For example, look at these graphs:

In the first graph, the answer is E but the author desperately wants you to pick C. In the second, the answer is B but the author is baiting you hard into picking C. And in the third, the answer is C but the author is tempting you with E. In any of these cases, the strategy behind the question is as important – if not more important – than the math itself. Because it’s usually fairly easy for an average (or below) student to eliminate 1-2 answer choices on Data Sufficiency questions, the authors have to “get their odds back” through gamesmanship, by showing you a statement (or two) that look one way (sufficient or not) but that act counterintuitively. And to understand how to play this game well, it may be helpful to see Data Sufficiency through the lens of another popular game, the card game Hearts.

In Hearts, the goal of the game is to avoid getting “points”, and you get points when you end up with any hearts (one point each) or the Queen of Spades (13 points) after having taken a trick. And like with Data Sufficiency, there are really two ways to play: the way you’d play with a middle-schooler who’s learning the game, and the way you’d play with a group of adults who are each trying to win.

Playing Hearts with kids is like doing Data Sufficiency questions below the 550 level – you pretty much just play it straight. In Hearts, that means that when you don’t have any cards of the suit that was led, you try to get rid of your highest point-value cards immediately. If clubs are led and you don’t have clubs, you either get rid of the Queen of Spades if you have it, or you pick your highest heart and unload that. Your goal is to get rid of high cards and point cards quickly so that you end up with as few points as possible.

But if you’re playing with adults, you have to consider the possibility that someone may be trying to “Shoot the Moon” – getting *all* of the points cards in which case they get 0 points and every other player gets 26. What might seem like a counter-intuitive strategy to a 12-year old is often quite necessary when you suspect an opponent may be trying to shoot the moon: even though you may have a chance to get rid of your king-of-hearts, you might hold on to it because you want a high heart in case you need to “win” one of the last tricks to stop the opponent from getting all of the hearts. When you’re playing with adults (or attempting Data Sufficiency questions in the high 600s and into the 700s), you need to see the game with more nuance and develop an instinct for when to avoid the “obvious” play to save yourself from a more-catastrophic outcome.

This is especially true when you notice something suspicious from your opponent; if in one of the first few hands an opponent leads with, say, the jack of hearts, that’s a suspicious play. Why would she fairly-willingly open herself up to taking four points? Or if the first time a heart is played, an opponent swoops in with a high card of the suit that was led, but you know they probably have a lower card that would have let them avoid taking the heart, you again should be suspicious. In either of these cases, an astute player will make a mental note to hold back a high card or two just in case shooting-the-moon is in play. Playing hearts as an adult, you’re often playing the opponent as much as you’re playing the cards.

How does this apply to Data Sufficiency?

Consider this question:

Is a > bc?

(1) a/c > b

(2) c > 3

Playing “middle school hearts”, many test-takers will run through this progression:

Step one: If you multiply both sides by c, you get a > bc so this looks sufficient*. The answer, then, would be A or D.

Step two: Forget everything you learned about statement 1 since you’ve already made your decision about it. Statement 2 is clearly insufficient on its own, so the answer must be A*.

(*we know the math here is slightly flawed; demonstration purposes only!)

But here’s how you’d play the game as an adult, or as a 700-level test-taker:

Step one: Same thing – if you multiply both sides by c you’ll get a > bc, so this one looks sufficient.

Step two: Wait a second – statement 2 is absolutely worthless. And statement one wasn’t *that* hard or interesting. Maybe the author of this question is “shooting the moon”…

Step three: Look at both statements together, reconsidering statement 1 by asking myself if statement 2 matters. If statement 2 is true and c is, say, 10, then a/10 > b would mean that a > 10b, so this still holds. But what if c is -10, and statement 2 is not true. a/(-10) > b would mean that when I multiply both sides by -10 I have to flip the sign, leaving a < -10b. This time it’s not true. Statement 2 *seems* worthless but in actuality it’s essential. Statement 1 is not sufficient alone; as it turns out I need statement 2.

What’s the difference between the two methodologies?

