Here’s what these two types of scaffolding are all about:

**Content scaffolding** consists of reminding students of critical concepts, presenting a multi-step problem as a series of smaller problems, and otherwise breaking down a problem into its constituent components. It’s used to help students synthesize concepts when those concepts are still new to them.

**Metacognitive scaffolding**, on the other hand, asks students to reflect upon the process they use in approaching a problem. This process allows students to generalize and prompts them to think analogously. Metacognitive scaffolding helps students extend the application of their knowledge to new situations.

For this project, we worked with high-school students to apply the principles used in scaffolding to the reflection and reinforcement stage of the learning process. Knewton’s adaptive system is designed to provide different follow-up questions to different students, depending on their needs. How, we wondered, would using content scaffolding and/or metacognitive scaffolding within these follow-up questions affect student learning and engagement?

The high schoolers who participated attempted to answer a question and then read its explanation. Next, they were given follow-up questions designed either to reinforce concepts (a form of content scaffolding) or to stimulate metacognition.

The follow-up questions designed to reinforce concepts were very similar to a certain step of the original problem. For example, if the first problem asked students to reduce a fraction whose numerator and denominator were each quadratic expressions, the second might ask students to factor a quadratic equation.

On the other hand, the follow-up questions designed to stimulate metacognition required students to apply the original concept to a different but analogous situation. If the first problem was about converting rates involving physical dimensions, the second might be about converting rates with dollars and services.

The results? Students definitely found the first type of follow-up question more accessible—no surprise there, since the concepts the original questions tested were generally new to the student.

These concept follow-ups helped reinforce the steps the students learned to take while solving the original problem. As for the latter, metacognitive type of follow-up, it was more helpful to students who already had a good handle on the basic concepts and were ready to expand their application.

Content-reinforcing follow-ups were gratifying because students were really excited to be able to answer a question related to the harder question they’d just attempted. When prompted to explain how the follow-up related to the original question, the students enthusiastically explained how it was just like the first step of the original. Students jumped at the chance to demonstrate immediately the understanding they had gained from the explanation of the original problem.

Why is this important? Ultimately, it provides us with yet another way to engage students—something all educators are continuously striving for. And while we love to incorporate innovative features like gaming elements into our courses, it’s also nice to see that sometimes it’s the simple stuff that matters most.

Content scaffolding (and metacognitive scaffolding, when students are ready for it) facilitates those super-rewarding “a-ha!” moments that give students the motivation they need to stay engaged.

]]>Here’s how to bounce back if you get a score much lower than your target:

The GMAC claims that statistically speaking, retaking the GMAT is unlikely to raise your score. But don’t give up hope! We’ve seen students get huge score gains from their first attempt to their last, and there are many factors that can lead to someone falling short of their best possible performance.

If you feel that “something” wasn’t up to par on test day, getting a better score might be as simple as fixing that something. Maybe you could have studied harder; maybe test day presented unexpected psychological challenges; maybe you just weren’t feeling well.

If you did poorly on the GMAT, ask yourself a few questions to help guide your thoughts about what to do next:

**1. How far is your score from where you would like it to be?**

** ** Start by assessing the damage. You should have had a realistic target score in mind. The Standard Error of Measurement (SEM) on the overall score is 29 points (David Kuntz, Knewton VP of research, can explain more on that). If you were aiming for a 670 and got a 650, your target score and your actual score fall within the standard error; 20 points lower does not constitute “bombing” the test. Retaking may not be worth it if you’re only hoping to gain 20 points or so.

Remember: when you submit your scores to a b-school, they receive **all** of your GMAT scores from the last five years. Admissions officers will see not just your scores—they will see your decision to retake the test. And they will evaluate whether or not you made a good decision. If your score was well below your target, retaking the test might be a good idea. A much-improved score will illustrate your perseverance.

So, if your score was well below your target, ask yourself this next question:

**2. What, if anything, made your performance on test day less than optimal?**

Inadequate preparation is an obvious culprit. Most test-takers spend several months of concerted effort preparing for test day. Even if you have the best GMAT teachers, not practicing is a surefire way to keep your score lower than it could be.

Maybe you did practice as hard as you could, but you did so without the right guidance. If you self-studied, try to assess your methods. Did you target your GMAT weaknesses, while still setting aside time to “maintain” your stronger skills? Studying for the GMAT is like working your muscles – if you do a month of chin-ups, and then stop to focus solely on sit-ups, your upper body strength will fade away. The same logic applies to studying Verbal and Quant: for optimal performance, it’s important to develop your skills on both sections in tandem.

