Analogy Strategy: Degree

jordan schonig September 2, 2010

After you do a few analogy problems, you’ll probably realize that, even if the words are new, the relationships tend to repeat themselves. The more familiar you become with these stock relationships, the better. One common relationship that often throws off students is degree.

In a degree analogy, one word is often a stronger, more intense, or more extreme version of the other word. When you are trying to articulate the relationship between the stem words, the words ‘very’ and ‘extreme’ will be very helpful.

1. EMACIATED: THIN

In this example, your first instinct might be to identify the stem words as synonyms. After all, emaciated and thin mean close to the same thing. Whenever you instinctually identify two words as synonyms, however, always ask yourself if they differ in degree. In this case, they do. Emaciated can be described as very thin. Calling somebody emaciated and calling somebody thin are two very different things, and you should be able to identify the difference.

2. INDULGENCE: DEBAUCHERY

In this case, using the word ‘very’ will not help you. Why not try using the word ‘extreme’ to help you form a relationship between the words? We can say that debauchery is an extreme form of indulgence, involving excessive drinking and promiscuity. Because you cannot qualify a noun with the word ‘very,’ using the word ‘extreme’ would make more sense. However, you can always change the part of speech in your mind. You could say that a debauched person is very indulgent. If you wish to change the part of speech, though, remember to do the same with the answer choices.

3. POKE: BLOW

Here, we might be confused by the ambiguous word ‘blow.’ The only definition of blow related to poke would have to be ‘a punch.’ In that case, then, a poke is a weak or less intense punch.

4. EUPHORIC: CONTENTED

Euphoric is an extreme version of contended, or euphoric is very contented.

5. MURMUR: YELL

A murmur is a much softer, less intense, or less extreme version of a yell. Or, if we determine the stem words to be verbs, we can say that ‘to murmur’ is to ‘yell softly.’ We can even reverse the relationship: “to yell is to murmur loudly.”

The main tip to remember with degree relationships is to get used to distinguishing between synonyms and closely related words that vary by degree. Try to imagine using the words in context. Would you use the words differently? Would somebody react differently to the substitution of one word for the other? Once you become comfortable with these questions, identifying degree relationships will be quite simple.

Please visit the Grockit forum or leave a comment here to discuss further.

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Structuring Your Analysis of An Argument Essay

andrea alexander August 31, 2010

Your GRE essays are unlikely to be the linchpin of your application.  Although I don’t like to say “never,” I personally have not heard of a student getting into grad school because of his or her GRE essays.  It certainly seems possible, though, that your essays could keep you out, if your entire application package is borderline and you write one or two truly awful essays.  For that reason, it’s important that you keep the AWA in perspective: it shouldn’t take up much of your prep time, but it’s certainly to your advantage to spend some time familiarizing yourself with what makes for a good essay, and getting some feedback from a qualified source, whether that is a professional mentor, a professor, or a test-prep specialist.

Of the two essays you’ll be expected to write, the Analysis of an Argument is likely to be the more challenging, if only because the task is not a familiar one to most grad school candidates.  The easiest format to use in writing this essay is the classic 5-paragraph style, and a simple, effective format will look something like this:

  • Paragraph 1: Brief recap of argument and statement that the argument has merit but also contains multiple flaws.  Also include a “roadmap” of the points that you will make, in the order that you will make them.
  • Paragraph 2: Explanation of first flaw– this paragraph should have a strong topic sentence and then several sentences explaining the flaw in detail.
  • Paragraph 3: The second flaw gets the same treatment here as the first one did in the previous paragraph.
  • Paragraph 4: The third flaw is explained here in the manner established in the previous two paragraphs.
  • Paragraph 5: Briefly recap the flaws you’ve presented and diplomatically explain how those flaws could be remedied to present a stronger argument.

A good rule of thumb is that your reader should be able to get the gist of your entire argument just by skimming the first sentence of each paragraph.  Remember, your reader is probably going to devote no more than three to five minutes to your essay.  Take a few minutes at the beginning of your AWA to outline the five sentences that will begin your paragraphs; this strategy can make your reader’s job far easier, and a happy reader is probably more apt to make those tricky 4/5 line calls in your favor.  Similarly, the e-reader is programmed to assess organization, and well-written topic sentences that use transition words and clearly state the point of each paragraph are a big help in creating the kind of organizational structure that earns you points on test day.