The 500-level, “middle school hearts” approach – NEVER consider the statements together unless they’re each insufficient alone – leaves you vulnerable to the author’s bait. On hard questions, authors love to shoot the moon…that’s their best chance of tricking savvy test-takers.

The 700-level, “playing hearts with grownups” approach seems counterintuitive, much like saving your king of hearts and knowingly accepting points in a hearts game would seem strange to a seventh-grader. But it’s important because it saves you from that bait. On a question like this, it’s easy to think that statement 1 is sufficient; abstract algebra is great at getting your mind away from numbers like negatives, zero, fractions… But statement 2′s worthlessness (ALONE) functions two ways: it’s a trap for the unsuspecting 500-level types, and it’s a reward for those who know how to play the game. That worthless statement 2 is akin to the author leading a high heart early in the game – the novice player sees it as a freebie; the expert considers “why did she do that?” and re-examines statement 1 by asking specifically “what if statement 2 weren’t true; would that change anything?”.

Remember, when you’re taking the GMAT you’re playing against other very-intelligent adults, and so the authors of these questions have a responsibility to “shoot the moon”. While the rules of the game dictate that you don’t want to consider the statements together until you’ve eliminated A, B, and D, there’s a caveat – if you have reason to believe that the author of the question is trying to trick you (which is very frequently the case on 600+ level questions), you have to consider what one statement might tell you about the other; you have to play the game.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*By Brian Galvin*

The campus at the Naval Academy is referred to as “The Yard,” where the majestic Severn River flows into Chesapeake Bay. Annapolis is a historical city where the early twentieth century structures intermingle with modern buildings. Combining tradition with advanced technology gives the academy all the tools needed for the success of its midshipmen. The Academy takes pride in the student body – past, present, and future. This is made clear by a stroll down walkways that pass buildings named after the outstanding midshipmen that used to attend this Academy. Head over to any of the three monuments devoted to the brave men and women whose heroism is part of the Academy’s extensive heritage.

There are three basic elements to the academic structure at the United States Naval Academy:

- A core requirement in humanities, engineering, social sciences, or natural sciences to develop critical thinking
- Core academic courses to teach leadership and professionalism for officer training
- The student’s academic major

On top of this three part structure there are many other resources and programs that advance midshipmen to the next level in academics. The core focus of the academic program is STEM, keeping the future of the Navy as technologically advanced as possible. While every other college in America allows the student to choose their respective field, at the Academy the needs of naval service come first, therefore a student may not get to choose his or her major. At graduation all midshipmen by law are given a Bachelor of Science degree due to the amount of technical content learned through the core curriculum.

Student life at the Naval Academy is wildly different than that of other traditional colleges. The curriculum, daily life expectations, and philosophy are far more intense than most. The rigor starts the summer before freshman year where students spend eight weeks in training for the intensity of the program and what the next four years will look like. This is more than a college; this is a complete lifestyle change from civilian to midshipmen. Students will have a regimented schedule that will test them physically, mentally, and emotionally; they will be pushed to their limits and beyond. This Academy is not for the faint of heart, students will have a tight structure that promises to constantly challenge them. All midshipmen are required to participate in extracurricular activities as well as athletics on some level, ensuring all midshipmen are well-rounded.

As with everything in the Academy, the athletics are demanding, and those who play one of the 33 varsity sports are pushed to the limits. Excellence is an expectation; more than thirty percent of midshipmen play on Division I varsity teams and sacrifice what little free time is allotted to participate in their respective sports. At the Academy there is not an off season; student-athletes train year round to garner optimum skill and excellence in their sports. The Naval Academy competes in over ten league affiliations and conferences; student-athletes are known to graduate at a higher level than those who do not play sports. There are club leagues and intramural sports for all other brigade members to participate in, and every midshipmen has access to the over fifteen state-of-the-art athletic facilities.

The United States Naval Academy has many deep and meaningful traditions as well as a few fun ones to boost morale and show pride in the Academy. A main tradition is the singing of “Blue and Gold” after every alumni gathering, sports event, and pep rally. This tradition is one of the many showcasing the pride and respect of the Academy. “Beat Army” which started as a chant said after the “Blue and Gold” song manifested into “plebes” showing off, trying to impress their upper-classmen. They drink a concoction of food and condiments and upon completion yell “Beat Army,” followed by the cheers of their fellow classmates. If you hear someone brag about having a “Beat Army,” you’ll know why, so show them some respect and give them a pat on the back.

