Thursday, May 31, 2012

when and how the French subjunctive is used

Before I get into how the French subjunctive (le subjonctif) is formed, I'd like to go over when and how it is employed. Off the top of my head, I remember the following contexts:

1. émotion: Je suis contente que tu sois là.

2. antériorité: Fais-le avant qu'il n'arrive.

3. nécessité: Il faut qu'il sache combien elle l'aime.

4. désir/souhait: Que la Force soit avec toi. Je veux que tu viennes.

5. conséquence: J'ai trois jobs pour que tu puisses aller à l'université.

6. unicité: ...la seule personne que je connaisse...

7. doute: Je ne crois pas que ce soit vrai.

8. faits contrefactuels: Bien que je sois américain, je sais parler français. Qu'il soit mort ou vivant, peu importe.

The subjunctive is a mood, not a tense-- a fact you can see reflected in the above list. The French tend to use the subjunctive in more contexts then we use it in English, but it's not foreign to us:

It's important that you be on time. (not "you are on time")

May there be peace on earth. (not "may there is")

(etc.)

In a subsequent post, I'll go over how the French subjunctive is formed.


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Wednesday, May 30, 2012

don't overcorrect!

I find myself increasingly annoyed by the smug idiots who say, "Decimate does not mean destroy: it means remove or kill a tenth of."

Folks, decimate may have had that latter meaning as its only meaning when the word first came into existence, but nowadays, it's perfectly fine to say The bomb decimated the city. This might not imply total destruction, but the word in modern English can mean anything up to near-total destruction. It's a perfectly fine descriptor of what a bomb can do.

People who make such foolish "corrections" are mistaking original meanings for proper meanings. Notions of proper change with the times. The next time someone tries to tell you you're misusing decimate, ask him whether he thinks his best friend is a nice person. When he says "yes," look shocked and ask him whether he really believes his friend is foolish and stupid. This is, after all, the older-- and therefore proper!-- use of the word nice.

Right?

I once heard a man of Scottish extraction claim that no self-respecting Scotsman would ever use the term "Scotch-Irish." "Scotch is a drink!" he said, to much polite laughter from a crowd that knew no better. "The proper term is "Scots-Irish." But he was wrong: "Scotch" is a perfectly serviceable term in the perfectly legitimate expression "Scotch-Irish." Wikipedia has an interesting write-up on this expression, and notes that "Scotch-Irish" is current only in North America, while "Scots-Irish" is a term of more recent invention, and is also confined to North American usage.

This makes our man wrong twice over: if "Scotch-Irish" isn't heard outside of North America (the demographic in question is apparently referred to as "Ulster Scots" in the UK), then how does calling oneself "Scots-Irish" prove that one is a self-respecting Scotsman? This terminological quibble seems to have little, if anything, to do with the monikers used in the Old Country, and that reinforces the point I'm making in this post: in trying to sound smart, don't sound stupid.

(Click this link to see the etymology of nice.)


ADDENDUM: Here's an interesting article on the "singular they."


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Monday, May 28, 2012

answer to last week's MGRE Math Beast Challenge

The answer to last week's challenge is indeed (A)! That means Charles and I are both right. But here's the thing: I had anticipated that MGRE would take Charles's tack and use the plug-and-chug method, but instead they went full-on algebra, as I did, and offered their own version of plug-and-chug only at the very end as an afterthought, and only as a way to check their algebra. To review, then-- here's what Charles had written in his comment:

Yeah, I got A, too, although my process was not nearly as detailed. I just took 15 as a possible number of women at the party, subtracted 8, and multiplied by 4 to get 28 men originally at the party. Since the question then says that 35 men left the party, I knew that the original number of women had to be greater than 15, so the answer was A.

It took me about five times as long to write the above paragraph as it did to work out the answer. I never did figure out how many women were originally at the party.

Disgustingly simple. My own approach, you may recall, went for the algebra:

Let m = original # of men.

Let w = original # of women.

1st phase: we have m and w.
[All men & women are present.]

2nd phase: we have m and (w - 8).
[Eight women have left.]

3rd phase: we have (m - 35) and (w - 8).
[Thirty-five men have left.]

