Archive for October, 2009

Fractions, Proportions and Ratios, Oh My!

Friday, October 30th, 2009

GMAT questions are notorious for seeming harder than they actually are. The writers recognize time is short, and will give you ostensibly time-consuming calculations. One way to mitigate this is by retaining a rockstar aptitude in manipulating fractions, which occur in a large portion of the questions.

Dividing by 5 is the same as multiplying by 2/10. For example:

  • 840/5 = ?
  • 840/5 = 840*(2/10) = 84*2 = 168
  • Multiplying or dividing by 10’s and 2’s is generally easier than using 5’s.

90% of the time, fractions will be easier to perform arithmetic. Decimals are sometimes more useful when comparing numbers relative to one another, such as in a number line, but these questions are the exception. Even if given a decimal (or percent) looks easy, quickly convert to a fraction. Some common ones to memorize:

  • 1/9 = 0.111 repeating
  • 1/8 = 0.125
  • 1/7 = ~0.14
  • 1/6 = 0.166 repeating
  • 1/5 = 0.20
  • 1/4 = 0.25
  • 1/3 = 0.333 repeating
  • 1/2 = 0.5 repeating
  • Note: Multiples of these, such as 3/8 (0.375) are also important to remember, but can easily be derived by multiplying the original fraction (1/8 * 3 = 3/8 = 0.125 * 3 = 0.375)

Denominators are super important. A denominator of a reduced fraction with a multiple of 7 will not have a finite decimal, for example. Keep in mind what you can logically combine, and what you cannot.

This list is by no means extensive. There are many many more shortcuts. If you have some, leave them in the comment field, but generally practice and familiarity with the numbers helps a lot in doing quick arithmetic.

Ratios

A ratio is both a comparison and division, and can simply be treated as such. “The ratio of boys to girls is seven to two” can be expressed as the proportion: B/G = 7/2. Do with this what you like: 7G = 2B or B = 7G/2, whatever. Forget the “:” with ratios.

GMAT writers love to provide ratios (which are multiplicative relationships) and then add an absolute component (addition/subtraction). Note that when you have a ratio like B/G = 7/2, we don’t actually know the number of girls and boys. There can be 14 boys and 4 girls, or 70 boys and 20 girls. Questions that insert absolute numbers should be taken with caution. For example:

At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?

A. 4
B. 6
C. 9
D. 12
E. 15

The key here is setting up the equation. Since we don’t know the initial scale of the number of cooks and waiters, we can express this scale by “x”.

C/W = 3x/13x.

Notice that whatever x is, the ratio will hold true. (x must be an integer, since you can’t have a portion of a cook, unless of course he chops his finger off by accident!)

“When 12 more waiters are hired” is the insertion of an absolute. Adding the 12 waiters, the new ratio becomes:

C/W = 3x/(13x + 12)

“The ratio of the number of cooks to the number of waiters changes to 3 to 16” defines this new ratio:

C/W = 3x/(13x + 12) = 3/16

STOP! Before we cross multiply and solve for x, we want to cancel out the 3’s in both the numerator. (More on this below.) After cross-multiplying, we get:

16x = 13x + 12
3x = 12
x = 4

Sweet. Answer A, right? Well, recall that x represents the scaling factor. The stimulus asks for the number of cooks, which we originally represented by 3x. So, 3*4 = 12 cooks. That’s 120 fingers. Choice D.

Proportions

A proportion is two ratios set equal to each other like the question above. Generally, there is a variable in one of the four slots, and we are taught to cross-multiply and solve for that variable. Before you do that, however, it’s best to reduce top-bottom AND left-right before cross multiplying. This will ensure you work with the smallest (and easiest) (and fastest) numbers possible. For example:

A football field is 9600 square yards.  If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards?

A. 450
B. 600
C. 750
D. 2400
E. 3200

The key word here is “spread evenly”. This implies that the relationship of fertilizer per square foot is uniform, and you can set equal the relationship of the wholes to the relationship of the parts.

A/F = 9600/1200 = 3600/x

Clearly, we can eliminate the zeros on the left side:

9600/1200 = 3600/x

96/12 = 3600/x

Then we can divide 96/12:

8 = 3600/x

Here, we can still reduce left-to-right, by canceling 4 in both:

2 = 900/x

Oh wait! There’s more! Both 2 and 900 are divisible by 2!

1 = 450/x
x = 450

It DOES NOT matter whether you start top-bottom or left-right, so long as you are reducing by the same factor. Also, start with small numbers. No need to go for the biggest common factor. You’ll eventually work your way down as the numbers progressively get easier. For this question we could have started by canceling 9600 and 3600 in the numerators, which are both divisible by 400 to get:

24/1200 = 9/x. You can take it from here. Check out Grockit for more quantitative practice!