We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter! Also, take a look at our profiles for The University of Chicago, Pomona College, and Amherst College, and more to see if those schools are a good fit for you.

*By Colleen Hill*

Similarly, when answering a Sentence Correction question, there are many types of errors that can appear in a single sentence. Some questions will be one-trick ponies (I’m looking at you, Bitcoins), in which you can just solve one issue and get the correct answer. However, most will have two or three types of errors that you need to avoid, and identifying these errors will often make the difference between knowing which answers cannot be correct and guessing based on how the sentence sounds.

When looking through the initial sentence, you might notice some errors right away, such as pronoun (she vs. they) or verb agreement (is vs. are) errors. However some errors are more subtle and you must look through the answer choices to confidently narrow down the options. Once you have a good handle on the types of errors occurring in the sentence, you can begin eliminating answer choices that do not dodge (or dodgecoin) the error.

Let’s look at a question that contains multiple issues, but they may not be obvious upon first glance:

*An auteur whose movies define the genre, Jean-Luc Godard’s films are to the French New Wave what Sergio Leone’s The Good, The Bad and The Ugly is to the spaghetti western.*

*(A) **Jean-Luc Godard’s films are to the French New Wave what*

*(B) **Jean-Luc Godard’s films are to the French New Wave like*

*(C) **Jean-Luc Godard’s films are to the French New Wave just as*

*(D) **Jean-Luc Godard directed films that are to the French New Wave similar to*

*(E) **Jean-Luc Godard directed films that are to the French New Wave what*

The sentence begins with a modifier that is not underlined, which means the subsequent underlined portion must necessarily be the subject of the modifier. If it is not, then the sentence will contain a modifier error from the get go and will not be the correct choice. A little further on, a comparison is made between films and other films. If the comparison were to be between two incongruent items (worse than apples and oranges, say apples and androids), the sentence would contain a comparison error. There may be other errors but these are the two most glaring issues to keep in mind.

Looking over the answer choices, we see a 3-2 split between the choices that keep the director’s films as the subject of the verb and the choices that change the subject to the director himself. From a comparison point of view, all the choices seem to keep the comparison between Godard’s films and Leone’s cult masterpiece.

The non-underlined first part of the passage is a modifier that is describing a specific person. The sentence even begins with “An auteur”, which is the French word for author. The subject of the sentence must therefore be a noun that can logically be described by the modifier at the beginning of the sentence. However, the restriction of the comparison also dictates that the sentence compare films with films. The only way to accommodate both limitations is to select either answer choice D or E, both of which keep Jean-Luc Godard as the subject of the phrase while supplying the proper film comparison at the end.

How do we go about differentiating between answer choices D and E (other than flipping a coin)? The difference is in the idiom that connects the underlined portion to the second part of the sentence. The first option indicates that the films are to a certain group *similar to* another movie to a different group. Apart from not being a correct idiom, it also doesn’t make logical sense. The second option indicates that the films are to a certain group *what* another film is to the different group. This is a perfectly acceptable idiom that conveys the meaning properly.

The only answer choice that avoids making a modifier error, a comparison error or a logical error is answer choice E. These errors may not have all been evident at first glance, but we can see why the four other answer choices contain some kind of error. Even though the comparison error ended up being largely irrelevant in this process of elimination, it is the type of error you always need to be aware of when correcting sentences. In fact, juggling many potential error types is a vital skill in solving these types of questions. While not always obvious, the correct answer will be the only option that doesn’t make at least one of the errors you’ve identified. Remember that, no matter how hard the GMAT may seem at times, it is easier (and safer) than juggling flaming chainsaws.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.*

Here is an example problem:

“Susanne Summers, acclaimed actress and fitness guru, is an example of people who are able to transcend their initial notoriety in one area and achieve success in another. ”

In checking for all the different types of agreement problems it is good to start by checking subject-verb agreement as every sentence has a subject and a verb. “Susanne…is” works just fine and there are no other verbs that could be mismatched to the main subject. There are not any lists, which are giveaways that there may be a problem with parallel structure, though there are two constructions involving the word “in” that looks like they demand parallelism. The constructions are “transcend…notoriety in” and “achieve success in” and these look good because they share the same structure (verb, noun, and the preposition “in”). The only other conjugated verb in this sentence to check for agreement is “are”, which matches its subject “people”. This would imply that there is no error, right?