Given (per what we know of the second phase, and what the word problem tells us):

m = 4(w - 8)

And for the third phase:

(w - 8) = 2(m - 35)

At this point, it's a matter of systems of equations.

m = 4w - 32 (2nd phase)

2m = w + 62 (3rd phase)

Multiply the first equation by 2:

2m = 8w - 64

Match it up with the other equation and solve:

2m = 8w - 64
-(2m = w + 62)

=

0 = 7w - 126

7w = 126

w = 18

The original number of women was 18, so Quantity A is greater.

I'm going with (A).

Not simple, but definitely thorough. And here, finally, is how MGRE tackled the problem:

This problem can be solved with a system of two equations.

First, “after 8 women leave, there are four times as many men as women.” Thus, once 8 is subtracted from the number of women, there is a 4 to 1 male/female ratio:

m/(w - 8) = 4/1

Cross-multiply and simplify:

m = 4(w – 8)
m = 4w – 32

Then, 35 men leave, and the 8 women don’t come back, resulting in a 1 to 2 male/female ratio:

(m - 35)/(w - 8) = 1/2

Cross-multiply and simplify:

2(m – 35) = (w – 8)
2m – 70 = w – 8

We now have two equations in two variables.
1st equation: m = 4w – 32
2nd equation: 2m – 70 = w – 8

Since the 1st equation is already solved for m, simply plug into the 2nd equation for m:

2(4w – 32) – 70 = w – 8
8w – 64 – 70 = w – 8
8w – 134 = w – 8
8w = w + 126
7w = 126
w = 18

Since 18 is more than 15, the correct answer is A.

Although we are not asked for the number of men, note that we could easily generate it by plugging w = 18 into either equation:

m = 4w – 32
m = 4(18) – 32
m = 40

This would allow us to check our answer. If we begin with 18 women and 40 men, and then 8 women leave, we would have 10 women and 40 men, which indeed would be a 1 to 4 ratio of women to men. If 35 men then leave, we would have 10 women and 5 men, which indeed would be a 2 to 1 ratio of women to men.

The correct answer is A.

Friday, May 25, 2012

on profiling

I normally blog about religion on Fridays, since religious studies is one of my fields of interest. In this case, though, I'm going to provide a link to a long conversation between atheist thinker Sam Harris and security expert Bruce Schneier. When it comes to national security, Harris is pro-profiling; his belief is that it's ridiculous for US airline security to waste its time "randomly" plucking, say, 80-year-old white grandmothers from the line for a pat-down (or four-year-old East Asian kids, for that matter) when the demographic from which suicide bombers come is known to all. Schneier rejects Harris's view and defends the current approach to airline security. Harris responds that the type of profiling he advocates is not based on a correlation between a certain demographic and terrorism, but is, rather, based on a causal relationship, in which religion is the basic cause. (See why I want to link to this exchange?) Specifically, Harris writes:

And I am not proposing a mere correlation between extremist Islam and suicidal terrorism. I am claiming that the relationship is causal. There are many ways to see this, and not too many ways to credibly deny it (though Robert Pape keeps at it by skewing his data with the Tamil Tigers).

The first sign of a religious cause comes from what the terrorists say of themselves: al Qaeda and its sympathizers have not been shy about discussing their motives in public. The second indication is what they say when they think no one is listening. As you know, we now have a trove of private communications among jihadists. The fine points of theology are never far from their thoughts and regularly constrain their actions. The 19 hijackers were under surveillance by German police for months before September 11, 2001 (read Perfect Soldiers). Islam was all that these men appeared to care about.

And we should recall how other people behave when subjected to military occupation or political abuse. Where are the Tibetan Buddhist suicide bombers? They have the suicide part down, because they are now practicing a campaign of self-immolation—which, being the incendiary equivalent of a hunger strike, is about as far from suicide bombing as can be conceived. And where is that long list of Palestinian Christian suicide bombers you’ve been keeping in your desk? Now would be a good time to produce it. As you know, Palestinian Christians suffer the same Israeli occupation. How many have blown themselves up on a bus in Tel Aviv? One? Two? Where, for that matter, are the Pakistani, Iraqi, or Egyptian suicide bombers killing for the glory of Christ? These Christian communities are regularly attacked by suicidal jihadists—why don’t they respond with the same sort of violence? This is practically a science experiment: We’ve got the same people, speaking the same language, living in the same places, eating the same food—and one group forms a death cult of aspiring martyrs and the other does not.