Good luck!

Coordinating Conjunctions: “And,” FANBOYS Part 2/7

Thursday, October 29th, 2009

This is the second of a short series of articles on the short list of what are known as coordinating conjunctions, short words themselves that show up very frequently in the GMAT Sentence Correction questions. Learning them can save you time, allowing you to eliminate wrong answer choices quickly and confidently; understanding them will of course also help add style and clarity to your AWA and admissions applications.  These coordinating conjunctions are often remembered by the acronym FANBOYS (For, And, Nor, But, Or, Yet, So); their job in a sentence is joining two or more parallel  . . . well, things in a sentence.

  1. These words can join single words (Would you like sausage or mushrooms on your pizza?);
  2. whole phrases (He plans to sit around in his underwear today and put off doing laundry until the end of the week);
  3. or entire independent clauses — things that would stand alone as complete sentences without the conjunction (I would love to try the peaches, but the fuzz gives me the chills).

The things these conjunctions connect must be the same type of thing — an adverb and another adverb, a noun and a noun, an independent clause with another independent clause.  Just as you can only add fractions when they have the same denominator, you can only use parallel parts with coordinating conjunctions.  All of these coordinating conjunctions also have at least one other job in English.

II.  AND

And is the second of our FANBOYS; it is the most common of them all.  You are likely familiar enough with it from everyday use, but and does have a few uses you might not have considered; and also provides one major source of Sentence Correction errors for the GMAT.  And is the “+” of the verbal world at its most basic level, but can also be used (sometimes in place of other words) to show unexpected opposition, result, comparison, contrast, consequence, and order of events in time.

  • Unexpected opposition (the word yet is used more commonly): He drank, smoked, and ate red meat every day for 77 years, and he died in an accident at the age of 98.
  • Result: She failed the test and was not admitted into the journalism program.
  • Comparison (the word but is used more commonly): In the same concentration, sugar is sweet and sucralose is 600 times sweeter.
  • Contrast (the word but is used more commonly): For most people, being kissed on the lips feels good and being punched in the face feels bad.
  • Consequence: Ignore my advice and you’ll be sorry!
  • Order of events: The bus driver saw the tornado and turned down a country road to avoid it.

That said, there are two principal rules of and that should concern you on Test Day:

  • Rule 1: Things joined by and need to be parallel.
  • Rule 2: And is the only word that can make a plural subject out of singular nouns.

The first rule should be familiar to you from the many, many places where the GMAT and the English language require parallelism, so we will focus on the second one.  As you will have seen if you have done any GMAT Verbal practice at all, the makers of the test love to put modifying phrases between the subject and the verb.  It is important to remember the subject of the sentence, no matter how many other people, places, and things get added in by means of these other phrases.

My dog has fleas.
My dog, Kitty, has fleas.
My dog, a large German Shepherd named Kitty, has fleas.
My dog, a large German Shepherd that I named Kitty in honor of a comic book character from some of my favorite stories and movies, has fleas.

Note that dog is the singular subject, and despite all the intervening words, it has a singular verb.  The GMAT will frequently separate the subject from the verb, place non-subject words of a different number closer to the verb (as I did with movies right before has above), or both.  However:

My dog and my cat have fleas. (the word and makes the subject plural, since two creatures have fleas)
My dog, along with all other dogs in my neighborhood, has fleas. (even though many dogs have fleas in this sentence, the other dogs are not part of the subject, and therefore have no impact on the singular verb)

In the next article we will cover: Nor

Read other articles in this series:
Coordinating Conjunctions: “And,” FANBOYS Part 1 of 7

HBS 2+2: The Timeline

Wednesday, October 28th, 2009

It’s your junior year of college and you think you’re interested in applying for Harvard’s 2+2 Program. What do you do now?

First, why Harvard 2+2? Entering its third application cycle in 2010, the 2+2 program is open only to college juniors or the equivalent, basically any students that have at least one term left in their undergraduate careers. Rumors abound about what types of students HBS is looking for, but the bottom line is that they want leaders across the spectrum, beyond just the traditional consulting-to-business school track.

While the application isn’t due until July 1st, so the summer after your junior year, don’t leave everything for those last few weeks. Planning ahead is crucial in order to get a solid GMAT/GRE score as well as work on those essays.

Check out Harvard’s website for more information and a timeline. But here are the major things to consider as you’re preparing your application.

1. Taking the GRE or GMAT

First, which exam should you take? While both are graduate entrance exams, the GMAT and GRE differ in format and focus. Both start with two essays designed to examine your analytical writing skills. Then the GMAT has two 75-minute sections (38 questions in Quantitative, 41 in Verbal) while the GRE has four 30-minute sections, two each in Verbal and Quantitative. Take a look at some practice questions for each exam and use the freedom you’re given to take the exam that best fits your skill set.