Alas, it is not so simple. Though there are no traditional pronouns, the word “people” still must agree with its referent! This is an example of a hidden word that must agree with another word in the sentence. “People” in this case is a dependent noun because it is representing another noun. In this case, “people” is referring to “Susanne Summers”, and the two nouns must agree in number. “Susanne” cannot be an example of more than one person, so the error is with the word “people”.

Here is another example:

“Though Douglass had concocted many possible solutions to help with a number of problems within the organization’s bureaucracy, the idea didn’t help solve the major problem of the organization’s lack of direction.”

Again, in this example all the subjects and verbs seem to match up (“Douglass had” and “the idea didn’t”). Once more, there are no pronouns in the strictest sense, but there is a word that has a referent that it does not agree with. Here, “the idea” is referencing the “many possible solutions” that Douglass had concocted, but “the idea” is singular and “many possible solutions” is plural. Any two nouns that are supposed to represent the same person or thing in a sentence must agree in number and in type (is it a person, or a thing?). Though these kinds of agreement errors are tough to spot at first, it becomes second nature after a few tries.

Being able to check agreement in sentences is a tricky task, but very important for taking the writing scores to the next level. With a little practice, these hidden agreement problems will elucidate hidden solutions. Happy studying!

Plan on taking the SAT soon? We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*David Greenslade* is a Veritas Prep SAT instructor based in New York. His passion for education began while tutoring students in underrepresented areas during his time at the University of North Carolina. After receiving a degree in Biology, he studied language in China and then moved to New York where he teaches SAT prep and participates in improv comedy. Read more of his articles here, including How I Scored in the 99th Percentile and How to Effectively Study for the SAT.

Stanford’s traditional MBA program is the only one in the world with an acceptance rate and average work experience both in the single digits; so experienced applicants have started flocking to this alternative option in droves. Make no mistake, though, “alternative” does not mean “easy!”

The program consists of only 83 fellows, with an average GMAT of 700 and a minimum work experience requirement of 8 years.

How do you get in? You must focus on 3 core things.

**1. Career Goals**

First, your career goals must be clear and well-articulated. This is not the place to “find yourself.” What is your specific focus, and how will the MSx program help you get there?

**2. Leadership**

Second, your entire application must send a message that you are an accomplished manager and leader, as opposed to merely a person who has put time in to his career. It isn’t enough to merely say that you are experienced and successful manager, you have to show or prove it to them. How? Your resume! Your recommendation letters! Your extracurricular activities! See the pattern? Show them; don’t just tell them.

**3. Value**

Finally, prove to them that you will add something wonderful to their program. They want to ensure that the Master Black Belt from GE enriches the experience of the M&A Tax Manager from Cisco. Remember, they only have 83 spots. The more you can add to your classmates’ experience, the more they will have to admit you. Make sense?

At the end of the day, you want something from the program, and they want something from you. Tell them what you want, and what you will offer in return! Good luck!

If you want to talk to us about how you can stand out, call us at 1-800-925-7737 and speak with an MBA admissions expert today. Click here to take our Free MBA Admissions Profile Evaluation! As always, be sure to find us on Facebook and Google+, and follow us on Twitter!

*By Richard Vincent*

Here, students tailor their educational plans to their aspirations in liberal arts and sciences, engineering, music, and education and human development. In addition to global study opportunities and a chance to do independent projects, students also have unprecedented access to assisting researchers who are going about the business of solving some of the most difficult and complex challenges facing society.