I'm still going through the exchange. It's been a fascinating read thus far, and I encourage you to read the whole thing.


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Thursday, May 24, 2012

quirks with the imperfect tense in French

You may recall my post on how to form the imperfect tense in French. I mentioned some freakiness with the double-i:

Nous étudiions. (We were studying.)

Nous skiions. (We were skiing.)

Another quirk to watch out for has to do with the letters c and g. I believe I've explained this in another post, but to reiterate:

When placed in front of the vowels a and o, the consonants c and g undergo a slight change if they're to be pronounced softly (i.e., the "s" sound for c, the "zh" sound for g): the c gains a cedilla, and the g takes on an extra e after it.

Examples: le français, nous mangeons

This is relevant when forming the imperfect tense. Take commencer, for example:

je commençais (note the cedilla)
tu commençais
elle commençait
nous commencions (note the lack of cedilla, because the c is followed by an i, not a or o)
vous commenciez
ils commençaient (cedilla again!)

Now watch what happens with manger:

je mangeais (note the additional e)
tu mangeais
il mangeait
nous mangions (no e!)
vous mangiez
elles mangeaient (e again!)

Keep these changes in mind as you master l'imparfait!


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Wednesday, May 23, 2012

sentence equivalence!

Here's a GRE Sentence Completion problem from Manhattan Prep's blog.

The exhibit is not so much a retrospective as a __________ ; the artist’s weaker early work is glossed over and any evidence of his ultimate dissolution is absent entirely.

Select two correct answers.

(A) paean
(B) philippic
(C) tirade
(D) panacea
(E) eulogy
(F) crescendo

In the revised GRE's Sentence Completion section, the object of the game is to select TWO words that are each capable of (1) completing the sentence correctly and (2) giving the sentence a similar meaning. In other words, the words you select need to be either synonyms or almost-synonyms. Two antonyms might conceivably complete the sentence, but this would violate criterion (2). To get around this problem, the GRE Sentence Completion questions are designed so that a pair of antonyms can't be selected without one or the other word in the selected pair sounding ridiculous in context.

Have at it, then click the above link for the answer and explanation. I was able to answer correctly despite not knowing the meaning of "philippic," which is not a word I'd normally expect to see on the GRE.


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Tuesday, May 22, 2012

this week's MGRE Math Beast Challenge

From here:

Everyone at a party is either a man or a woman. After 8 women leave, there are four times as many men as women. After 35 men leave (and the 8 women do not return), there are twice as many women as men.

Quantity A
The number of women originally at the party

Quantity B
15

(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 answer will appear in the comments.


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Monday, May 21, 2012

answer to last week's MGRE Math Beast Challenge

The correct answer was indeed (B)!

Here's MGRE's explanation:

This problem gives us an equilateral triangle and a circle, and tells us that the perimeter of the equilateral is 1.25 times the circumference of the circle.

This is license to plug in. Since both an equilateral and a circle are regular figures—that is, all equilaterals are in the same proportion as all other equilaterals, and all circles are in the same proportion as all other circles—we can be certain that we only need to plug in one set of values in order to be sure of the answer. Because we have regular figures and a way to relate them (triangle perimeter = 1.25 × circumference), we will not need to repeatedly try different values as we often do on Quantitative Comparisons.

We could say the radius of the circle is 2, so the circumference is 4π. Then, the perimeter of the equilateral triangle is (1.25)(4π) = 5π . This isn’t ideal, because then we are stuck with π in the calculations for the triangle, where it is unnecessarily awkward.

We could say circumference = 4 and therefore the perimeter of the triangle = (1.25)(4) = 5. But then the side of the equilateral triangle is 5/3, a non-integer, which is inconvenient. We can avoid this by using larger numbers (multiplied by a factor of 3).

