = 110.4

x = 2.76

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house-sitting this week

I'm house-sitting for a friend this week, so blogging is going to be spotty at best. My apologies in advance.

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Thursday, June 21, 2012

la sexualité: un sondage

Voici un petit sondage fait dans onze pays (y compris la France) intérrogeant les citoyens sur leur sexualité (positions sexuelles préférées, etc.). Quelques-uns des résultats vous seront un peu surprenants, j'imagine...

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Wednesday, June 20, 2012

hierophany

In a term coined by Romanian historian of religions Mircea Eliade (meer-CHAY-uh ell-YAH-dih), a hierophany is an eruption of the sacred into the realm of the profane (i.e., the ordinary, not the vulgar/obscene). One suddenly finds oneself standing in the presence of the holy, a fact that disrupts the normal, mundane continuity of human existence.

I'm fascinated by theistic fiction, i.e., fiction about the presence of the holy in our midst. A great example of this sort of fiction is the short story titled "The Visitation," by sci-fi author Greg Bear. You can read a truncated version of the story for yourself here.

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Tuesday, June 19, 2012

this week's MGRE Math Beast Challenge

From here:

The 11th-grade girls at Stumpville High School have an average GPA of 3.1, and the overall 11th-grade average GPA is 3.05. If all of the boys enrolled in Honors Chemistry are in the 11th grade and those boys have an average GPA of 3.8, what is the average GPA of all the 11th-grade boys who are not enrolled in Honors Chemistry?

(A) 2.2
(B) 2.76
(C) 2.96
(D) 3.05
(E) 3.16

Go to it! My own attempted solution will appear in the comments.

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Monday, June 18, 2012

answer to last week's MGRE Math Beast Challenge

Yes! I got the answer to last week's MGRE Math Beast Challenge problem correct! The answer was indeed 3, 5, 41, and 43. Here's MGRE's explanation:

The prime numbers less than 12 are 2, 3, 5, 7, and 11. There are five possible ages for the two children, or 5!/2!3! = (5)(4)/(2)(1) = 10 possible combinations for the children’s ages.

The prime numbers between 40 and 52 are 41, 43, and 47. There are three possible ages for the two adults, or 3!/2!1! = 3 possible combinations for the adults’ ages.

In total, there are (10)(3) = 30 possible age combinations—far too many to test each scenario looking for a prime number average age.

An alternative is to start from the resulting average age. The minimum ages of the family members are 2, 3, 41, and 43, which average to 22.25. The maximum ages of the family members are 7, 11, 43, and 47, which average to 27. The only prime number in this range is 23, which implies an age sum of (4)(23) = 92.

If the adults are 43 and 47, the sum of their ages is 90. The sum of the children’s ages would need to be 92 – 90 = 2. The minimum sum of the children’s ages is 2 + 3 = 5, so no need to continue checking these possibilities.

If the adults are 41 and 47, the sum of their ages is 88. The sum of the children’s ages would need to be 92 – 88 = 4. The minimum sum of the children’s ages is 2 + 3 = 5, so again, no need to continue checking these possibilities.

If the adults are 41 and 43, the sum of their ages is 84. The sum of the children’s ages would need to be 92 – 84 = 8. This is only possible if the children are 3 and 5.

Check: (3 + 5 + 41 + 43) = 92, so the average is 92/4 = 23, which is prime.

The correct answers are 3, 5, 41, and 43.

Interesting deductive process! I think I arrived at my answer more intuitively.

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Wednesday, June 13, 2012

so you think you speak Amurrican

A quick test for people who think they know American English! Select the answer that is most American and/or most grammatically correct.

1. Which is correct?

a. Thanks Fred.
b. Thanks, Fred.

2. Let's just leave this _____ .

a. between you and I
b. between you and me

3. She's a real _____ .

a. trouper
b. trooper

4. If I _____ I wouldn't have farted in the tub.

a. could have known about her phobia,

5. Give this prize to _____ ate the most hot dogs.

a. whoever
b. whomever

6. Which is correct?

a. She said, "Sit down."
b. She said, "Sit down".