Vanderbilt draws from among the best and brightest students in the world; admission to the university has become increasingly competitive in recent years. Students can earn bachelors, masters, and doctorates from the university’s ten colleges; College of Arts and Science, Blair School of Music, Divinity School, School of Engineering, Graduate School, Law school, School of Medicine, School of Nursing, Owen Graduate School of Management, and Peabody College of Education and Human Development.

Vanderbilt University has a long tradition of excellence. Its alumni and researchers include six Nobel Laureates, including former Vice President Al Gore. The school’s research library is among the most important in the nation. Vanderbilt’s Medical Center specializes in nursing, medicine, psychiatric, rehabilitation, and more. They have the only Level I trauma center in Tennessee, plus comprehensive burn, pediatric, cancer, and organ transplant centers. Students who are looking to work hard and be part of exciting, meaningful, cutting-edge research not only in medicine, but law, social issues, and more, would do well at Vanderbilt.

Vanderbilt, or Vandy as it’s affectionately referred to by students, has a great idea in place for helping incoming freshman acclimate to college life. All freshmen, from each of the four undergraduate programs, live in one of ten houses on the Martha Rivers Ingram Commons, where they share a diverse living learning community. Residential choices open up for students their sophomore year. There is a strong Greek presence at Vanderbilt, lots of student organizations in which to participate, a plethora of sporting events, extraordinary live music events, and a local college bar scene. In fact, some students may have trouble finding a balance between social and academic pursuits.

Many students stay close to the university in what is commonly referred to as the “Vandy bubble,” which includes the Hillsboro Village neighborhood adjacent to the university, rather than going into Nashville. Those who do venture into Nashville are richly rewarded; Music City, U.S.A has been rated the friendliest city in America for three consecutive years. Nashville is home to the Tennessee Titans NFL team and the Country Music Hall of Fame, to name two of the more famous of the city’s many attractions. Students won’t be at a loss for things to do both on and off campus.

The Vanderbilt University Commodores have a total of 15 varsity sports teams; six men’s teams and nine women’s teams. The NCAA Division I school is a member of the Southeastern Conference (SEC). The football team has had several players go on to play in the NFL, most famously Jay Cutler, and the team has risen to a Top 25 school for the first time in years. Their long-standing football rival is Ole Miss. The Vanderbilt men’s basketball has long been a powerhouse, and the women’s basketball team has a long history of success as well. The University of Kentucky is the primary rival in basketball. The men’s and women’s tennis teams are also among Vanderbilt’s most successful teams.

One of the most unusual, and perhaps most welcoming traditions ever is Move-In Day, where upperclassmen storm the cars of incoming freshmen and help them move all their things into their rooms. Freshman Walk is another bonding tradition where freshman rush the football field before the start of the season opening football game; even the school’s chancellor gets in on the action. Students display the VU hand sign at athletic events, and win or lose, sing the “Alma Mater” at the end of each game. The annual music event Commodore Quake is another popular tradition at Vanderbilt. Traditions at Vanderbilt are more about unity, community, and having fun than stuffier traditions at some other elite universities. Vandy is for the student who is looking for the challenging demands of a highly respected research university, but who also embraces the camaraderie of a close-knit academic and social community.

We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter! Also, take a look at our profiles for The University of Chicago, Pomona College, and Amherst College, and more to see if those schools are a good fit for you.

*By Colleen Hill*

Question: If two integers are chosen at random out of first 5 positive integers, what is the probability that their product will be of the form a^2 – b^2, where a and b are both positive integers?

A. 2/5

B. 3/5

C. 7/10

D. 4/5

E. 9/10

Solution: This might look like a probability question but isn’t. Questions like these are the reason we ask you to go through basics of every topic including probability. If you do not know probability at all, you may skip this question even though it needs very basic knowledge of probability.

Probability will tell you that

Required probability = Favorable cases/Total cases

Total cases are very easy to find: 5C2 = 10 or 5*4/2 = 10 whatever you prefer. This is the number of ways in which you select any 2 distinct numbers out of the given 5 distinct numbers.