Check my article on taking the GMAT in college for tips on scheduling your exam around your academic schedule and responsibilities.

Note that international applicants must also take the TOEFL or IEST to prove proficiency in English.

2. Recommendations

Two recommendations are required for the application and they are submitted online. You will be asked to provide the names, titles and email addresses for your recommenders and they will be contacted electronically to submit the recommendation.

Whether you choose to ask a former professor or an employer at your on-campus job, choose someone who knows you, your motivations, your career goals, etc. The recommender will be asked to rate you on a variety of skills and traits, as well as provide paragraph-length responses. The more your recommender knows about you, the better and the more powerful their recommendation.

It’s your responsibility to make sure the recommenders fill out the forms by July 1st. Your application will not be considered complete without the two recommendations, so be sure to ask early and don’t be afraid to send a reminder or two if you see that they haven’t submitted it yet.

Also, don’t forget to thank your recommenders for taking the time to fill out the recommendation. A hand-written card and small gift (e.g. box of chocolates, gift card to a coffee shop, etc.) go a long way.

3. Essays

There are four essays that are part of the application. Three are required and the fourth gives you three options.

For the 2009 application, the questions were as follows:

1. What are your three most substantial accomplishments and why do you view them as such? (600-word limit)

2. What would you like us to know about your undergraduate academic experience? (400-word limit)

3. What have you learned from a mistake? (400-word limit)

4. Please answer one of the following (400-word limit each):

  • Discuss how you have engaged with a community or organization.
  • What area of the world are you most curious about and why?
  • What is your career vision and why is this choice meaningful to you?

Since these essays are really a window into your personality and motivations, make sure you show the admissions commitee what you’re all about. Your transcript, resume and recommendations already say a lot about your academics and work experience, so use your essays wisely and either cover elements mentioned in those other components more in-depth, or explore other interests that are not covered elsewhere in the application.

4. Transcript

There are two options for reporting your academic record. You can either submit a self-reported transcript by filling out a pre-formatted Excel spreadsheet, or scan a copy of your official transcript. Both must be uploaded to the application website.

Depending on how your college organizes classes, it may be easier to obtain a transcript and upload it. The self-reported form is not the most conducive to recording AP credits or colleges who offer a system that is not based on credit hours.

Grades are required through the end of your junior year, so plan ahead. If you go to a school on a quarter system, in which the year does not end until mid-June, remember that the registrar’s office will be busy with the graduating class. Familiarize yourself with the procedures of obtaining an official transcript and understand that some offices take a few days to process a transcript request, so don’t wait until June 29th to request a transcript.

The 2010 application will officially be available in the spring 2010, but start planning ahead if you truly think you’re interested. Plus, since scores are good for five years, taking the GMAT/GRE would be nice to get out of the way while you’re still in school.

Best of luck! Check out more blog posts on the application process and visit the Grockit forums for more tips!

The Semicolon: Not Just Another Winky Face, Part II

Tuesday, October 27th, 2009

In the last article on the semicolon, we covered how it’s used as a kind of “meta-comma,” separating list items that already have commas themselves.  The second of the two uses requires a definition: the clause. In grammatical terms, a clause has a subject and a verb. Clauses are either independent or dependent; independent clauses can stand on their own as complete sentences ( . . . which is why they’re labeled “independent”), while dependent clauses cannot.

Do you need to know that in order to use semicolons correctly? No, but some people like to know that sort of thing.

the empire strikes back
I ate all of my pudding

where is that darn cat?

leave it to Beaver

girls rock

Independent clauses (“complete sentences”):

Dependent clauses (not complete sentences):

while you were sleeping
when Harry met Sally

ever since I bought that monkey

because the fuzz gives me the chills

(You might have noticed that if you were to take away the first word or two from each of those dependent clauses, you would have an independent clause again [“Harry met Sally”]; that’s a topic for another time. Our topic is semicolons!)

So, simply put: if the clause on each side of the typographical spot in question is an independent clause – if each of them can stand alone as a complete sentence – if you could sleep at night knowing you put a period and a capital letter there instead, then you can put a semicolon in there. If not, you can’t. Stylistically, some places are better for semicolons than others, of course, but the two parts connected by a semicolon should be related in some way, connected a little more closely than a period would suggest in the same place.

We’ve covered the rules, and how they can help your writing, but what about the test? Take this GMAT-type Sentence Correction question as an example:

The chairman of the board, who was very sorry to learn that he’d acted on incorrect information, should not be held responsible to decreasing revenues or falling stock prices; though many have suggested he should.