7. If you want to succeed in this company, _____ and don't make waves.

a. tow the line
b. toe the line

8. That was a strange proposition to Fred and _____ .

a. I
b. me

9. I try to brush my teeth _____ .

a. everyday
b. every day

10. This restaurant has a great _____ .

a. ambience
b. ambiance
c. either A or B
d. neither

11. I saw her in the woods-- _____ .

a. butt naked
b. buck naked

12. When I finally found her ring and ran up, gasping, to give it to her, she sighed and said, "_____ ."

a. Never mind
b. Nevermind

13. I'll _____ be there.

a. definately
b. definitely

14. The sky boomed with thunder and sizzled with _____ .

a. lightning
b. lightening

15. Visiting the White House is quite a _____ !

a. priviledge
b. privilege

16. I'm not _____ to being set up on a blind date.

b. averse

17. _____ elementary, Watson.

a. It's
b. Its

18. I felt so _____ about how disastrous her birthday party was.

19. Despite the chaos around him, Phineas was _____ .

a. unfazed
b. unphased

20. Which is correct?

a. I wonder where my car went.
b. I wonder where my car went?

21. She stared in frank amazement at his _____ salmon.

a. enormous, twenty inch
b. enormous twenty-inch

22. As the Titanic tilted crazily, she held _____ the railing for dear life.

a. onto
b. on to

23. Watch out for the thundering _____ !

a. hoard
b. horde

24. All that has happened has been in accordance with the _____ .

a. prophesy
b. prophecy

25. Einstein, not merely a genius, was a kind _____ he once rescued a treed cat.

a. soul;
b. soul,

How'd you do?

Answers follow; highlight the space between the brackets to see them.

[1. B; 2. B; 3. A; 4. B; 5. A; 6. A; 7. B; 8. B; 9. B; 10. C; 11. B; 12. A; 13. B; 14. A; 15. B; 16. B; 17. A; 18. A; 19. A; 20. A; 21. B; 22. B; 23. B; 24. B; 25. A]

Scale of Achievement:

25: "I am a Jedi, like my father before me."
24: "Impressive. Most impressive."
20-23: "You are not a Jedi yet."
15-19: "You will pay the price for your lack of vision."
10-14: "Scruffy-looking nerfherder!"
5-9: "Your feeble skills are no match for the power of the dark side!"
0: "Noooooooooooo!"

What language rant topics do the above questions cover? Highlight the [bracketed area below] to see.

[1. vocative comma: always use when addressing someone!
2. pronoun case: object of preposition
3. diction (trouper = member of troupe = stalwart team player, not a soldier)
4. verb tense in conditional sentences: if (pluperfect) ➞ main (conditional past)
5. pronoun case: "whoever" is correct as subject of clause
6. US vs. UK punctuation (too many Americans forget what country they live in)
7. idioms: people put their toes up against the painted line
8. pronoun case: don't be an idiot and use a subject pronoun when an object pronoun is called for
9. adverb of frequency = every day; "everyday" = adjective meaning "ordinary"
10. spelling trivia: some words have more than one acceptable spelling
11. idioms: village idiots mishear this as "butt nekkid"
12. compounds: or, more precisely, when not to use compounds
13. spelling: there is no "a" in "definitely"!!!!!
14. spelling/diction: "lightening" comes from the verb "to lighten (a load, the sky, etc.)"
15. spelling: no "d" in "privilege"
16. diction: adverse [conditions], averse [attitude]
17. spelling/diction: it's = it is; its = possessive adjective
19. spelling/diction: only someone who had never actually read the word "to faze" would get this wrong
20. mood: "I wonder" is always declarative-- NEVER interrogative!
21. punctuation: hyphenate phrasal adjectives before a noun; no comma for non-coordinate adjectives
22. diction: the phrasal verb's infinitive form is "to hold on" not "to hold onto," which makes the "to" separate
23. spelling/diction: you'd have to be a moron not to get this one
24. spelling/diction: as above. "Prophesy" (-"sigh") is a verb; prophecy (-"see") is a noun
25. punctuation: a semicolon separates two related or contrastive clauses
]

Tuesday, June 12, 2012

this week's MGRE Math Beast Challenge

From here:

"The Prime of Life"

In a family of four people, none of the people [has] the same age, but all are a prime number of years old. Two of the people are less than 12 years old, and the other two people are between 40 and 52 years old. If the average of their four ages is also a prime number, what are the ages of the family members?