To start your essay on the right note, make sure that your first paragraph does what it needs to do (recap the argument, state your position, and map out your three points) without any attempts at rhetorical bells and whistles.  At some point in high school or college, a composition instructor may have told you to use an “attention-getting” opening to really draw your audience in, but your GRE AWA reader doesn’t need to be “drawn in;” she is getting paid to read your essay, and wants to do her job as efficiently as possible.  She’s likely to regard literary flourishes as a waste of your energy and her time.  Now, let’s look at a sample prompt and opening paragraph:

Prompt:

WPTK, the most popular television station in Metropolis, does not currently provide traffic updates to viewers.  Since Metropolis is located in a Midwestern state with serious winter weather road delays 4 months out of the year, WPTK would significantly reduce the incidence of auto accidents on Metropolis-area roads by providing traffic updates.

Response Paragraph 1:

The argument, which states that WPTK’s broadcast of traffic updates would reduce the incidence of auto accidents on Metropolis-area roads, has merit.  However, the argument also exhibits several serious flaws which could limit its persuasiveness.  The author weakens his claim by assuming that televised traffic updates would be timely enough to impact drivers’ actions, by failing to explicitly state how the updates would affect auto accidents, and by predicting a “significant” reduction in Metropolis auto accidents without specifying what kind of a reduction would be deemed “significant.”

As you can see, the opening paragraph responds to the prompt by taking a clear position, referring back to the issue briefly, and outlining the points that the essay will be addressing.  Let your concise, informative opening paragraph set the tone for your essay!

Please visit the Grockit forum or leave a comment here to post questions on essay structures.

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Tips For Percent Math Problems on the GRE

jake becker August 27, 2010

In this article, we will discuss some common problems students encounter with percent problems, which can come in a variety of formats. Here are some quick pointers:

Percents MUST be APPLIED to something

A percent means nothing on it’s own.

Example: 16% of men, or 30% off the sales price

Percents are basically fractions with a denominator of 100

Learn your common percents, and convert to fractions whenever possible.

Example: 20% = 1/5, 62.5% = 5/8

The word “of” means multiply

Example: 80% of men = 4/5 * (total # of men)

Percents higher than 100 are numbers higher than 1

Example: 125% = 100% + 25% = 1 + 0.25 = 1.25

Recognize the difference between percent MORE/LESS THAN and percent OF

Example:
What is 25% less than 8?
¼* 8 = 2, so 8 – 2 = 6

Example:
What is 25% of 8?
¼*8 = 2

Use shortcuts

20% less than means 80% of. So instead of taking 20%, then subtracting from the original, just take 80% and be done. Conversely, 50% more than 10 should be calculated by multiplying 10*3/2 [10*(1 + 0.5)] in one neat step, versus two tougher ones.

See the previous example:
What is 25% less than 8?
¾*8 = 6, and we’re done! On easy numbers like this, it might not seem necessary, but as numbers get larger, it will save lots of time.

The higher the number, the higher the resulting percent

Applying the same percent to a higher number will yield a higher number.

Example:
A certain positive integer x is increased by 10%, and then decreased by 10%. Which is bigger, x or the resulting number?
The 10% increase of x in the first round increases x by a certain amount. The 10% decrease in the 2nd round is applied to a higher number, so will yield a larger change. The original x will be bigger.

Percent change = Total Change/Original Value

Example:
Before trading began, James’ investment portfolio was worth $10,000.  At the end of market close, James’ investment portfolio grew by $2,000.  What was the percent change in James’ portfolio?
Percent change = $2,000/$10,000 = 0.2, or 20%

Don’t add constants and percents

You should never find yourself trying to figure out what 5 + 6% equals. In this case, you are probably missing what to apply the percent to.

Let’s take a look at two examples!

Example 1:

A tour group of 25 people paid a total of $630 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?