Number of favorable cases is the challenge here. That is why it is a number properties question and not so much a probability question. Let’s focus on the main part of the question:

First five positive integers: 1, 2, 3, 4, 5

We need to select two integers such that their product is of the form a^2 – b^2. What does a^2 – b^2 remind you of? It reminds me of (a + b)(a – b). So the product needs to be of the form (a + b)(a – b). So is it necessary that of the two numbers we pick, one must be of the form (a + b) and the other must be (a – b)? No. Note that we should be able to write the product in this form. It is not necessary that the numbers must be of this form only.

But first let’s focus on numbers which are already of the form (a + b) and (a – b).

Say you pick two numbers, 2 and 5. Are they of the form (a + b) and (a – b) such that a and b are integers? No.

5 = 3.5 + 1.5

2 = 3.5 – 1.5

So a = 3.5, b = 1.5.

a and b are not integers.

What about numbers such as 3 and 5? Are they of the form (a + b) and (a – b) such that a and b are integers? Yes.

5 = 4 + 1

3 = 4 – 1

Note that whenever the average of the numbers will be an integer, we will be able to write them as a+b and a – b because one number will be some number more than the average and the other will be the same number less than average. So a will be the average and the amount more or less will be b.

When will the average of two numbers (Number1 + Number2)/2 be an integer? When the sum of the two numbers is even! When is the sum of two numbers even? It is when both the numbers are even or when both are odd. So then does the question boil down to “favorable cases are when we select both numbers even or both numbers odd?” Yes and No. When we select both even numbers or both odd numbers, the product can be written as a^2 – b^2. But are those the only cases when the product can be written as a^2 – b^2?

The question is not so much as whether both the numbers are even or both are odd as whether the product of the numbers can be written as product of two even numbers or two odd numbers. We need to be able to write the product (whatever we obtain) as product of two even or two odd numbers.

To explain this, let’s say we pick two numbers 4 and 5

4*5 = 20

Can we write 20 as product of two even numbers? Yes 2*10.

So even though, 4 is even and 5 is odd, their product can be written as product of two even numbers. So in which all cases will this happen?

- Whenever you have at least 4 in the product, you can write it as product of two even numbers: give one 2 to one number and the other 2 to the other number to make both even.

If the product is even but not a multiple of 4, it cannot be written as product of two even numbers or product of two odd numbers. It can only be written as product of one even and one odd number.

If the product is odd, it can always be written as product of two odd numbers.

Let’s go back to our question:

We have 5 numbers: 1, 2, 3, 4, 5

Our favorable cases constitute those in which either both numbers are odd or the product has 4 as a factor.

3 Odd numbers: 1, 3, 5

2 Even numbers: 2, 4

Number of cases when both numbers are odd = 3C2 = 3 (select 2 of the 3 odd numbers)

Number of cases when 4 is a factor of the product = Number of cases such that we select 4 and any other number = 1*4C1 = 4

Total number of favorable cases = 3 + 4 = 7

Note that this includes the case where we take both even numbers. Had there been more even numbers such as 6, we would have included more cases where we pick both even numbers such as 2 and 6 since their product would have 4 as a factor.

Required Probability = 7/10

Answer (C)

Takeaway:

When can we write a number as difference of squares?

- When the number is odd

or

- When the number has 4 as a factor

*Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the **GMAT** for Veritas Prep and regularly participates in content development projects such as this blog!*

On sunny spring Fridays when the Veritas Prep curriculum development team begins talking about weekend plans, it’s not uncommon to hear a conversation like:

Brian: I’m going to try to get a lot of running in this weekend.

Chris: Yeah, I’m going to make sure to do some trail running.

And what’s the major difference? Recognizing it can help you master Critical Reasoning on the GMAT; what did Chris not have to say, but add anyway?

**TRAIL** running.

Both are talking about running, but Chris took that extra second to put “trail” in there, making for a much more specific statement. He didn’t have to say “trail” but by doing so he created a conclusion, so to speak, that’s easier to weaken. If a news bulletin were to be released saying something like “Because of wildfires, all hiking and running trails will be closed to the public this weekend” or “With a risk of flooding due to excessive rain, residents are strongly urged to stay off all hiking and running trails”, Chris’s specific plans are in serious jeopardy, whereas Brian’s more general plans are still much more likely to happen (even if it means the dreaded treadmill…).