A. should not be held responsible to decreasing revenues or falling stock prices; though

B. should not be in a position of responsibility for decreasing revenues or falling stock prices, though

C. should not be held responsible for decreasing revenues or falling stock prices, though

D. was not to be held responsible for decreasing revenues or falling stock prices; though

E. was not to be held responsible to decreasing revenues or falling stock prices, though

One of the main Sentence Correction tactics is the elimination of repeated errors vertically in the answers, improving your odds dramatically. When faced with a semicolon (or more than one) in the answer choices, your instinctive reaction should be to judge quickly whether the clauses on both sides are independent; if both clauses are not, that answer with the semicolon is incorrect. Be careful; some Sentence Correction questions make more changes from answer to answer, so crossing off one choice with a semicolon does not automatically enable you to cross them all off.

In this question, ignoring the other errors, we see A and D have a semicolon before “though;” we react by distilling the sentence down to its bare minimum: “The chairman should not be held responsible; though many have suggested he should.” Is “the chairman should not be held responsible” able to stand on its own as a sentence? Yes, it is! Is “though many have suggested he should” able to stand alone as a sentence? No, it cannot – so we can eliminate choices A and D, improving our odds of getting the correct answer to 1 in 3, and we still have to look at the other errors!  ;)
See the first article in this series:
The Semicolon: Not Just Another Winky Face, Part I

Possessive Pronouns: His, Hers, Mine, and all Their Cohorts

Monday, October 26th, 2009

Grammar is, of course, an issue of concern on the Sentence Correction questions seen on the GMAT.  But good grammar is also generally helpful and is of special importance on the writing sample, which is your chance to show the admissions committee that you are adept at communicating in written English.  To improve your writing in general, sometimes it’s worthwhile to explore concepts in grammar that are only infrequently tested on the Verbal portion of the test.

One example of this kind of grammar issue is the possessive pronoun.  Possessive pronouns are similar to their non-possessive cousins, regular pronouns.  Both must have a clear antecedent, and both must agree with that antecedent in gender and in number.  There are a few tricky rules that come into play with possessive pronouns that you don’t see elsewhere, however.

1.  No apostrophes needed

When turning a regular singular noun into a possessive noun, one usually uses an apostrophe followed by an “s”.  An example would be “the librarian’s book.”  However, if we replace “the librarian’s” with a possessive pronoun, it would say “his book” or “her book,” no apostrophe needed.  People often become particularly confused by the possessive form of one specific pronoun: it.  The rule here is that “it” is followed by an apostrophe and an “s” only to indicate the contraction of “it is.”  The possessive form of the pronoun is “its.”

2.  Possessive pronouns typically function as adjectives

A possessive pronoun is used to describe a noun, as in the examples seen above.  The location of the adjective in the sentence can determine its form in some cases: one would speak of “her book,” but a descriptive sentence would say that “the book is hers.”  The same holds true for “their” and “theirs,” “your” and “yours,” and “our” and “ours.”  The possessive pronoun “my” changes form more dramatically; “my book” becomes “the book is mine.”

3.  Relative pronouns can also be possessive

Relative pronouns that we often use in the nominative case (who, whoever) or in the objective case (whom, whomever) also have a possessive case: “whose” and “whoever’s.”  “Whoever’s” is an exception to the “no apostrophes” rule, but you shouldn’t worry too much about it as it is rarely tested on the GMAT.

Example

A plan is being considered to cut costs by limiting the number of shrimp ingested by the flamingos at the zoo; one concern is that visitors may not be as interested in seeing the flamingos if their feathers aren’t as vividly pink.

A.  that visitors may not be as interested in seeing the flamingos if their feathers aren’t as vividly pink

B.  that visitors may not be as interested in seeing one once their feathers aren’t as vividly pink

C.  that visitors may not be as interested in seeing the flamingos if the birds’ feathers aren’t as vividly pink

D.  which visitors may not be as interested in seeing the flamingos if the birds’ feathers aren’t as vividly pink

E.  which visitors may not be as interested in seeing one once the birds’ feathers aren’t as vividly pink

In the original sentence, the possessive pronoun “their” is used; however, this pronoun has no clear antecedent, since there are two plural nouns in the sentence.  Although common sense tells us that “their” refers back to the flamingos, grammatically speaking, it could also refer to the visitors.  Therefore, the correct version of the sentence must clarify the possessors of the feathers.  That allows us to rule out both A and B.  “Which” versus “that” is another frequently tested issue, and here the correct choice is “that,” allowing us to rule out choices D and E.  “Which” in D and E would change the meaning of the sentence.  The remaining choice, C, correctly uses “that” and also replaces “their” with “the birds’,” which clarifies the sentence’s meaning.  While this choice is longer than some of the others, it is the only one to fix the possessive pronoun error without creating a new error.