A. $22

B. $23.94

C. $24

D. $25.20

E. $30

Without a calculator, fractions are always easier. They cancel well, and are typically neater.

5% = 1/20 since 5*20 = 100.

Now we set up the equation, setting x = ticket price before tax.

25 people * x dollars/person * 1.05 (with tax) = $630

Note we can convert to fractions, cancel and simplify. Look how easy it gets?

25*(21/20)*x = 630

5*(21/4)*x = 630

x = 630*4 / 5*21

x = $24

Choice C

Example 2:

During an auction, Jerome sold 75% of the first 1,000 items he offered for sale, and 30% of his remaining items. If he sold 40% of the total number of items he offered for sale, how many items did Jerome offer for sale?

A. 750

B. 1,050

C. 1,800

D. 3,500

E. 4,500

Again, we want to set up the equation – this will make things a lot easier. And again, switching to fractions is always best.

3/4*1000 + 3/10*R = 4/10*T

We have 2 equations, and 1 unknown. This is a good hint that there may be a hidden 2nd equation.

1000 + R = T

Now, we have 2 equations and 2 unknowns. We can solve!

750 + 3R/10 = 400 + 4R/10

350 = R/10

R = 3,500

We always look back to the original question to see exactly what we are looking for. In this case, T. Not R.

T = R + 1,000 = 3,500 + 1,000 = 4,500

Choice E

Please visit the Grockit forum or leave a comment here to discuss further.

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Number Theory

jordan schonig August 25, 2010

Number theory may sound scary, but it’s just an intimidating name for some pretty elementary mathematical principles. You probably know most of these principles by memory; if not, you could easily execute a calculation to ascertain them. The best option, though, is to study these principles enough that they seem intuitive. The GRE Quantitative section is all about saving time; making number theory second nature will definitely save you some valuable seconds.

1. Odds and Evens

Addition

Even + even = even (12+14=36)

Odd+ Odd = even (13+19=32)

Even + Odd =  odd (8 + 11 = 19)

To more easily remember these, just think that a sum is only odd if you add an even and an odd.

Multiplication

Even x even = even (6 x 4 = 24)

Odd x odd = odd  (5 x 3 = 15)

Even x odd = even (6 x 5= 30)

To more easily remember these, just think that a product is only odd if you multiply two odds.

Example Question

If r is even and t is odd, which of the following is odd?

A. rt

B. 5rt

C. 6(r²)t

D. 5r + 6t

E. 6r + 5t

In this example, we could either plug in numbers for r and t, or we could use our knowledge of number theory to figure out the answer. We instantly know that rt, an odd times an even, is even. 5rt means we multiply an odd times that even product, which is even. C translates to an even (even ²) times an odd (t), which is even, times another even (6), so that’s even. D adds an even (odd times even) to an even (even times odd) , so that’s even. E adds an even (even times even) to an odd (odd times odd), which is finally odd. E is our answer.

2. Primes: Prime numbers are numbers whose only factors are themselves and one. 11, for example, is a prime because it can only be evenly divided by itself and 1. In some questions, you will have to identify less recognizable primes. Note that 1 is not a prime.

If you were asked to identify the primes between 40 and 60, for example, you should quickly narrow down the primes with a sequence of steps.

First, write down the numbers, and cross out all the even numbers (all even numbers greater than 2 can be divided by 2, and thus are not primes); alternatively, you can just write down the odd numbers in the set.

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Then, cross out your multiples of 3; it may help you to recall that a number is divisible by 3 if its digits add up to 3)

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Then, cross out multiples of 5 (those that end in 5 or 0)

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

We are left with 41, 43, 47, 49, 53, and 59. Take one last look at your group, and you should notice that 49 is 7 squared. So we are now left with 41, 43, 47, 53, and 59.

The more you practice finding primes, the less often you’ll have to do this. But, in the beginning, it’s more important to be thorough than it is to be fast. Missing just one prime means missing the question, so be sure to watch out for those pesky composite numbers like 51 and 57. Remember, practice makes perfect, and Grockit makes great practice.