Indicate four such ages (check 4 slots).

( ) 2
( ) 3
( ) 5
( ) 7
( ) 11
( ) 41
( ) 43
( ) 47

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

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Monday, June 11, 2012

answer to last week's MGRE Math Beast Challenge

Well, nuts. The answer to last week's MGRE Math Beast Challenge isn't (D); it's (A). [Never pick (D), Kevin!] Here's MGRE's multi-pronged explanation:

This problem could be solved through logic, algebraically, or by plugging in numbers. For all three solutions, our first task is to simplify y – x > x – y. Notice that it has like terms that can be combined – it would be very bad to neglect to simplify this before plowing ahead with the problem!

y – x > x – y
y > 2x – y
2y > 2x
y > x

So, y is greater than x.

The logic solution is certainly the fastest. Since all of the percent changes in Quantity A and Quantity B are changes through multiplication, order doesn’t matter. Thus, the 35% increase on both sides can be ignored – it is the same on both sides, and the order in which this occurs doesn’t matter.

Additionally, the order in which the other changes occur doesn’t matter. Also, the price p is a positive number that is the same on both sides, so it can be ignored as well.

All that’s left is: Quantity A decreases a smaller percent and increases a larger percent. Quantity B increases a smaller percent and decreases a larger percent. Quantity A is definitely greater.

Or, algebraically:

Since y is greater than x, Quantity A is positive and Quantity B is negative.

Finally, plugging in numbers would also work. To make things easy, make p = 100, and make x and y easy percents, like 10 and 50, making sure y is greater than x.

Of course, we still had to simplify y – x > x – y in order to pick valid numbers, and this method is even faster if we realize we can ignore the 35% change on both sides.

See sample solution with p = 100, x = 10, and y = 50 below. (To decrease by 10%, multiply by 0.9. To increase by 50%, multiply by 1.5. To decrease by 50%, multiply by 0.5. To increase by 10%, multiply by 1.1).

Quantity A
100(0.9)(1.5) = 135

Quantity B
100(0.5)(1.1) = 55

Quantity A will be greater no matter what numbers you choose, provided that you make y > x.

I was so close to the above conclusion, dammit. I had successfully deduced that Quantity B was the negative of Quantity A, but not that A was always positive and B was always negative. In my own explanation, I had even mentioned that it would be tempting to pick (A). I should have followed my instincts, I guess. But where did I go wrong in my math, such that (A) produced a negative result in my own calculations?

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Friday, June 8, 2012

oxen and kitties

In Zen, there's a famous series of pictures known as The Ten Ox-herding Pictures by Kakuan, a Chinese Ch'an (Zen) master. Here's a good, brief article on what the pictures mean.

And here, Dear Reader, is a paradoxically reverent parody: The Ten Cat-herding Pictures.

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le subjonctif

A good page on the French subjunctive mood is here.

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Wednesday, June 6, 2012

the ghost and the tinker: a study in contrasts

It's difficult to imagine a more disparate pair of movies than "Mission: Impossible-- Ghost Protocol" (MIGP) and "Tinker, Tailor, Soldier, Spy" (TTSS). While both films are members of the spy genre, their approaches to that genre differ in almost every respect. And yet, despite their diametrically opposed sensibilities, they're both thoroughly entertaining. Holding them up together for comparison will give us a chance to explore the depth of their differences, and also to ponder what it means to be entertained by a film.

Two quick, one-paragraph summaries, then, to orient the newbie.