If you self-studied, you should also be sure that you didn’t overlook any key strategies: sometimes, a simple tip on a certain section of the test can help shave off time, increase accuracy – and improve your score.

Or maybe you took a GMAT course, but still didn’t get the score you wanted. Did you attend class regularly? Did you complete your homework assignments? When you had trouble with a question type, did you seek extra help and/or complete additional exercises until you had the question type down pat? Taking a GMAT course can be very helpful in providing structure and guidance, but you still have to do the heavy lifting.

**3.** **How much of your difficulty with the test was mental?**

A test like the GMAT doesn’t just require verbal and quant practice; success also depends on mental preparation and focus. Sometimes, even if you’ve prepped as much — and as wisely — as possible, you still don’t achieve your target score.

Did test anxiety affect your performance? Maybe you were so nervous about not finishing or doing poorly that you weren’t able to focus on the questions. Or perhaps you weren’t able to sleep in the days or weeks before the test, and fatigue threw you off your game. If this is the case, check out our blog posts on how to conquer GMAT test anxiety and how to train your body for the GMAT.

Were you exhausted halfway through the test? This might be a result of not doing any (or enough) full-length GMAT practice tests under test-like conditions. In a sense, the GMAT is like a marathon. Just as you wouldn’t run 26.2 miles without adequate practice beforehand, you shouldn’t take the GMAT without preparing yourself for the mental strain.

If there were legitimate short-comings that you can address, move on to the next question:

**4. How do I retake the test?**

First, note that you can only take the GMAT once per calendar month. Also, note that schools won’t receive your new score automatically. If you’ve already sent your scores to any schools, you’ll need to do so again. (This will require re-selecting the programs when you retake the test, or ordering an Additional Score Report later, which requires an additional fee.)

When you do reschedule, don’t panic and select the soonest possible date. Give yourself enough time to actually address the issue(s) from question 2. Again, honesty is key—if it you have a lot of work coming up, don’t lie to yourself and think that you’ll take the next month to study more. Take the time you need to feel confident. Three months is often a good timeline to shoot for. If you feel like this timeframe is right for you check out this post on How to Study for the GMAT in 3 months. Then retake the test and show those admissions officers that you take self-improvement seriously.

]]>*Why did you choose Columbia Business School? What makes it different from other business schools?*

I wanted to have a business education in the business capital of the world. Being in NYC was a big factor in my choice of b-schools. Columbia also had a very good percentage of top international students which provided a better perspective on the global economy. What makes Columbia different from other business schools is that it is in Manhattan and it has such great alumni and corporate partners to connect with. We could do a case study about how Colgate-Palmolive handled a go-to-market strategy for a new product in the morning and be at their headquarters in midtown speaking with their marketing team by the afternoon. The list of examples of like that go on and on (in Finance—I-banks, hedge funds, private equity shops, etc.). It is similar to what Stanford has with respect to its computer science department and being immersed in Silicon Valley.

*Businessweek reports that Columbia uses a relatively mixed set of teaching methods, at least compared to some institutions—Case Study: 40%; Experiential Learning: 7%; Lectures: 38%; Team Projects: 15%. Can you tell us how you felt about the academic experience?*

It was a top notch academic experience. What I liked about the program was that it was not rigid about how it approached teaching. The methods were different for different courses and that made for a more dynamic environment. You never felt force-fit into a case study method when that may not have been the right way to teach a topic, but case study materials were always available.

*What about your professors?*

We had top professors from around the world in every discipline. * *

*Do you have any comments on the facilities at the school?*

The facilities were a bit cramped when I attended, but I understand that the school has expanded its facilities in recent years. * *

*And on the topic of your physical surroundings, what kind of advantages did you experience getting your MBA in New York City? Disadvantages?*

Being in NYC certainly had its advantages in terms of being able to easily connect and network with people in the majority of industries that students wanted to learn about and get into. Meetings are a subway or cab ride away. Columbia tends to have a lot of alumni in NYC so we had very good access to companies/execs to enrich research projects and case studies. * *

*The size of a graduating class at Columbia is roughly midway between that of a graduating class at Harvard (around 900 students) and at Stanford (roughly 375). How did you feel about the size of your class? *

* *

The class size was about right. We had around 450 students in our graduating class (with the January starts, we had about 600). The class was subdivided into clusters of about 60-70 students. We took all of our 1^{st} year courses with people from our cluster. * *

*Business school can be a very social experience. Can you describe your interaction with your classmates?*

At Columbia, the b-school can be as social as you want it to be. The experience is social at its core and you could easily make new friends, while those who had been living in NYC could continue to have a life outside of business school. As at most business schools, there was no shortage of opportunities to socialize.