Overall, possessive pronouns should be handled much the same way as the nominative and objective pronouns: check for agreement, and make sure that there is a clear antecedent in the sentence.  The less-common issues associated with possessive pronouns are rarely tested in sentence corrections, so a brief review of apostrophe placement and forms should be sufficient to help polish your writing sample.

Go to Grockit and join a GMAT verbal game for more sentence correction practice!

The Semicolon: Not Just Another Winky Face, Part I

Friday, October 23rd, 2009

There are two absolutely central and simple rules for the use of the semicolon (“;”), and learning these will improve both your Sentence Correction skills and your writing in general — remember, in addition to getting lots of questions right on the GMAT, you will need to write actual sentences on your AWA, in your personal statement, and in your MBA classes!  The rules for the use of the semicolon are:

  1. When writing a list of things, and those listed things have commas themselves, separate the items in the list with semicolons.
  2. When joining two related independent clauses (“complete sentences”) into a single sentence, place a semicolon between them.

That’s all! The first is the simpler of the two; we’ll cover the second in another post.  According to the first rule, the semicolon acts as a kind of “meta-comma,” a bigger divider separating the other dividers properly so that the reader can make sense of a list:

“Erika loves to travel and has visited many places: Iona, Scotland, Seattle, Washington, Beijing, China, and Calgary, Alberta.”

A less careful reader might think she’s visited eight different places rather than four; a careful reader will get it right, but may well become frustrated with the author. It is not in your best interest to frustrate the admissions officer reading your personal statement! A semicolon makes it clearer:

“Erika loves to travel, and has visited many places: Iona, Scotland; Seattle, Washington; Beijing, China; and Calgary, Alberta.”

You might also see commas setting off modifying phrases within a list:

“Henrik couldn’t stand to eat certain foods: sushi, which made him jealous of people who lived near the sea; anything that came from sheep, such as lamb and mutton; and peaches, because the fuzz gave him the chills.”

It’s not important to remember any of the different reasons you might have commas within your list, though, as long as you remember to separate your list items (when you do have commas within them) with the “meta-comma,” the semicolon.  In the next article, we’ll cover the other, more-tested use of the semicolon (joining two independent clauses).

Make sure to visit Grockit’s GMAT blog for part 2!

Passive and Active Voices on the GMAT, and When They Matter

Thursday, October 22nd, 2009

What’s the difference between these two sentences?

He spoke clearly, articulating the points of his plan.

The points of his plan were articulated in his clear speech.

The first sentence is written in the active voice, and the second is written in the passive voice.  In the first sentence above, the subject is “he,” and the verb is “spoke.”  In the second sentence, the subject is “the points of his plan” and the verb is “were articulated.”  When writing in the active voice, the subject of the sentence is performing the action; in the passive voice, the subject of the sentence is the object of an action. Distinguishing between passive and active voices can be tricky, but it’s worth some practice.  This is because sometimes, on GMAT Sentence Corrections, you will narrow the choices down to two correct answers.  Both are grammatically sound, and you end up guessing because you can’t think of any good reason to reject either of them.  That’s a frustrating situation, and often the difference between the two answer choices comes down to passive and active voices.

Passive and active voices are troubling for some test-takers, because their application seems to be random; sometimes, the credited answer to a Sentence Correction will be in the passive voice, but other times, a choice will be eliminated for being in the passive voice.  How can you tell when it matters and when it doesn’t?  Generally speaking, the GMAT favors the active voice.  Sentences written in the passive voice can still be correct, though, if every other choice has a grammatical flaw.  Passive voice should never be used to eliminate an answer in your first glance through the choices.  However, if you’ve narrowed the answers down to two grammatically correct options, and the ONLY difference is that one is active and the other is passive, then you can eliminate the passive choice.

Basically, the use of the passive voice isn’t considered an error in GMAT Sentence Corrections.  It’s more of a style issue.  The GMAT favors concise writing: statements are ideally made as succinctly as possible.  The use of the passive voice tends to clutter sentences up, making them lengthier and more complicated than necessary.  But if every other choice has definite error—incorrect pronoun usage, subject-verb disagreement, or a misplaced modifier, for instance—a choice using the passive voice can be correct.  Let’s look at an example:

According to the manager, his plan could be successfully implemented by all of the company’s branch offices before the end of the fiscal year.

A.  his plan could be successfully implemented by all of the company’s branch offices before the end of the fiscal year.

B.  his plan being the subject of successful implementation by all of the company’s branch offices before the end of the fiscal year.