MIGP (2011) is the fourth of the Mission: Impossible films. Tom Cruise and Simon Pegg are back as super-agent Ethan Hunt and super-techie Benji Dunn, respectively. Benji's passed his field exam, so he can now run around with Ethan while wearing disguises, speaking Russian, and even holding a gun. Benji's paired up with Jane Carter (Paula Patton), and the team soon acquires a fourth: William Brandt (Jeremy Renner, who's on a cinematic roll). The movie begins with several converging plot lines: (1) Ethan's in a Russian prison, gathering intelligence; (2) Benji and Carter, unaware of Ethan's real mission, have come to Russia to break him out; (3) Carter is fresh off a failed mission in Budapest, in which Russian nuclear launch codes have been stolen by a French assassin (who also killed Carter's boyfriend); (4) a terrorist rogue codenamed Cobalt (Kurt Hendricks, played by Michael Nyqvist) is planning to use those codes to provoke a nuclear war between Russia and the US as part of his belief that humanity is strengthened by the occasional apocalypse. That's the basic setup. What follows is essentially a chase movie: Hendricks blows up part of the Kremlin, pinning the blame on Ethan's team ("Ghost Protocol" refers to the US president's disavowal of Ethan et al.); in Dubai, Hendricks also gets the launch codes from Sabine Moreau (a disconcertingly baggy-eyed Léa Seydoux), the French assassin. The chase leads to India, where Hendricks and his sidekick Wistrom (Samuli Edelmann) break into an Indian TV station and manage to relay a missile launch command to a Russian submarine. The action-packed remainder of the film is all about stopping the missile. Does the team succeed? Well, what do you think?

TTSS (2011) is based on the John Le Carré novel of the same name (Le Carré, pulling a Stan Lee, appears at least twice in quick cameos). The story, which takes place in the 1970s, begins with a passing of the torch at the highest levels of British intelligence-- MI6, nicknamed the Circus: hoary old Control (John Hurt, looking miserable as usual) is stepping down along with his trusted lieutenant, George Smiley (Gary Oldman). Taking Control's place is puny, pugnacious Scotsman Percy Alleline (Toby Jones), whose brainchild is a network codenamed Witchcraft. Control's departure comes on the heels of a failed mission in Budapest (cf. MIGP, above), in which Control's man Jim Prideaux (Mark Strong) is shot and apparently killed. Soviet agents spread the word that Prideaux had attempted the kidnapping of a Hungarian general, but in reality the mission was predicated on Control's suspicion that the Russians have had a mole inside the Circus for years. Control dies soon after his "retirement," and government intelligence liaison Oliver Lacon (the always-smarmy Simon McBurney) asks Smiley to pursue Control's theory. Smiley enlists the aid of young Peter Guillam (Benedict Cumberbatch-- he of the infamous cheekbones) to suss out the Circus members, all of whom had been given codenames by Control: Percy Alleline (Tinker), Bill Haydon (Colin Firth as Tailor), Roy Bland (Ciáran Hinds as Soldier), and Toby Esterhase (David Dencik as Poorman). One of these men is the mole, and each one could fit the profile. The movie proceeds as a sort of whodunit, with the selling of British secrets replacing the traditional murder victim. As Smiley meticulously and inexorably deduces his way to the truth, he comes to realize that, in the larger scheme of the Cold War, the Brits are the dupes: Russia's intention, all along, has been to use Alleline's Witchcraft network to spy on the Americans, with whom Alleline has been keen to make friends. Behind these machinations is the specter of Karla, a Russian operative who has risen in the Soviet ranks and is now the puppet master making the Brits dance. Does Smiley figure out who the mole is? You get only one guess.

On almost every level, with almost every aspect of filmmaking you can think of, these two movies are diametrically opposed. It matters little which aspect I begin with, so I'll plunge in with a discussion of how each film handles its main villain, then go from there.

Visibility of the main villain. The big bad guy in MIGP is Kurt Hendricks, an insane genius who, thanks to his espionage training and his time with the Swedish Special Forces, does his own infiltration work despite his advanced age.* The movie is at pains to build Hendricks up as physically imposing, and he enjoys quite a bit of screen time. Hendricks is, you might say, a very hands-on baddie, as physical as he is intellectual, always one step ahead of the IMF** team. By contrast, in TTSS, the main villain-- Karla-- is never seen directly: we receive only glimpses. His presence is nonetheless felt thanks to a marvelous script that makes him into a pervasive, Sauron-like phantom. When the normally taciturn Smiley has a drink and opens up to young Peter Guillam about his long-ago encounter with Karla, we learn that Karla never said a word during the encounter. The irony, here, is that this is normally Smiley's tactic: our protagonist quietly gathers data and makes his careful deductions before acting. I was very impressed with how the script made Karla a real presence, a real threat, throughout the movie. The search for the mole inside the Circus, which occupies most of the film, is actually a sideshow: the main event is the battle of wills and wits between Smiley and Karla.