*And of course, quality of alumni networks is a big factor in a choosing a business school. Have you utilized Columbia’s alumni network?*

I end up tapping into every network I have in some way. Whether it’s Columbia classmates, former colleagues, or friends, the quality of the network is a function of what you put into maintaining it. * *

*Is there anything else that you feel illustrates your MBA experience?*

I had a great time in business school. It was competitive, intellectually stimulating, social, and fun. I would recommend Columbia to anyone interested in getting an MBA.

]]>*A circular table consists of a glass center surrounded by a metal ring of uniform width. If the metal ring has a width of 2 inches, and the glass center has a diameter of 4x inches, what fraction of the table’s surface is made up by the metal ring, in terms of x?*

There’s no underhanded trick in this question, nor is there anything super complicated to incorporate into your diagram. But you should always be very mindful of the details of the question while drawing your diagram, since after you do so, you’re less likely to look at the information given in the problem. Indeed, it’s a waste of time to do so, since the information is presented much more usefully in your diagram! But this also means that if you make a mistake in the diagram, you may not correct it – and it’s very frustrating to get a problem wrong simply because your diagram was drawn incorrectly.

If it helps you to think figuratively, consider this metaphor I’ve *ahem* cooked up recently: If GMAT number properties are like soup, then GMAT geometry problems are like baking. Soup is a very forgiving dish: you can double the vegetables and halve the salt and the soup will still taste great. Same with number properties problems: for example, you can determine that the sum of an odd number and an even number is odd by memorizing that number property, or you can just take a half second to plug in numbers (3 +2 = 5, 13 + -4 = 9, etc).

Baking, on the other hand, is a precise science: if you leave out the butter or salt, your cookies are going to fall flat. Same with GMAT geometry: you must take each step precisely, and there’s very little flexibility. When you draw a diagram, you must follow the “recipe” very precisely. Transferring information from text to diagram is a common place for careless mistakes to occur. Let’s look at the example problem again and draw the diagram step by step, keeping our eyes open for any places where mistakes might occur. Here is the problem again:

*A circular table consists of a glass center surrounded by a metal ring of uniform width. If the metal ring has a width of 2 inches, and the glass center has a diameter of 4x inches, what fraction of the table’s surface is made up by the metal ring, in terms of x?*

The first thing we are told is that the table consists of a circular glass center surrounded by a metal ring of uniform width. Thus, we have two concentric circles:

Next, a diameter and a width are given. The 2 inch width is fairly straightforward to fit into the diagram. The width of the orange band can be referred to, but width would not be used to describe a dimension of the glass circle. With respect to the diameter, the words are also clear: the glass center has a diameter of 4x inches. But this is actually where the trouble starts. This question is only one out of 37; we are worried about how much time we spend on any one problem. So, maybe we draw 4x as a radius instead of a diameter (diagram *i*) , or as the diameter of the whole table instead of only the glass center (diagram *ii*), or as the radius of the whole table (diagram *iii*).

The last diagram (iv) is of course correct. This isn’t complicated, but it is important to realize that these are the situations where we can slip and lose points needlessly.

And of course, once you draw the diagram, you still have to do the rest of the work. What did you get for this problem? Let us know in the comments.

]]>Still, a lot of the time, a manager’s job is to tell people what to do. Chris Wu, one of Knewton’s star GMAT teachers, likes to point out that data sufficiency problems are actually excellent precursors to this duty at your future job. Maybe you’re a finance whiz going to business school to take your career to the next level. When you start your new job after b-school, you’ll deal with many difficult analytical problems. Some problems may require your own expertise; with others, though, you’ll recognize right away that the problem is solvable and pass it on to a first year analyst to work out the details.

Or maybe you’re an experienced software developer who will exit business school with a job at some technology behemoth. You may be the master architect of a program, but you’ll have other coders who write various sections of the code for you. When you ask them to work on something, you’ll probably know all of the hurdles that the junior coder will encounter and how to get over them. But that doesn’t mean you should do the work yourself. Knowing that the problem can be solved, you delegate it to someone else.