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All About Remainders

jake becker August 23, 2010

Remainders are the NUMERATOR of a fraction from a mixed number that results from division. For example, 19/3 leaves a remainder of 1, since 19/3  = 6 1/3.

Some quick tips:

  1. Your remainder can only range from zero to the denominator of the fraction. For example, when dividing by 9, your remainder options are 0-8, since a remainder of 9 leaves you a new whole number (with a remainder of 0).
  2. Look for the closest whole number and count up or down from there. For example, when trying to find the remainder of 146/15, you can see that 15 would go into 150 evenly. You then count down four from 150 to 146, so your remainder is (15 -4) = 11. This is easier than recognizing 135/15 is a whole number and counting up.
  3. Become familiar with common trends or patterns. For example, multiples of even numbers are even, so 167/(even #) must have an ODD remainder.
  4. The remainder should NOT be reduced. 18/4 = 4 2/4. The remainder stays equal to 2, even though you can reduce 4 2/4 to  4 1/2.

I recently came across this question, which I think is a good introduction:

What is the remainder of 3^(4n+3) divided by 5, assuming n is a positive integer?

Firstly, when dividing by 5, we are looking for the remainder above a one’s digit of either 0 or 5. In this scenario, we only care about the one’s digit, so we only need to look at the one’s digit while multiplying.

We can break 3^(4n+3) into 3^4n * 3^3 by the rules of exponents.

If n = 1, 3^4n = 3^4 = 81 = one’s digit of 1.

If n = 2, 3^4n = 3^8 = 81*81 = one’s digit of 1.

We detect the pattern that regardless the value of n, we will be multiplying a term with a one’s digit of 1 with a term with a one’s digit of 7 (3³), so the result will have a one’s digit of 7. When and number with a one’s digit of 7 dividing by 5, we are left with a remainder of 2.

Pattern questions with division are many times Remainder questions at their core

The 4 members of the Jones Family rotate who takes out the trash on a daily basis. The order goes as follows: Mom, Dad, Brother, Sister. If Dad takes out the trash on January 18th, who takes out the trash on March 26th? (There are 31 days in January and 28 days in February.)

It’s clear that we don’t want to whip out our calendars and start counting. (A general rule of thumb is that if you think it’s taking too long, it probably is….)

Instead, we see how many days pass between January 18 and March 26:

January 19-31: 13 +

February 1-28: 28 +

March 1 – 26:  26  = 67 days.

67/4 leaves you will a remainder of 3, so we count 3 from Dad, leaving us with Mom on March 26th.

Fractions and Decimals are the same thing

You should be familiar with common decimals, mainly:

1/2 = .5

1/3 = .33 repeating

1/4 = .25

1/5 = .20

1/6 = .166 repeating

1/8 = .125

1/9 = .11 repeating

Note that multiplying these by constants will leave similarly instructive results, such as:

3/8 = 3*1/8 = 3*0.125 = 0.375

The more familiar with these you become, the quicker you can eliminate answer choices are clearly wrong. For example:

If x is an integer, which of the following is a possible value of (x² +2x – 7)/9?

A. 0.268

B. 4.555 repeating

C. -2.4

D. 1.166 repeating

E. 8.125

We don’t have to start plugging in. We know that when divided by 9, the remainder will be a number repeating to the right of the decimal place. Only choice (B) fits that description. ((C) is divided by a factor of 5, (D) by a factor of 6, and (E) by a factor of 8.)

Join a Grockit game for more GMAT math practice with Jake!

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Prime Factorization

jordan schonig August 19, 2010

Finding factors of integers should become second nature on the GRE; many questions will require you to find the factors of an integer, even if they do not ask you explicitly.

A factor is a divisor, a number that an integer can be evenly divided by. The factors of 8, for example, are 1, 2, 4, 8, -1, -2, -4, and -8. The multiples of an integer x are the infinite products of x and another integer. The multiples of 8 include …-32, -24, -16, -8, 0, 8, 16, 32, 64… and so on.