Pace and visuals. Here as well, MIGP and TTSS stand in contrast with each other. MIGP is a young person's movie: its scenes are, for the most part, brightly and unsubtly lit, and the script propels us forward at breakneck speed. The Russian prison has its stark fluorescent lights; the dramatic Kremlin explosion (I wonder what Russian audiences thought of that) occurs in the daytime; the Burj Khalifa scenes-- even the sandstorm!-- were all the opposite of murky; even the interior and exterior scenes in India made use of strong color contrasts. TTSS, meanwhile, is drab and subdued: London is stereotypically gray (so gray that it was grey); the scenes in Budapest are either interior shots or cloudy exteriors; most of the London interiors are wan and shadowy. TTSS's pace is different, too; this isn't an action movie so much as a thinker's movie, and there were moments when I felt that the film had been directed by Clint Eastwood. The camera work is stately and unpretentious; there are no violent smash cuts to get our blood pumping, no complicated chase scenes. TTSS's antiquated costume design does a marvelous job of evoking the Cold War era,*** and most of its intrigue comes from ambient hints, subtle facial expressions, and layered dialogue. Which leads me to...

Expository dialogue. MIGP's script is written like a condensed version of the TV series "24." Most of its dialogue is expository-- not so much about revealing character as about keeping the viewer abreast of the rapidly changing circumstances. TTSS, on the other hand, uses dialogue both to develop character and to provide the watchful viewer with hints as to what is to come. While some of TTSS's dialogue is occasionally expository, the story requires the viewer to do his own thinking. When a character like field agent Ricky Tarr (Tom Hardy) delivers a long spiel, it's not so much the content of Tarr's discourse that matters as what Smiley makes of it.

Music. MIGP's soundtrack comes courtesy of the talented Michael Giacchino (juh-KEE-noh), who also scored "The Incredibles" and 2009's "Star Trek." I thoroughly enjoyed Giacchino's versatility in his scoring of "The Incredibles," a movie that mixed the superhero and spy genres. The music for that film had a cool retro feel at times, but easily transitioned into the more grandiose strains that we expect when titans are dueling-- all without losing that lighthearted tone that is a Giacchino trademark. I think this style worked less well with "Star Trek": I have a hard time forgiving Giacchino for creating such a catchy theme, then beating that theme to death in almost every scene. And the lightheartedness that worked so well for a Pixar animation didn't work nearly as well for a science-fiction blockbuster. I didn't hate the soundtrack for "Star Trek," but I did feel that it revealed Giacchino's limits. His score for MIGP confirmed those limits: I've begun to realize that Giacchino is a director's go-to guy if the movie in question isn't particularly deep. That said, the best musical moment, for me, was the soundtrack's soaring tribute to the majestic Burj Khalifa. The worst moments were the intros to Russia and India: both were painfully stereotypical. I cringed.

By contrast, the soundtrack for TTSS was marked by its thoughtful, slow-jazz leitmotifs. Original music was provided by Alberto Iglesias, who is not, as far as I can tell, related to singer Julio Iglesias, whose version of Charles Trenet's "La Mer" is what we hear during the movie's conclusion. TTSS's music is subtle, the opposite of bombast; it never dominates a scene. I don't know much about Iglesias's career in the movie business, but I can see him being in demand among noir directors.