Perhaps you’re doing a JD/MBA and will one day be a managing partner at a top 10 firm. Some case matters might be in uncharted territory and so may require your personal touch, but others will be issues you’ve seen before. You’ll know that there is relevant precedent, you’ll see the course that an argument must take, but you won’t write the motion yourself. Knowing that the problem can be solved, you assign the case to an associate.

The common thread here? Sometimes, your time is too valuable to be spent solving problems you know how to solve. You delegate tasks to those you manage; you may provide some guidance on how to tackle a sticky issue, but you let others put all the work together.

Data Sufficiency is the exact same process. Sometimes, it may be necessary to work through all the computation to be sure that the information you have is sufficient. But other times, it becomes clear at a certain point that the problem is solvable. You deem the statement sufficient and move on.

It’s an old theme, but always worth reinforcing: Don’t waste your valuable time solving when you don’t have to.

]]>If you look at the graph of y = 1/*x*, the *y* value approaches +âˆž as *x* approaches zero from the right, and the *y* value approaches —âˆž as *x* approaches zero from the left. But the graph never reaches *x* = 0, **because you cannot divide by zero**. Dividing 1 by smaller and smaller fractions results in larger and larger quotients, because many tiny bits can fit into one whole. But you can’t answer the question of how many zeros fit into 1; the question doesn’t make sense conceptually.

All this is interesting, and the history of zero is at least a little bit interesting, too. But for the purposes of the GMAT, we have already thought much more about zero than we have to. If we remember not to divide by zero, we have remembered everything we need to know for test day. Or have we?

Here is a problem where aspiring GMAT 800′s tend to forget that dividing by zero can cause trouble on the Quant section:

If (*x* + 4)(3x + 1) = 3*x*^{2} + *x*, what is a possible value of *x*?

(A) 1

(B) 1/2

(C) 1/3

(D) -1/3

(E) -1/2

There are a couple potential approaches to this problem. We could FOIL the expression on the left side of the equation. That won’t take too long, but if we’re really up on our game, we might notice that if we factor an *x* from the expression on the right side of the equation, there will be a (3*x* + 1) on both sides, which will let us cancel and simplify. That would be faster, and every second helps, so let’s use that method.

(*x* + 4)(3x + 1) = 3*x*^{2} + *x â†’*

(*x* + 4)(3x + 1) = *x*(3*x* + 1)

We cancel the (3*x* + 1) on both sides, giving us:

*x* + 4 = *x*

Now we subtract *x* from both sides and get:

4 = 0

Wait a minute. Something went wrong. It is quite certain that 4 does not equal 0, so what happened? We can go over our calculations, but we didn’t make any errors. And this is the GMAT; 75 minutes are ticking away fast, so we don’t have time to ponder the rift in the universe that allows 4 = 0. Let’s just do the problem again really quickly with the first method. (We’ll take a second look after we finish.)

(*x* + 4)(3x + 1) = 3*x*^{2} + *x â†’*

3*x*^{2} + *x* + 12*x* + 4 = 3*x*^{2} + *x
*

Now we combine like terms by subtracting 3*x*^{2} andÂ *x *from both sides, and we solve:

12*x* + 4 = 0

12*x* = —4

*x* = —1/3

So, —1/3 is a possible value of *x*, and answer **choice D** is correct.

Now let’s take a look at what went wrong when we factored and canceled. When we first pulled out an *x*, giving us (*x* + 4)(3x + 1) = *x*(3*x* + 1), everything was going fine. We hadn’t broken any rules yet.

And then we canceled the (3*x *+ 1). When we cancel in this situation, what we are doing is dividing both sides by (3*x* + 1). The factors essentially go away, since (3*x* + 1)/(3*x* + 1) is always equal to 1. **Except** when (3*x* + 1) is equal to zero! Hindsight is 20/20, so let’s plug in *x* = —1/3, and sure enough it turns out that (3*x* + 1) is zero.

The takeaway:Â We can never divide by a variable, or by a variable expression, unless we know that the variable or expression **does not equal zero**. Remember, canceling is dividing, too.

Keep this in mind and you’ll avoid the head-scratching realization that 4=0. This will save you some troubling philosophical pondering, not to mention a lot of valuable time on test day.

]]>*Kyle Hausmann is a Content Developer at Knewton, where he helps students with their GMAT prep.*

In the first installment of our MBA Life series, we talked to Knewton’s Nathan Lasche about his experience at HBS. We found out how Nate felt about class size, the people he met, Cambridge and Boston, and the weather. Now we’ll hear from Ben Jackson, friend of Knewton and current JD/MBA student at Stanford. And, in fantastic life-path chiasmus, Ben was an undergrad at Harvard just as Nate was an undergrad at Stanford. Ben was kind enough to speak to me a few days ago about his experience with Stanford GSB.