Why is this important for the GMAT? Because those one-word (or phrase) specifics can make all the difference in the world when you’re trying to strengthen, weaken, or draw a conclusion. Consider an example:

*With increased demand for natural resources from developing nations, the price of steel is dramatically increasing for manufacturers of durable goods. As these resources become ever more expensive and as developing nations are able to pay less in employee wages, American manufacturers’ only hope to compete is to significantly decrease their labor costs.*

Which of the following would cast the most doubt upon the conclusion above?

Now, as you consider this argument, one word should stand out. What one word did the author not have to say but say anyway in regard to the only hope for American manufacturers to compete? Not costs in general; **LABOR** costs. That one word will make all the difference – without it, the argument is a whole lot harder to criticize. But with it, note that there are all kinds of costs that can be cut: distribution costs, machinery costs, plant maintenance costs, packaging costs… By adding that word “labor” to costs, the conclusion became unnecessarily specific, and you should be ready to pounce on that. **ANY** other type of cost that could be cut is not a weapon in your arsenal to show that the conclusion isn’t necessarily true, as there is now an alternative way to compete by reducing *that* other cost even if labor stays constant. The specificity of the conclusion leaves it all the more vulnerable, and provides you with a clue as to what the right answer will likely have.

Often, the correct answer to a Weaken CR question is an “alternative explanation” – a different way for the facts in the argument to be true without the conclusion also being true. The more specific the conclusion, the more alternative explanations are available. So seek out that specificity and look for the single word or phrase in a conclusion that dramatically limits its scope.

]]>Of course, giving you all the time in the world to break through the confusion would be counterproductive, because then there’d be no way to differentiate between those who understand concepts and those who use brute force to simply try every possible combination of answer choices (think of MacGruber as someone who wastes a lot of time solving problems).

The questions on the quantitative section of the GMAT often appear very complicated and daunting, but can usually be solved quickly using a little logic. Of course, since the exam can potentially ask you hundreds of different questions, you can’t reasonably memorize every type of trick that can be thrown at you. You can, however, identify some recurring themes that appear frequently and understand why they are tricky. On test day, you still have to apply logic on a case by case basis, but some overarching themes are definitely more prevalent than others.

One such theme used frequently is that of turning a math problem into a story that you have to interpret. Today I want to talk about the compound interest problem. This type of problem is common in finance, but most financiers simply input the arguments into their calculators (or abaci) and spit out a solution. The compound interest situation presented is simply a layering mechanism designed to make the underlying exponent problem harder to see. Breaking through the prose of the question and seeing the fundamental problem for what it is can be the difference between a 1-minute solution and a 4-minute solution.

Let’s look at a compound interest problem that highlights the nature of these questions:

*A bank offers an interest of 5% per annum compounded annually on all of its deposits. If 10,000$ is deposited, what will be the ratio of the interest earned in the 4 ^{th} year to the interest earned in the 5^{th} year?*

*(A) **1:5*

*(B) **625 : 3125*

*(C) **100 : 105*

*(D) **100 ^{4} : 100^{5}*

*(E) **725 : 3225*

The first thing to note about this question is that it’s asking about a ratio, which means that the 10,000$ sum will be irrelevant. If you’d put in 100$ instead, or 359$, the ratio would still be the same. The correct answer will therefore not be related to 10,000$ in any way, but it’s also important to try and understand the question being asked before answering in order to avoid getting the right answer to the wrong question.

So what exactly is this question asking? What is the ratio of the interest earned in year 4 to the interest in year 5? This can lead us to some tedious calculations if we’re not careful. We start off with 100$ (or 10,000$, it doesn’t matter). At the end of the first year, we’ll have 5% more, so 105$. I could calculate it for year 2 as well, taking 105$ and multiplying by 1.05. This might take 20 seconds on paper, but will (hopefully) yield a result of 110.25$ I could go through years 3, 4 and 5 to get the respective answers (115.76$, 121.55$ and 127.63$), but that would take a while to calculate by hand.