Prime Factorization: Prime factorization, a.k.a. the factor tree, is a process by which we present an integer as a product of all its primes. The easiest way to do is to make a factor tree. A factor tree is a diagram that breaks down a number into its corresponding factors. Let’s see an example:

Above are the factor trees for 108 and 92. Notice that all the ends of the tree (those numbers that cannot be divided) are primes. So, 108 can be written as 2 x 2 x 3 x 3 x 3, or, more simply, 2² x 3³.  92 can be written as 2 x 2 x 23, or 2² x 23. This practice may seem purposeless, but it has many practical applications.

Factor trees help us simply radicals (answer choices with radicals are almost always in simplified form).

For example, if your answer to a multiple choice question was √96, chances are you won’t see √96 in your answer choices; you’ll probably see the simplified version. To simply a radical, first diagram the factor tree:

So, I know that 96 is the same thing as 2 x 2 x 2 x 2 x 2 x 3.

Since I am trying to simplify the square root, I need to figure out the biggest square in those primes. Because I have five 2s in my primes, I know that the biggest perfect square is 2 x 2 x 2 x 2, or 16, which is 4². Thus, I know that sqrt96 = √16 x√3 x √2. Simplifying this, I know that √96 = 4√6.

Greatest Common Factor: The greatest common factor (GCF) of two or more integers is the greatest integer that is a factor of those integers. For example, the GCF of 24 and 16 is 8, since 8 is the greatest number that is a factor of both. Similarly, the GCF of 60 and 15 is 15. Taking the GCF of bigger numbers, however, is not always so easy. Sometimes, you will be able to arrive at the answer mentally.  When the calculations are more difficult, however, you can use the factor tree to directly arrive at your answer.

Suppose I want to find the GCF of 256 and 72. I’m not quite sure what it is off the top of my head, so I’ll use factor trees to directly arrive at the answer.

Once you perform the prime factorization, it helps to write each as a product of powers: 256 = 2^8 and 72= 2³ x 3². To find the GCF, first find how many primes are common to each prime factorization; in this case, only 2 is common to both. The GCF is the product of all the primes that appear in each factorization, using each prime the smallest number of times in any of the factorizations. In this case, 2³ is smaller than 2^8, so 2³, or 8, is the GCF.

Let’s see another example:

GCF of 68 and 102 and 204.

Using factor trees would yield: 68 = 2² x 17       102 = 2 x 3 x 17      204= 2² x 3 x 17

Here, we have the common factors 17 and 2. 102 has the lowest power of 2, so our GCF is just 2 x 17 = 34. Note: this one would be pretty difficult to figure out without the factor tree.

The best way to get faster at prime factorizations and GCFs is to practice. The good news is, you can practice without looking for sample problems–just make some up on your own.

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How to Get the Most Out of Your GRE Lessons

andrea alexander August 16, 2010

People prepare for the GRE in many different ways.  Some use books to do practice questions on their own; others spend time on Grockit.  And of course, some take a class or have a private tutor.  I’m here to offer a few tips to the people in that last group, to help them get the most out of one-on-one time with their teachers or tutors (herein referred to as your Expert).

1. Come prepared!

If there’s any kind of background information that you should know before class, know it.  Preview reading or practice problems ensure that you’re coming to your lesson with the basic foundation of knowledge that you will build upon to master the skills being taught.  And homework regarding a lesson you’ve already learned will help cement the methods that have been demonstrated.  If you’re not sure what, if anything, you need to be doing, ask your Expert; he or she should be happy to clarify any issues regarding the type or amount of work you should do.

2. Ask the right questions.

I can’t speak for other Experts here, but I know that I find it much easier and more productive to address specific queries than extremely general ones.  A great question is something like, “I’ve noticed that I have trouble with Reading Comp detail questions, like the one in this sample.  Can you explain to me why choice C is the correct answer, and not choice E?  And how can I apply that to other RC detail questions?”  I will be able to offer much more productive feedback to that than to someone saying, “I have trouble with Reading Comp.  Can you give me some tips?”  I may have tips to offer, but without specific knowledge of your trouble areas, there’s no guarantee that I’ll be giving you the kind of information that will help you as an individual test-taker.