So our smartest numbers are circumference = 12 and therefore the perimeter of the triangle = (1.25)(12) = 15, so each side of the triangle is 5. The height of an equilateral triangle is always (√3)/2 the side length. You can always derive this yourself by splitting the equilateral triangle into two 30–60–90 triangles, with known side ratio 1x : (√3)x : 2x. So, the area of the triangle is

(1/2)bh =

(1/2) • (5) • ((5)((√3)/2)) =

(25√3)/4 =

approx. 10.625. (Use the calculator.)

In the circle, circumference = 12 = 2πr, so

r = 12/(2π) = 6/π. The area of the circle is

π(r^2) = π((6/π)^2) = 36/π = approx. 11.46.

(Use the calculator and the approximation 3.14 for π.)

The correct answer is B.

I have to say... I like my method a lot better.


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Friday, May 18, 2012

monks who gamble with other people's money

This link, about gambling Buddhist monks in Korea, comes from my brother David. I'd heard the stories for years: monks who sneak out to eat meat, monks involved in sexual indiscretions... it comes as little surprise to learn that, yes, there are monks who gamble:

SEOUL -- Six leaders from South Korea's biggest Buddhist order have quit after secret video footage showed some supposedly serene monks raising hell, playing high-stakes poker, drinking and smoking.

The scandal erupted just days before Koreans observe a national holiday to celebrate the birth of Buddha, the holiest day of the religion's calendar.

The head of the Jogye order (external link to Jogye Order of Korean Buddhism's site), which has some 10 million followers, or about a fifth of the country's population, made a public apology on Friday, vowing "self-repentance."

South Korean TV networks aired shots of eight monks playing poker, some smoking and drinking, after gathering at a luxury lakeside hotel in late April for a fellow monk's memorial service.

"The stakes for 13 hours of gambling were more than 1 billion won ($875,300)," Seongho, a senior monk who uses one name, told Reuters on Friday.

Seung Sahn, founder of the Korean monastic order Kwaneum, was lauded for his wisdom, wit, and humor. With his energetic marketing of Korean Seon (i.e., Zen) Buddhism, he was able to spread his school all over the world. Unfortunately, as is true with many men in power, he abused his authority and was caught in a sex scandal involving several women.

It amazes me that there are people within Seung Sahn's Kwaneum Order who have tried to justify his unethical, precepts-breaking behavior. The women were willing! they say. That's a defense? I wonder, now, what defense would be given on behalf of the Jogye Order monks just caught gambling. "If Kwaneum-bosal (bosal = bodhisattva) can do it,* then so can we"?

My view: if you take precepts, whether in Buddhist monasticism or Catholic monasticism or any other sort of clerical endeavor, you're supposed to adhere to them. Such people have chosen to take on the yoke of higher standards. If they can't abide by those standards because of their own human failings, there's no need for us to defend them. In the above case, the Jogye Order did the right thing by apologizing. We can only hope that this will translate into more stringency within the order.





*The Lotus Sutra says the Bodhisattva of Compassion (Avalokiteshvara, Kuan-shih-yin [Chn.], Kanseon/Kannon [Jpn.], Kwaneum/Kwansaeeum [Kor.]) can assume any form to save beings from suffering. If I remember correctly, my old Buddhism prof said there are stories of the bodhisattva assuming the form of a gambler to rescue gamblers from their destructive habits. This would be in consonance with the Lotus Sutra's emphasis on the concept of upaya, i.e., skillful means. One does what one can to bring people to enlightenment. If it helps to appear to mortals as a gambler, then so be it.


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Thursday, May 17, 2012

contrastive tenses: l'imparfait et le passé composé

First a quick review of the French imperfect tense (l'imparfait), then a little demonstration of how the tense is used contrastively.

To form the imperfect tense, remove the "-ons" ending from the first-person plural conjugation of a verb to create a stem:

parler: parlons: parl-
choisir: choisissons: choisiss-
vendre: vendons: vend-
prendre: prenons: pren-
appeler: appelons: appel-
lire: lisons: lis-
vouloir: voulons: voul-
savoir: savons: sav-
devoir: devons: dev-


(irregular form) être: ét-

(etc.)