Our protagonists, and how the good guys win. Because MIGP and TTSS occupy such different cinematic universes, it's nearly impossible to imagine a crossover film in which the respective protagonists have a chance to match wits. Ethan Hunt's kinetic modus operandi involves a lot of running, jumping, climbing, and hand-to-hand combat (I'm trying to remember whether he fired a single shot in the entire film); George Smiley, meanwhile, is like the spider that sits at the center of its web, immovable, patiently testing the vibrations and allowing all enemies and information to flow toward him. Smiley's style isn't merely the result of his age; it's a function of his personality. While Hunt and Smiley both recognize the need for teamwork, their management styles differ. Hunt's unspoken motto seems to be the Marines' "Improvise, adapt, overcome"; his team spends much of its time coping with faulty technology, and with an enemy who seems able to anticipate their every move. At the end of the film, Hunt even notes that "the only thing that functioned properly on that mission was this team." The socially awkward Smiley, meanwhile, isn't nearly so chummy with his underlings. At one point he tells his right-hand man, Peter Guillam, that he's sending the younger man "into the lion's den" and that Guillam will, if caught, have to disavow any knowledge of Smiley's activities, just as Smiley will do of Guillam's. It's a far cry from the ethic of "no man left behind," but Smiley's stance makes sense given the circumstances.

The IMF team's struggles involve playing catch-up against a clever enemy; Smiley and his men, meanwhile, gather their data and pounce only when they're absolutely sure. The closest Smiley gets to seeing any real action is when he removes his shoes while in the London-based Russian safe house and pads softly across the floor, gun in hand. In the end, when Smiley gets his man, there's no need even to fire it.

As I mentioned at the beginning, I found both of these movies, MIGP and TTSS, quite entertaining. MIGP isn't particularly cerebral; it's all about the chase-- the action, the adrenaline, the humor, the suspense. Kurt Hendricks, MIGP's villain, has a simple agenda: he wants to instigate a nuclear war as a way to pare down and purify the human race, for strength is born through struggle. TTSS, though, is all about the cerebral. It's not obvious what Karla wants, and Karla's presence is more inferred than revealed. Far from leading us viewers by the nose and keeping us abreast of the plot twists through clear-cut camera work and detailed expository dialogue, TTSS obliges us to deduce, interpret, surmise, and conjecture-- right along with the characters themselves. We're given hints, phrases, and shadowy implications. Much of the important information is non-verbal. The movie doesn't treat the audience as stupid, and it definitely rewards multiple viewings. The plot of TTSS is beautifully put together, and it's certainly the more profound of the two movies.

But both films are ably directed (Brad Bird for MIGP; Tomas Alfredson for TTSS), and both understand economy of expression: not a single moment is wasted in either film. How is it possible to be almost equally entertained by two such different stories? I imagine it's because the eyes and the brain need different sorts of food. Sometimes the eyes-- and the adrenal glands-- demand good, heart-pounding action; sometimes the brain harrumphs and demands a good puzzle. Entertainment comes in all shapes and sizes; surely there's room in this world for two very different approaches to the spy genre!

*This required a rather significant suspension of disbelief, but the story asks us to take on faith that the old, plump Hendricks is the physical match of Tom Cruise.

**IMF stands for Impossible Mission Force. Hard to say with a straight face.

***One of TTSS's main costume designers, Jacqueline Durran, said that she had deliberately chosen 1960s-style clothing as an exaggerated way to evoke the 1970s. I'd say her trick worked.

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Tuesday, June 5, 2012

this week's MGRE Math Beast Challenge

From here:

An item originally cost p dollars, where p > 0.

y – x > x – y

Quantity A
The price of the item if the original price were decreased by x%, increased by 35%, and then increased by y%

Quantity B
The price of the item if the original price were increased by x%, decreased by y%, and then increased by 35%

(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.

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

_

Monday, June 4, 2012

answer to last week's MGRE Math Beast Challenge

The answer to last week's MGRE Math Beast Challenge was indeed (B). But MGRE shows how to arrive at this answer without using Heron's Formula. To wit:

To find the area of triangle PQR we need a base and a height. If we consider side PR the base of the triangle, then QS, which is at a right angle to PR, is the height. We know that both triangle PQS and triangle SQR are right triangles, but to find the height QS we’ll need to know the length of either PS or SR. Unfortunately we don’t know either one, so we’ll have to name variables for several legs of the triangle.