3.  Take advantage of all the resources available to you.

In live classes, Experts often have time before or after class specifically set aside for questions.  Often, if you arrive 20 minutes early, you’ll find your Expert sitting, waiting for someone just like you to come in for help.  (The Expert may be reading the newspaper or Facebooking on his or her Blackbery while waiting, but will be more than happy to put that aside to answer your questions or discuss your concerns.)  Online learning tools also have potential applications that many people never fully explore.  Post questions on Grockit forums and reach out for help; there are huge communities of online students and Experts who can give you feedback or guide you in the right direction.

4.  Don’t be afraid to look for clarification if something doesn’t make sense.

Just because one of your classmates understands the question doesn’t mean that you are expected to understand it the same way.  People learn differently, and sometimes all a student needs is for something to be explained in a different way.  That’s what the Experts are here for, so don’t be afraid to approach yours to ask him or her to try to reframe the issue for you.

5.  Finally, try to have some fun with the studying process!

Yes, the GRE is a challenging test, preparing for it is often a rigorous experience, and your future is a serious thing.  But questions are sometimes funny, mistakes should be learned from and sometimes laughed off, and your Experts and fellow students could probably use a light moment as much as you could.  So remember that even as you’re working hard, you should take some time out to play, too.

To summarize, remember that your GRE prep is a collaboration between you, your fellow students, and your Expert.  Be proactive about your practice and about asking questions, and take advantage of the many ways that you can study for the exam.  And, finally, try to enjoy the process as much as you can, and remember to take time to relax a little!  What are some of your favorite ways to relieve GRE preparation pressure?

Categories: GRE, GRE Prep, strategy • 1 Comment »

Fractions, Proportions and Ratios, Oh My!

jake becker August 13, 2010

GRE 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.

GRE 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!

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Mnemonic Vocabulary

jordan schonig August 10, 2010

Studying reams of vocabulary words can be a mind-numbing process. When faced with the task of memorizing 1000+ unfamiliar (and sometimes useless) words, most of us will either behave like a lost child or a disaffected teenager; that is, we’ll either cower in fear or reject the whole endeavor completely. Believe it or not, the ETS has a reason for this. Chances are, a career in public administration will not require you to know the proper definition of peregrinate, but the prodigious task of learning these daunting words is analogous to the rigors of graduate school (even if the analogy is a bit of stretch).

Luckily, our brains are a built for more complicated and efficient processes than rote memorization; we can actually use creativity to improve the efficiency of learning vocabulary words. If you’ve made it through college, you’ve heard of mnemonic devices. To refresh your memory (I wonder if there’s a mnemonic to remember the definition of mnemonic?), a mnemonic is a linguistic device, often a rhyme, acronym, or anecdote, that aids recall. This is one of my favorites from AP Biology that helped me remember the order of taxonomic classifications: Kingdom, Phylum, Class, Order, Family, Genus, Species = King Philip, come on for God sakes! You likely may have heard a different version of this, but the best part is, they all will help you memorize this specific information.

Now, you may be thinking that such information lends itself well to a mnemonic, but obscure words may not. Indeed, that is partly true. But, many words do happen to conduce corresponding mnemonics–it’s all a matter of using your creativity and finding that customized mnemonic that works for you. Let’s look at a few examples.

  1. Nostrum: 1. Hypothetical remedy for all ills or diseases; once sought by the alchemists 2.Patent medicine whose efficacy is questionable 

Nostrum is a pretty rare word but a surprisingly useful one since one of its definitions is pretty unique. The first definition is basically the same definition as the more familiar word panacea–a cure-all, a hypothetical remedy for all ills.

The second definition, though, is best encapsulated by the idiomatic expression “snake oil,” which is defined as “a worthless preparation fraudulently peddled as a cure for many ills.” In essence, the English word for “snake oil” is “nostrum.”

Because I find this definition more interesting and useful, I will think of a mnemonic for that definition.

The Mnemonic: Put rum in your nostrils (or nose) to cure a cold.

Indeed, this mnemonic as not as catchy as some others you’ve heard, but I find it pretty effective. Putting rum in your nostrils sounds like those many specious home remedies for preventing colds that you may have heard about (most of which have been debunked by scientists).