C.  his plan could be successfully implemented by all of their branch offices before the end of the fiscal year.

D.  the company’s branch offices successfully implementing his plan before the end of the fiscal year.

E.  the company’s branch offices could be successfully implemented to his plan before the end of the fiscal year.

In this Sentence Correction, the sentence as written displays the passive voice, although it is otherwise correct.  Each of the other choices has a distinct error: choice B uses “being,” which is virtually never correct on the GMAT; choice C replaces “the company’s” with “their,” a possessive pronoun with no clear antecedent in the sentence; choice D’s use of the gerund creates a sentence fragment; choice E uses an incorrect idiom.  Therefore, the passive construction is correct.  However, an active construction would be the preferred style, and that would look like this:

According to the manager, all of the company’s branch offices could successfully implement his plan before the end of the fiscal year.

When it comes to dealing with passive and active voices on the GMAT, think of this style issue as your second line of defense.  Real grammatical errors should be the first thing that you address when you’re going through the answers and eliminating them, but in the event of a tie, the use of passive voice can be a tie-breaker.  This should help you recognize when the use of passive voice matters to you in choosing an answer, and when it doesn’t.

Join a customized tutoring game on Grockit for more sentence correction practice!

When to Use “That” and When to Use “Which” on the GMAT

Wednesday, October 21st, 2009

A common point of confusion among those studying for the GMAT—as well as the general writing public—is the difference between “that” and “which.”  Knowing which of these words to use in a given situation can often allow you to eliminate a couple of answer choices, speeding up your verbal test-taking and ultimately helping to improve your score.

The simplest way to remember the difference is by noting that “which” introduces information that isn’t crucial to the meaning of the sentence, known as a non-restrictive or non-essential clause, while “that” introduces a restrictive clause.  For example,

I am going to wear the sweater that is blue.

I am going to wear the sweater, which is blue.

In the former sentence, “that is blue” functions to restrict the meaning; the implication is that there is more than one sweater, but only one blue one, and the blue one is the one I’m going to wear.  In the latter sentence, the phrase “which is blue” merely provides more information about the sweater.  The sentence’s meaning wouldn’t change dramatically without the “which is blue,” because the information is non-essential.

An example of this kind of sentence on GMAT Sentence Corrections might look like this:

Thanks to medical research, many diseases which might have been fatal at one time are now easily prevented by childhood vaccines.

A.  which might have been fatal at one time are now easily prevented by childhood vaccines

B.  that might have been fatal at one time are now easily prevented for childhood vaccines

C.  which might at one time have been fatal without childhood vaccines

D.  that might have been fatal at one time are now easily prevented by childhood vaccines

E.  which might, without the current prevention by childhood vaccines, have been fatal

In this sentence, the meaning should be restricted; the diseases to which the sentence refers are specifically those that might have been fatal at one time.  Therefore, the correct answer choice will use “that” instead of “which.”  Choice A can therefore be eliminated, as can C and E.  In addition, the structures of both C and E are sentence fragments; everything following “which” in those choices functions to describe “diseases,” leaving the sentence without a central verb.  Choices B and D both use “that,” but choice B uses the wrong idiom: it says “prevented for” instead of “prevented by,” which changes the meaning of the sentence.

A second example might look like this:

Global warming that has attracted a great deal of media coverage recently will be a central issue in the upcoming campaign, since both candidates champion environmental causes.

A.  Global warming that has attracted a great deal of media coverage recently will be

B.  Global warming that will be attracting a great deal of media coverage recently will be

C.  Global warming, which will be attracting a great deal of media coverage recently, will be

D.  Global warming, which recently is being the subject of a great deal of media coverage will be

E.  Global warming, which has attracted a great deal of media coverage recently, will be

Here, the adjective clause “has attracted a great deal of media coverage recently” should be non-restrictive.  There is no indication that a specific kind of global warming will be a central issue.  Instead, the sentence implies that global warming will be a central issue in the upcoming campaign, and “global warming” is further described as having “attracted a great deal of media coverage recently”.  The meaning of the sentence would not be substantially changed by removing the information about media coverage.  Therefore, “which” is appropriate in this sentence.  A and B can be eliminated for this reason; in addition, B can be eliminated because the future tense “will be attracting” is inconsistent with “recently.”  Choice C has the same verb tense issue as choice B, and can therefore be eliminated.  Choice D uses “being,” which is almost never correct on the GMAT, and also neglects to put the necessary comma after “coverage” at the end of the adjective clause.  The final choice, E, does everything right: the verb tenses are appropriate, punctuation is correct, and “which” is properly used.

FINAL THOUGHT: Separating restrictive and non-restrictive or non-essential clauses allows you to correctly choose whether to use “that” or “which” in GMAT Sentence Corrections, and like most grammar issues, it becomes much easier with practice on Grockit!

The Business School Application Process: Step 3: Test preparation

Tuesday, October 20th, 2009

You’ve decided you want to go to business school. You’ve done your research. You’ve created your own system to manage your application process. Next, it’s time to get the biggest hurdle out of the way:
Step 3: Prepare for and take the GMAT.