Depending on person and number, add these endings:

je: -ais
tu: -ais
il/elle/on: -ait
nous: -ions
vous: -iez
ils/elles



In French, the imperfect tense is equivalent to the past progressive tense in English: was ...ing. So:

Je parlais = I was speaking
Tu choisissais = You were choosing
Elle vendait = She was selling
Nous prenions = We were taking
Vous appeliez = You were calling
Ils lisaient = They (masc.) were reading
Je voulais = I was wanting (to)...
Tu savais = You knew (a bit awkward to translate this is as "You were knowing")
Il devait = He had to...


As in English, French verb tenses can be used contrastively. Here's an English example of a contrast between the past progressive and the simple past tense:

I was sleeping when my cell phone rang.

In French, the same contrast is expressed with l'imparfait and le passé composé. To wit:

Je dormais quand mon portable a sonné.

The imperfect tense is used for the "background action," i.e., for actions or events that occur over a period of time. The passé composé, like the simple past tense in English, is used for the "interrupting action," i.e., for actions or events that tend to be sudden and of very short duration. In the above examples, sleeping is the background action; the phone's ringing is the interrupting action.

What if I gave you a problem like this:

Je (regarder) la télé quand le martien (frapper) à la porte.

You'd ask yourself, first, what the background action was: watching TV or the Martian knocking? Obviously, watching TV occurs over a longer period of time than a sudden knock, so regarder should be in the imperfect. Thus:

Je regardais la télé quand le martien a frappé à la porte.

Try this one, which may be a bit more difficult:

Mes copains (arriver) quand je/j' (être) dans la salle à manger.

What's the background action? My being in the dining room or my friends' arriving? It helps to remember that, technically speaking, an arrival happens in a single moment-- the moment the arriving person or thing stops moving. It's only at the very instant that my friends are at the door that I can say they have arrived. Knowing this, we can say that:

Mes copains sont arrivés quand j'étais dans la salle à manger.
My friends arrived when I was in the dining room.

Try your hand at the following sentences.

1. Maman (parler) au téléphone quand notre chat (miauler). (miauler = to meow/mew)

2. Nous (conduire) quand nous (percuter) le cerf. (le cerf = the deer; percuter = to hit, crash into)

3. Quand il (casser) son crayon, je/j' (étudier).

4. Robert et Maxine (skier) quand le bâtiment (exploser). (bâtiment = building)

5. Tu (être) où quand le vol (avoir lieu)? (vol = theft; avoir lieu = to take place)


Final note: The imperfect tense can lead to strange spellings, especially the double-i in the nous form:

Nous étudiions (the imperfect stem of étudier is étudi-)
Nous skiions (the imperfect stem of skier is ski-)

Beware!


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Wednesday, May 16, 2012

the poetry of Stephen R. Donaldson

Two of my favorite poems are by fantasy/SF writer Stephen R. Donaldson, whom I will always associate with his Chronicles of Thomas Covenant the Unbeliever series: two trilogies and a tetralogy-in-progress. The first poem I'll place here is about death and bereavement:

Death reaps the beauty of the world--
bundles old crops to hasten new.
Be still, heart:
hold peace.
Growing is better than decay:
I hear the blade which severs life from life.
Be still, peace:
hold heart.
Death is passing on--
the making way of life and time for life.
Hate dying and killing, not death.
Be still, heart:
make no expostulation.
Hold peace and grief
and be still.


--Stephen R. Donaldson, 1977
Lord Foul's Bane, Chapter 17, "End in Fire"


The second poem, about the last defense of nature, requires a bit of explanation. The being reciting this poem is a Forestal, a powerful spirit of the woods whose function is the guardianship of forest life: trees, plants, and forest creatures. This particular Forestal, Caer-Caveral, is also trying his best to hold the beautiful region of Andelain together. Andelain is the heart of the Land, but like the rest of the Land, it is under attack by an invention of the Despiser (a satanic/Sauron-like figure): the Sunbane, a curse that drives the Land's natural cycles into unnatural frenzy, forcing earth and sky into a cruel series of rapid changes: desert, rain, pestilence, fertility, etc.-- each phase lasting only a few days, then quickly changing, in random sequence, to a new phase in under a day. The Sunbane, a violation of the natural Law, is ripping the earth apart, and Caer-Caveral knows that even he cannot win against its onslaught. This song, then, is his lament.