So let’s get right into it:

**Ben’s general impression of the GSB?** “It’s a fun place to get an awesome education. I was immediately struck by how comfortable I felt there.” (A little research had told me that Stanford makes great efforts at reinforcing community, by, for one thing, bringing together academic and residential life.) “The campus is about three minutes from residence where everyone lives their first year… The new campus will be only 20 seconds away from that residence.”

**Pros and cons of the enmeshed community:** “When you’re in this intense first year experience, it’s great to be around people with the same stresses. They understand… But being so close can also reinforce your stress. Hearing someone else describe a worry, you might think, ‘Well, I wasn’t stressed about that, but now I am.’”

**What happens after the first year? ** “The majority of GSB students move off campus with other GSB students and live near other GSB students.” About 60 or 70 other GSB students live in Ben’s neighborhood. “There’s really no downside. Off campus, you have a little more space, a little more freedom… [But] to get a bit business school-y, there are a lot of efficiencies to being near everyone, like if you need a ride to school or if you want a quick study break. You’re still near everyone, but you also have a critical distance.”

**Speaking of distance:** “Palo Alto is about 45 minutes from San Francisco. It’s undeniably suburban. You pretty much have to have a car… Having lived in Cambridge and Boston for eight years, it took a little while to get used to not being able to wake up on a Saturday morning and get a breakfast sandwich from down the street… It’s a lifestyle thing. I don’t go to the city [San Francisco] that much, which suggests I’ve gotten used to the suburban life. It feels like a vacation when you’re in that kind of environment. Part of the relaxed atmosphere is that you aren’t in an urban setting where you have to fight with cars and tourists all the time. It’s also a lot easier to get a tennis court.”

**What about community? **(The key difference from HBS is the size, since a Harvard class is about two and a half times larger than a Stanford class.) “What we lack in size, we make up for in responsiveness… When you call someone, they’ll actually take your call. They do a lot to keep alumni engaged, and I’ve had success reaching out for class projects and internships… To reinforce the community, Stanford hosts a weekly speaker series — called Talk 10, or Talk 11 [if you're the class of 2010 or 2011] — where students volunteer to give a talk of about 30 minutes, with 30 minutes of Q&A… Usually around 50 to 100 people show up to hear someone give their autobiography. It’s great to hear their stories and see them opening up… so much more than resume highlights… People can get emotional sometimes. It’s something I didn’t expect. No one feels they have to give a speech, or to attend, but I’m amazed at the depth people go into and also at the regularity of attendance.”

*Kyle Hausmann is a Content Developer at Knewton, where he helps students with their GMAT prep. *

Many of Knewton’s GMAT students are aiming for the top MBA programs in the world. Comparing those programs can be difficult —HBS and Stanford GSB both look pretty darn good on a resume, after all.Â In the end, deciding between those two business behemoths largely comes down to personality. The learning experience will not be the same — the case method dominates at Harvard, for example — but there’s no question you’ll get a first class education at either one.

With the recent addition to our Product Team of Nathan Lasche, a 2010 MBA from Harvard, we thought it the perfect time to take an inside look at these top institutions.

So, here begins Knewton’s series, MBA Life*:* Insiders’ Perspectives on Business School. First, we’ll hear from Nate about his experience at Harvard Business School. And stay tuned for Ben Jackson, a friend of Knewton, currently at the Stanford Graduate School of Business. We’ll mostly steer clear of the education itself and delve more into the experience, what it’s like to live there, who you’ll meet, how you’ll feel at these schools.

**

I spoke with Nate last week about his experience as part of Harvard’s class of 2010. Nathan did his undergrad at Stanford, so he also had some insight into differences between HBS and Stanford’s GSB.

**On networking at b-school: **According to Nate, **“**It was awesome. HBS is incredibly international. You end up with friends from all over the world, from Russia, from India, from Africa. They’re known for that… Your alumni network is likely to range more widely across the globe.” Stanford claims a very similar percentage of international students per class, but, Nate explains, “It’s a volume thing. With three times the number of students, your network will probably be dispersed a little more broadly. Stanford has a reputation of being a bit more regional, not in terms of where students are coming from, but post-graduation — people of course head there from all over, but they may be more likely to be interested in staying in Silicon Valley afterward.”