I could write about test prep all day, but the goal for this entry is to help you setup a study-and-execution plan for tackling the GMAT.
Determine which test(s) you will need to take.

This may sound like a no-brainer, given that the GMAT is the standard exam for business schools, but most schools now accept the GRE as well. Take advantage of this and take the exam that fits your skill set best. Additionally, for students who were educated abroad (in locations other than the U.S.), most graduate programs require a TOEFL (Test of English as a Foreign Language). Research your particular program(s) at your particular school(s) to ensure you’re covering all your bases.
Learn all about the test(s).

Enter the name of the test (GMAT, GRE, TOEFL) into a search engine. Find out the test provider, then go to the testmaker’s website. Read up on the format and scoring of the test, content tested, and time restrictions. Find out where you’ll be taking the test and what you are and are not allowed to bring with you to the test center.

Questions you should be able to answer about the test(s) you need to take:

* Is this a paper-and-pencil test, a computer-based test, or a computer-adaptive test?
* What’s the difference between a computer-based test and a computer-adaptive test? (if applicable)
* Will I be penalized for wrong answers or unanswered questions?
* What content is tested?
* What types of questions appear in each section?
* How many questions of each type in each section?
* How much time is allotted for each section?

To help you on your way, here’s where you can find information on the GMAT and GRE from the testmakers:

* GMAT — test administration organization: GMAC; website: www.mba.com
* GRE — test administration organization: ETS; website: www.ets.org/gre/

Devise a well-rounded and layered study plan.

There are countless different preparation methods available to you; the sheer volume of materials and resources available can be overwhelming. Should you take a class? Study alone? Hire a tutor? Which books should you use to study? Should you practice on the computer? Should you study math content? If so, which content? Should you focus solely on testing strategy? If so, what strategies are most effective?

How you prepare–class, solo study, tutor–is up to you. But here’s what you must do:

* Always start with an actual practice test, preferably a sample test released by the testmaker. That’s your baseline, and it’ll help you figure out your natural strengths and weaknesses in both content and strategy. Both the GRE and GMAT have these available, for free, on their websites.
* Balance your approach. Your preparation should include a combination of content-based study, test/question/section strategy, and test simulations.
* Your early preparation should be dominantly content-oriented, with a moderate dose of question-type strategy and very little, if any, test-like practice. Take advantage of the time you have to really shore up your weaker areas, but make sure you don’t neglect your strengths. Taking too many practice tests or sections too early in the game merely reinforces bad habits, making them harder to break later on.
* Your mid-range preparation should be a balance between content-oriented study and question- and section-strategy practice, with some test simulations.
* The final stage of your preparation should be primarily test simulations, with detailed post-mortem analysis of each test from all points of view (weak content areas, troublesome question types, and section/test strategy issue management). Make sure you take adequate time in your analysis to learn from your mistakes.

As for the solo study/class/tutor question, you’ll need to do some self-reflection here. If you tend to do well on standardized tests and you have great self-discipline, then solo study might be fine. If you’re slightly less disciplined, then the structure of a class might do you well. And it’s always great to have the advice of an expert available in a class or through a tutor, but cost is a factor to consider (and add to your budget, should you choose one of these options).
Use quality materials.

With the stockpiles of material available to you, it’s easy to get overwhelmed. The first and best material to use is the material released by the testmaker. Get your hands on previously released tests and free practice materials, usually available on the testmaker’s website. You may also be able to purchase additional prep materials through the website or at your local or online bookstore.

To supplement the testmaker’s resources, join some online forums and read through the posts of other test takers. Use an internet search engine. Play on Grockit!

Your materials should provide a mix of formats, at least some of which should be very similar to that of the test.
Do test simulations.

Never, and I mean never ever, take a standardized test without doing a healthy amount of test simulation practice. Make sure your test simulations are as test-like as possible: place yourself in a similar environment, observe time constraints strictly, use only the resources you will be permitted at the test site (i.e., don’t use your calculator unless your test permits the use of one), and take only the allotted breaks.

After learning about the test format, always start your preparation with an actual practice test, preferably a sample test released by the testmaker. Take it before you review any content (and likely waste time reviewing stuff you already know or didn’t need to know). That’s your baseline, and it’ll help you figure out your natural strengths and weaknesses in both content and strategy.

Don’t do too many prep tests until you’re comfortable with the knowledge that your test-taking habits are correct and consistent. As you shift into your later phases of preparation, you should ramp up the frequency of your simulations. Once you’ve scored three times at in acceptable score range, you’re ready to take the real thing.

Once that’s done and your scores are finalized, it’s time to get to the paperwork.