  1. Abrogate: 1. Revoke formally

Abrogate is not a notoriously complicated word, but it has special relevance for me. I remember having a difficult time remembering the word when I was studying for my GRE. I would recognize the word, I would know that it had a simple definition, but I could never recall it. Then, it dawned on me. Abrogate means almost the same thing as Abolish, and, of course, both those words begin with “ab.”

The Mnemonic: Abrogate= Abolish

This is an example of the simplest kind of mnemonic you can imagine. There is no fancy anecdote, rhyme, or acronym here, just an easy way to remember a close synonym. Sometimes, that’s all you need.

Remember, if the mnemonic works for you, then use it. If it doesn’t, drop it. There’s no use in struggling to remember the mnemonic device on top of remembering these words.

For an impressively comprehensive list of vocabulary mnemonics, visit mnemonicdictionary.com. It’s a brilliant site that exploits the power of online collaboration (not unlike Grockit) to enhance education.

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Ratios and Proportions

jordan schonig August 5, 2010

Ratios and proportions are favorites of most standardized tests, and the GRE is no exception. They may be a bit intimidating if you are unfamiliar with how to approach them, but once you learn the basics, you’ll learn that ratio and proportions problems require only simple algebra.
A ratio is a kind of fraction that measures two or more quantities in a group.

For example, a ratio of boys to girls (Boys: Girls) at a party is 3:4. You can also write this ratio as 3/4. That means that for every 3 boys at the party, there are 4 girls. This does not mean that 3/4 of the party goers are boys, nor does it mean that 4/3 of the party goers are girls.

If you do want to find out what proportion or percentage of the party goers are boys or girls, respectively, you add the numerator and the denominator, and then form a fraction in which this sum is the denominator.

So, if I want to find out what proportion of the party goers are boys, I add 3 and 4 (=7), and then I take the ratio quantity of boys, 3, and form the fraction 3/7.

3/7, or 42.9 %, of the party goers are boys.

4/7, or 57.1%, of the party goers are girls.

Stated algebraically, if we have a ratio x:y, then x / x+y and y /x+y express the proportions of x to the group and y to the group, respectively.

Let’s see what an example using this rule might look like:

Example 1: At a party, 40% of the party goers are male. What is the ratio of male to female party goers?

This question uses the aforementioned rule, but reverses the process. We now have to find the ratio.

If 40% of the party is male, then 4/10 or 2/5 of the party is male and 3/5 of the party is female.

Since we have two proportions expressed with the same denominator (2/5 and 3/5), we can simply express the ratio of males to females as 2/3 or 2:3.
Note: If the question had asked for the proportion of females to males, the answer would be 3:2.

Though we cannot find the total number of items in a group (e.g. number of people at the party) if we are given a ratio, we can deduce some important information about the number of items. A GRE question testing this rule may look like this:

Example 2: If the ratio of men to women at a party is 4:7, which of the following could be the number of people at the party?
A. 50 B. 64 C. 66 D. 70 E. 78

At first, you may think that you do not have enough information to answer this question, but you do.

To answer a problem like this, just add the coefficient x to each quantity and add: 4x+7x=11x.
We know that the sum of the quantities, 11, represents a fraction of the total number of party goers, so our answer MUST be a multiple of 11.

The only multiple of 11 in our choices is C. 66.

Extra Credit: If there were 66 people at the party, how many males and females would be there?

If 11x=66, then x = 6.
4x= 4*6= 24 men
7x=7*6=42 women

That last example was pretty simple, but how about a tougher one that uses the same concept:

Example 3: In a right triangle, the two acute angles have a ratio of 1:5. What’s the measure of the larger acute angle?

Before we apply the same method, let’s write down some important info. If this is a right triangle, then the largest angle is 90 degrees. Since the sum of the angles of a triangle equal 180 degrees, then the two acute angles must equal 90 degrees.

so: 1x+5x =90
6x=90
x=15

The larger angle is 5x, so 5*15 = 75

Hopefully, ratios and proportions aren’t so scary anymore. See if you can spot some ratio problems when you’re practicing on Grockit.

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