In this case we’ll let x represent the length of PS and y represent the height QS. Note that if PS has length x, then SR has length 21 – x, so we do not need to (and should not) name a variable for length SR. Updating our diagram yields the following:

Apply the Pythagorean Theorem to each right triangle.
From triangle PQS: x2 + y2 = 100
From triangle SQR: (21 – x)2 + y2 = 289

We solve each in terms of y2:
y2 = 100 – x2
y2 = 289 – (21 – x)2

Then set the two expressions equal to y2 equal to each other:
289 – (21 – x)2 = 100 – x2

Now simplify:
189 – (21 – x)2 = -x2
189 = (21 – x)2 – x2
189 = (441 – 42x + x2) – x2
189 = 441 – 42x
42x = 252
x = 6

Now that the value of x is known, solve for y:
100 = 36 + y2
64 = y2
8 = y
(Or just recognize that PQS is a 6 – 8 – 10 right triangle.)

Finally, we can solve for the area of triangle PQR:

(1/2)bh = (1/2)(21)(8) = 84

{Incidentally, this problem is named for Heron’s Formula, which is an alternative to the (1/2)bh triangle area formula. For a triangle with side lengths a, b, and c, the semiperimeter is defined as s = (a + b + c)/2. The area of the triangle equals √(s(s-a)(s-b)(s-c)). Note that this doesn’t require a right triangle, nor does it require knowledge of any heights measured perpendicular to any base. You will NOT need to know this for the GRE, as the original solution above attests.}

I was glad to see the above explanation, because I was honestly stumped as to how to approach the problem. I had thought that Heron's Formula would be the only way to solve it.

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Friday, June 1, 2012

"spiritual, not religious"?well, that's a punch in the face for you, then!

Quite possibly a new book for my collection: Dispirited: How Contemporary Spirituality Makes Us Selfish, Stupid, and Unhappy by Dr. Dave Webster, professor of religion, philosophy, and ethics at the University of Gloucestershire, England. Excerpt:

When someone tells me that they are “Not religious, but very spiritual,” I want to punch them in the face.

Hard…

[Interviewer (Webster himself, really)] What’s the most important take-home message for readers?

[Dave Webster] That the idea of being “spiritual, but not religious” is, at the very least, problematic. As I suggest in the book, mind-body-spirit spirituality is in danger of making us stupid, selfish, and unhappy.

Stupid—because its open-ended, inclusive and non-judgemental attitude to truth-claims actually becomes an obstacle to the combative, argumentative process whereby we discern sense from nonsense. To treat all claims as equivalent, as valid perspectives on an unsayable ultimate reality, is not to really take any of them seriously. It promotes a shallow, surface approach, whereby the work of discrimination, of testing claims against each other, and our experience in the light of method, is cast aside in favour of a lazy, bargain-basement-postmodernist relativism.

Selfish—because the ‘inner-turn’ drives us away from concerns with the material; so much so that being preoccupied with worldly matters is somehow portrayed as tawdry or shallow. It’s no accident that we see the wealthy and celebrities drawn to this very capitalist form of religion: most of the world realizes that material concerns do matter. I don’t believe that we find ourselves and meaning via an inner journey. I’m not even sure I know what it means. While of course there is course for introspection and self-examination, this, I argue, has to be in a context of concrete social realities.

Finally, I argue that the dissembling regarding death in most contemporary spirituality—the refusal to face it as the total absolute annihilation of the person and all about them—leaves it ill-equipped to help us truly engage with the existential reality of our own mortality and finitude. In much contemporary spirituality there is an insistence of survival (and a matching vagueness about its form) whenever death is discussed. I argue that any denial of death (and I look at the longevity movements briefly too) is an obstacle to a full, rich life, with emotional integrity. Death is the thing to be faced if we are to really live. Spirituality seems to me to be a consolation that refuses this challenge, rather seeking to hide in the only-half-believed reassurances of ‘spirit’, ‘energy’, previous lives, and ‘soul’.

I can tell already that I'm going to disagree with some or most of the author's contentions, but the book still sounds fascinating.

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