Andelain I hold and mold within my fragile spell,
While world's ruin ruins wood and wold.
Sap and bough are grief and grim to me, engrievement fell,
And petals fall without relief.
Astricken by my power's dearth,
I hold the glaive of Law against the Earth.

Andelain I cherish dear within my mortal breast;
And faithful I withhold Despiser's wish.
But faithless is my ache for dreams and slumbering and rest,
And burdens make my courage break.
The Sunbane mocks my best reply,
And all about and in me beauties die.

Andelain! I strive with need and loss, and ascertain
That the Despiser's might can rend and rive.
Each falter of my ancient heart is all the evil's gain;
And it appalls without relent.
I cannot spread my power more,
Though teary visions come of wail and gore.

Oh, Andelain! forgive! For I am doomed to fail this war.
I cannot bear to see you die-- and live,
Foredoomed to bitterness and all the gray Despiser's lore.
But while I can I heed the call
Of green and tree; and for their worth,
I hold the glaive of Law against the Earth.


--Stephen R. Donaldson, 1977
The Wounded Land, Chapter 12, "The Andelainian Hills"




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Tuesday, May 15, 2012

this week's MGRE Math Beast Challenge

From here:

The perimeter of an equilateral triangle is 1.25 times the circumference of a circle.

Quantity A
The area of the equilateral triangle

Quantity B
The area of the circle

(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 answer will appear in the comments.

By the way, sorry about the lack of posting last week. I think my sickness lingered on a bit longer than I had thought.


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Monday, May 14, 2012

answer to last week's MGRE Math Beast Challenge

Correct! The answer is indeed 14.286%. Strangely enough, MGRE's initial reasoning is rather tortured. Instead of following their own advice about solving a problem quickly through the plug-and-chug method, they went for the brute-force approach and solved the problem with variables. It's only at the end that the gurus discuss plug-and-chug as an afterthought. Here's what MGRE wrote:
When calculating a percent change “from (original) to (new),” be careful to use the ratio (change/original), not (change/new) or (new/original).

Create some variables:
x = attendance in 2010
y = attendance in 2011
z = attendance in 2012

In 2012, attendance was greater than in 2011, and even greater than it had been in 2010. So, x < y < z.

The question asks for the percent change from 2010 to 2011, or [(y - x)/x]•100%. This can be rewritten as [(y/x)-1]•100%, so what we really need to find is y/x.

We are given two percent changes from one year to another, but watch out! The “from (original)” year is different for each percent given.

“In 2012, attendance at an annual sporting event was 5% greater than it was in 2011”:
Note that “5% greater than” a number means “105% of” that number.
z = 105% of y
z = 1.05y

“In 2012, attendance at an annual sporting event was ... 20% greater than it was in 2010”:
Note that “20% greater than” a number means “120% of” that number.
z = 120% of x
z = 1.2x

To find y/x, we’ll first set both z equivalents equal:
z = 1.05y = 1.2x
y/x = 1.20/1.05

The answer is [(y/x) - 1]•100% = (1.14285714 - 1)•100% = 14.285714%. Rounded to the nearest 0.001%, the final answer is 14.286%.

Alternatively, we could pick numbers. A smart number for z would be a multiple of 120 and 105 (reflecting 5% and 20% increases from an easy base of 100).

z = (105)(120)
y = (100)(120)
x = (105)(100)

The answer is [(y/x) - 1]•100% = {[(100•120)/(105•100)] - 1}•100% = 14.285714%. Rounded to the nearest 0.001%, the final answer is 14.286%
For what it's worth, my own method took me 45 seconds with an on-screen calculator.


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Tuesday, May 8, 2012

this week's MGRE Math Beast Challenge

From here:

In 2012, attendance at an annual sporting event was 5% greater than it was in 2011 and 20% greater than it was in 2010. What was the percent increase in attendance from 2010 to 2011?

Give your answer to the nearest 0.001%.