Moreover, let’s say I have these 5 values; I am now tasked with finding the difference between year 4 and year 5. So now I need to calculate 127.63 / 121.55. Without a calculator… If you get to this point on the exam, you either spend more time trying to figure out the ratio, or you take an educated guess and move to the next question in frustration. Neither of these options is particularly good, so let’s backtrack to see where we veered off the path.

To calculate year one to year two, I took the initial arbitrary amount and multiplied it by 1.05. This is due to the interest compounding annually. The second year, I took the amount after year one and multiplied it by… 1.05 again! Eureka! Now, the pattern emerges. Every year, I take whatever the previous year was, and multiply it by 1.05. This means that, from year n to year n+1, the change will always just be 1.05, or a 5% increase.

Looking over the answers, answer choice C succinctly displays a 5% growth rate, taking whatever 100% of the previous year was and adding on 5%. This will be the correct answer for the growth rate from year one to two, as well as from year four to five. The question would have been much easier had the question been about years one and two, but the GMAT purposefully makes questions more difficult in order to differentiate between those who can identify the pattern and those who try to do each possibly calculation on paper.

On the GMAT, the correct answer can often be achieved by applying a brute force strategy. However, in business, you are rewarded for understanding the underlying concept and not wasting everyone’s time with meandering trial and error experiments. Understanding a concept such as this one about compound interest won’t single-handedly allow you to ace the exam. However, knowing that the exam is trying to appraise your ability to use logic to solve problems should incentivize you to look for the causal logic rather than to undertake tedious calculations.

Remember, there are computers, calculators and smart phones that complete routine computations in seconds. The GMAT is your opportunity to demonstrate not only that you can solve the question, but that you truly understand the question.

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“A circular field has a line drawn from one end through its center and continuing for ten meters past the edge of the field. A fence begins at one point on the field’s edge and ends at the end of the line not contained by the circle. If the distance from field to the fence is half the total length of the field, what is the total distance of the line and the fence combined?”

This is quite an intricate description and is very hard to visualize. Instead, draw a picture to approximate the description of the elements that have been provided.

This picture gives some helpful information. First off, the two lines are creating what appears to be two sides of a triangle. This is a common set up on SAT math questions and is good to recognize. It is also clear that the “fence” line is tangent to the circle. The question also stated that the distance from the field to the fence, which was given as ten yards, is half the length of the field. This means that the diameter of the circle is two times ten or twenty yards. This is a fantastic start and deserves some self congratulation, but there is still a bit more to be done. The length of the fence is still unknown. Even though the question didn’t state that this figure is a triangle, because a triangle is more useful than two lines it is a good idea to draw the triangle in. We are now imagining lines, who said math doesn’t use your imagination?

Because the fence is tangent to the circle, it creates a right angle with the radius that is drawn to it. We now have a very important piece of information that was previously missing. The third leg of the triangle is a radius of the circle! This means that its length is half the diameter of the circle, or ten meters, and the hypotenuse is the radius plus the ten meter piece of line, or twenty meters. If there is a right triangle which has a side of ten and a hypotenuse of twenty, alarm bells should start going off. What kind of triangle has a hypotenuse that is twice its small side? A 30-60-90 triangle! This means that the fence length is the length of the small side times the square root of three. Thus, the total length of the line plus the fence is twenty (the diameter) plus ten (the line between the circle and the fence) plus ten times the square root of three (the length of the fence). The answer would likely be listed as 30 + 10√3 in a multiple choice question.

This question is very difficult without the aid of the information provided by the pictures and imaginary lines. When it is possible to create a useful shape like a square or a right triangle by imagining lines, it is a good idea to draw those lines to help the test taker draw conclusions that would otherwise be difficult to draw. It can be hard to see what isn’t there, but with a little practice, the hidden pictures can reveal hidden solutions. Happy test preparation!

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*David Greenslade* is a Veritas Prep SAT instructor based in New York. His passion for education began while tutoring students in underrepresented areas during his time at the University of North Carolina. After receiving a degree in Biology, he studied language in China and then moved to New York where he teaches SAT prep and participates in improv comedy. Read more of his articles here, including How I Scored in the 99th Percentile and How to Effectively Study for the SAT.