Check out other articles in this series:
The Business School Application Process Part 1
The Business School Application Process Part 2

Systems of Equations in Data Sufficiency

Monday, October 19th, 2009

If the GMAT Quantitative section were 3 hours, all of our lives would be easier. We could take our time, work through each solution, check our choice, and sharpen our pencil before each question. Since we are not afforded this luxury, we must take back every second we can. Data Sufficiency questions are a great place to start, since most students take too much time solving the problem instead of assessing whether it’s possible to solve the problem. Here we’ll look at common DS time-saving techniques through the lens of systems of linear equations.

2 Linear Equations, 2 Variables, 1 Solution

We learned back in 9th Grade that if you have 2 linear equations with 2 variables, there will always be one unique solution. For Data Sufficiency questions, we can seek out these equations in the stimulus and statements and (without calculating) know if we have enough information. For example,

If the mileage on car X is currently exactly 3 times the mileage on car Y, what is the mileage on car X?

(1) When each car had 6,000 miles less than they have now, car X had 4.5 times the mileage that car Y had.

(2) When each car has 2,000 miles more than they have now, car X will have 2.75 times the mileage that car Y will have.

Stimulus: x = 3y

Statement 1: (x – 6000) = 4.5(y – 6000)

Statement 2: (x + 2000) = 2.75(y + 2000)

Visually, this is a lot easier than dealing with cars and mileage. Again, we do not need to calculate. Since an equation is GIVEN in the stimulus, we just need one more to find the unique solution for x. Each statement is sufficient. Choice (D).

Caveat #1: Same Equation Disguised

A dry cleaning store charges a certain price to clean either shirts or pants and a certain price to clean jackets. Robert, Scott, and Ted each had some clothing items cleaned at this store. How much did Scott pay to have 1 shirt and 1 jacket dry cleaned?

(1) Robert paid $15 to have 3 shirts, 1 pair of pants, and 2 jackets dry cleaned.
(2) Ted paid $30 to have 5 shirts, 3 pairs of pants, and 4 jackets dry cleaned.

The stimulus has no equation, but does show that shirts and pants costs the same, and in turn should be considered the same variable when extracting our equations.

Statement 1: 15 = 4s + 2j (s is the combined number of shirts and pants)

Statement 2: 30 = 8s + 4j

Here, we have two equations and two unknowns, so the answer should be (C), right? What’s interesting about these two equations is that they are exactly the same! Divide (2) by 2 and you get (1). Graphically, this is a line on top of itself, with an infinite number of solutions. Beware of caveat #1—one equation disguised as many. Choice (E) is correct.

Caveat #2: Non-Linear Equations

What is the value of x?

(1) 3y – 8 = x

(2) x(x+1) = 2y

Two equations and two unknowns. No problem, right? Well, first, let’s think of this graphically. Statement 1 is a simple line with a slope of 1/3 and a y-intercept of +8. Statement 2, however, is a parabola, not a line. Because the coefficient of the x^2 term is positive, the parabola will open upwards, and intersect the line from Statement 1 in two places. There is not a unique solution, because x is squared in Statement 2. However, depending on the restrictions in the stimulus (say, if x>0) can still assist in finding a unique situation. So beware of exponential equations, but also note any restrictions that may limit your options. (In fact, if this stimulus included x>0, then there is a unique solution for this question.)

Set up Equation Quickly and Move On, If At All

In many instances, the actual numbers do not matter for Quantitative DS questions. In fact, the more “wacky” the number looks to you, the more likely you won’t need to “use” it. For the question below, you may note $5,750 and think to yourself, “I’ve never done any calculation with that number, what the hell!” And you’re right. The more important piece of information is that there is a number, and for DS, sometimes that’s all you need.

For a certain company X, the average daily payroll for each 30-day payroll cycle is the average (arithmetic mean) of the daily payroll totals for each of the 30 days. During the first part of a recent 30-day payroll cycle, the daily payroll was a constant $5,750. When a new employee was hired during this 30-day cycle, the total payroll for each day rose by $280. If the new daily payroll total remained constant for the remainder of the cycle, what was the average daily payroll for the 30-day cycle?

(1) The new employee was hired on the 11th day of the payroll cycle.

(2) The average daily payroll was $5,890 through the first 20 days of the cycle.

To know any weighted average, we simply need the number of observations at each rate. Statement 1 tells us that we will be at one rate ($5,750) for 10 days, and another rate for the remaining 20 days ($5,750 + $280). Statement 2 tells us that for x days we are at a $5,750 rate, and then for (20 – x) days at that rate rose by $280, and provides the weighted average. We can solve for x in each, since each has one linear variable in an equation, and we have all the other information we need.

Spend time to set up equations only if there is confusion as to what information is missing, or as to what is needed. Otherwise, don’t waste your time on DS questions finding a concrete solution. Save that for the Problem Solving questions.

Any other time-saving tips? Please visit the Grockit forum or leave a comment here to discuss further.