Go to it! I'm no longer sick, so my answer will definitely appear in the comments sometime during the next 36 hours. As you can tell, this is a "grid-in" problem, i.e., you have to write the correct answer, not select an answer from multiple choices.


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answer to last week's MGRE Math Beast Challenge

I was still sick last week, so I failed to answer this rather complicated question. Here is MGRE's answer:

Rebecca began with 288 friends, evenly divided among 12 months. Thus, she had 24 friends with birthdays in each month.
Let’s make a simple chart:

[chart 1]

Now we’ll simply calculate and record all the changes. First, “the number of Rebecca’s friends with birthdays in the last quarter of the year increased by 25%.”

Thus, October, November, and December’s totals collectively increased by 25%, so from 3(24) = 72 to 72(1.25) = 90. We don’t actually know if each month increased by 25% (from 24 to 30) or if their total simply increased by 25% (for instance, maybe the entire increase of 18 occurred in one month, bringing that month’s total to 42, and the number of people with birthdays in the other two months remained at 24). The new total is 90 either way, and this question is ultimately about the total. However, one of the later constraints in this problem mentions “the month with the largest number of birthdays,” so let’s put the increase all in one month, as it might ultimately be the relevant month.

[chart 2]

Next, “the number of friends with birthdays in each month beginning with “J” increased by one-third.” To increase a number by one-third, multiply by one and one-third (this is faster than multiplying by one-third and then adding it back to the original): 24 (4/3) = 32

[chart 3]

Next, “the number of people with birthdays in February was increased by 12.5%.” Since 12.5% is 0.125, multiply by 1.125 to ADD 12.5% percent to the original number in one step: 24(1.125) = 27

[chart 4]

Next, “the number of people with birthdays in March became 166.6666...% of the new number of people with birthdays in February.”

166.6666...% of 27 is simply one hundred percent of the number, plus another two-thirds. Since 2/3 of 27 is 18, the new total for March is 45. Or, in the calculator: 27(1.666666666...) = 45. (Actually, putting this in the calculator will yield 44.9999999...., since you didn’t actually type in infinity 6’s. This is fine! The answer is 45.)

[chart 5]

Next, “the number of people with birthdays in April became five less than 75% of the new number of people with birthdays in February and March combined.”

February + March = 27 + 45 = 72
75% of 72 = 72(0.75) = 54.
We need the number 5 less than that: 54 – 5 = 49.

[chart 6]

Now, “the number of people with birthdays in May increased by 1, and the number of people with birthdays in August became one less than 20% greater than the new number of people with birthdays in May.”

May is now simply 24 + 1 = 25.
August is one less than 20% greater than 25. In the calculator: 25(1.2) = 30, then one less, or 29.

[chart 7]

Finally, “September’s total increased to 6% less than one more than the new total for the month with the largest number of birthdays.”

The month with the largest number of birthdays is April, with 49. Remember that even if the 25% increase in the total for the last quarter of the year occurred in a single month, that month (October in our chart) would only have 42 people.

One more than 49 is 50.

September’s total is 6% less than 50. To decrease a number by 6%, take 94% of it (this is faster than finding 6% and subtracting it from the original): 50(0.94) = 47

[chart 8]

To calculate the final answer, simply add the “AFTER” row of the chart:

32 + 27 + 45 + 49 + 25 + 32 + 32 + 29 + 47 + 42 + 24 + 24 = 408

The correct answer is B.


I don't have time to do it right now, but I'll be adding the charts later tonight.


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don't know much about history

My goddaughter suddenly canceled her geometry tutoring session with me because of a "music thing" (a performance, apparently) she hadn't known about until the last minute. This left me with some free time, so I spent some of it taking part of an AP World History exam. The College Board has a PDF that contains, among other things, thirty multiple-choice questions. Knowing full well that I'm terrible at history, I decided to see how I'd fare.

Final score: 23/30. Not horrible, but also not enough to rate more than a mediocre 3 on the exam. For the most part, I used a combination of guesswork and common sense-- strategies available to anyone who's facing a multiple-choice test.* Some of the questions were easy to figure out because they weren't exclusively history-oriented: they could just as easily have appeared in the SAT's Reading Comprehension section.

Here are the seven questions I got wrong:

8. Inca and Aztec societies were similar in that both

(A) developed from Mayan civilization
(B) acquired empires by means of military conquest
(C) independently developed iron technology
(D) depended entirely on oral record keeping


(The map below applies to question #10.)



10. The map above shows what significant economic developments?

(A) Trade connections that linked the Hellenistic and Maurya
empires to African cities from 300 through 150 B.C.E.
(B) Trading networks that promoted the growth of new cities
from 600 C.E. through 1450 C.E.
(C) Chinese dominance of Indian Ocean trading networks
because of the voyages of Zheng He in the 1400s C.E.
(D) Changes in Indian Ocean trading networks that resulted
from technological innovations from 1450 C.E. through 1750
C.E.


12. The Columbian Exchange involved which of the following new
connections in the era 1450–1750?

(A) European food to the Western Hemisphere; Western
Hemisphere diseases to Europe; African population to Europe
(B) Western Hemisphere technology to Africa; African food to
Europe; European population to the Western Hemisphere
(C) European technology to Africa; Western Hemisphere
population to Africa; African food to the Western Hemisphere
(D) African population to the Western Hemisphere; Western
Hemisphere food to Europe and Africa; African and European
diseases to the Western Hemisphere


14. Which of the following is most likely to have influenced
eighteenth-century population trends in both Europe and
China?

(A) A sharp decline in average global temperatures
(B) Introduction of Western Hemisphere crops
(C) Innovation in birth control measures
(D) Improvement in surgical procedures


16. In recent decades, many world historians have challenged the
commonly held view that Europeans controlled the largest
share of world trade in the seventeenth through the eighteenth
centuries. Which of the following evidence from the period
would best support this historical reinterpretation?

(A) Prices for Chinese goods were much higher in Europe than
in China.
(B) European trading companies often backed their long-distance
trading ventures with the threat of military force.
(C) Asian trading companies dominated trade in the Indian
Ocean region.
(D) European merchants transported only a fraction of the
goods shipped globally.


19. Which of the following statements is true about both the
Mughal and Ottoman empires in the sixteenth century?

(A) In both empires the majority of the people were Muslims.
(B) Both empires had powerful navies that engaged European
navies.
(C) Both empires expanded through the use of gunpowder
weapons and extensive bureaucracies.
(D) Both empires gave little monetary support to artistic and
cultural endeavors.


22. In contrast to initial industrialization, the second Industrial
Revolution in the last half of the nineteenth century was
particularly associated with the mass production of which of
the following?

(A) Textiles, iron, and coal
(B) Textiles, automobiles, and plastics
(C) Airplanes, ships, and radios
(D) Electricity, steel, and chemicals

Feel free to try your hand at these questions by leaving a comment. If you want, I can supply answers, but only to the curious, and only after they've tried to respond. History buffs will probably find the above questions easy.





*Long-time readers know I consider multiple choice to be the worst possible testing format.


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Wednesday, May 2, 2012

this week's Math Beast Challenge problem

From here:

Rebecca had 288 Facebook friends, and noticed that an equal number of these friends had birthdays in each of the twelve months of the year. Then, Rebecca approved many friend requests at once. After doing so, the number of Rebecca’s friends with birthdays in the last quarter of the year increased by 25%, the number of friends with birthdays in each month beginning with “J” increased by one-third, the number of people with birthdays in February was increased by 12.5%, the number of people with birthdays in March became 166.6666...% of the new number of people with birthdays in February, the number of people with birthdays in April became five less than 75% of the new number of people with birthdays in February and March combined, the number of people with birthdays in May increased by 1, and the number of people with birthdays in August became one less than 20% greater than the new number of people with birthdays in May. Finally, September’s total increased to 6% less than one more than the new total for the month with the largest number of birthdays. Assuming no one de-friended her, after approving all her friend requests, how many Facebook friends did Rebecca then have?

(A) 396

(B) 408

(C) 453

(D) 512

(E) 696

Good Lord. Given the time it takes to read this problem, you'd run out of time to do the rest of the Quant section if this were an actual GRE! Anyway, go to it! I'm still sick, so my answer may or may not appear in the comments section below.


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