**On class size: **“Classes at HBS are about 900. At Stanford, classes are about [370].Â [At Harvard] you’re constantly meeting new people, even up to your last semester. At Stanford, you might be a little more likely to max out. One of the consequences of the larger class size is that you’re always able to find your niche. There’s definitely going to be a full spectrum of students at both schools; there’s just more of a sense of magnitude at Harvard… Of course, at a smaller institution, you might get to know those three or four hundred classmates a little better. But Harvard tries to mitigate that with sections… Each class is broken up into sections of about 90 students, who go to the same classes their first year and share many activities.”

**As for the facilities: **“They’re perfect, all state-of-the-art.” (I can attest that myself — as an undergrad at Harvard, I used to walk over the river to study in the b-school’s library, with its row upon row of fine couches and arm chairs and huge windows letting in natural light. When I attended a couple of speeches over there, the lecture halls were stunning, with tight wood paneling and great desk chairs in tiered array. It’s all built to impress.) Nate adds that for those snowy New England winters, there are even “fully furnished tunnels connecting all the buildings.” Nevertheless, “You have to be alright with a little bit of snow [in Boston].”

**Speaking of Boston… **“Boston and the Bay Area are both really cool places. At HBS you’re in Cambridge, which is a cool, urban, college town. But Cambridge is also IN Boston, so you have that city life, whereas Stanford is a little further away from San Francisco. So, that’s something to consider, too, whether you’re looking for a more or less urban experience.”

Thanks, Nathan, for giving us a quick peek into life at HBS. My biggest take-away from the interview was Nate’s enthusiasm for my first question—he immediately started talking about how great all the people he met were.

Stay tuned for my interview with Ben Jackson on Stanford GSB.

]]>*Kyle Hausmann is a Content Developer at Knewton, where he helps students with their SAT prep. *

Translating words to algebra is hugely important on the SAT. The test contains trickily worded problems that are crafted specifically to test this skill. Fortunately, it’s something you can easily improve upon with a little bit of practice!

As you go through practice SAT math problems,Â focus on phrases which signify an operation, a fraction, an equality or inequality. Is there a “half as,” “five less than,” or “six times as many?” Write out all of the expressions these phrases signify. The goal is to get everything written out so do not need to look at the wording again. You can practice and re-practice on the same problem — don’t bother solving the equations if that isn’t your problem area. Then, move onto a new problem and see if your speed in translating has improved. Here’s a bit of a long example problem to get started. If you can handle this, you’re in pretty good shape.

*A large crate containing statuettes of ninjas, pirates, robots, and flying monkeys fell off a loading dock, and half of the statuettes break. Of those unbroken, one third are ninjas, three times as many are pirates as are robots, and half as many are flying monkeys as are pirates. If there are 20 unbroken robot statuettes, what was the total number of statuettes in the crate before it fell?*

After reading through the problem, you can see that we are looking for the total number of statues before the crate fell. But all of the information is about the unbroken statues that are left after the fall. So, let’s call the total** t**, and the number of unbroken statuettes **u**.

The first thing we learn is that half the statuettes broke. That means half remain unbroken. So, we can write:

1/2 Â t = u

Next, we learn, “Of those unbroken, one third are ninjas.” We can understand the word “of” to mean multiplication, but normally there is a noun before the word “of.” We can rewrite the sentence as, “One third of those unbroken are ninjas.” This is easier to translate. Calling the number of ninjas n, we turn “of” into a multiplication sign, and “are” into an equal sign:

1/3 u = n

Next, we are told, “Of those unbroken… three times as many are pirates as robots.” We need some new variables here. Let’s call the unbroken pirate statuettes** p** and the unbroken robot statuettes **r**. Now when we see “three times as many,” we have to be careful. There are more pirates than robots, so we should write 3r = p, not 3p = r.

Then, we learn, “Of those unbroken… half as many are flying monkeys as are pirates.” We’ll call flying monkeys** m**. Again, we must be careful when we see “half as many.” Since there are more pirates than flying monkeys, we have to write 1/2 p = m, not 1/2 m = p.

Lastly, we learn that there are 20 unbroken robot statuettes, so we write r = 20.

And, since there are no other kinds of statuettes, we can write n + p + r + m = u.

Now we put all of our equations together to figure out how many statuettes there were all together.

1/2 Â t = u

1/3 u = n

3r = p

1/2 p = m

r = 20

n + p + r + m = u

Since we know r, we can plug it into 3r = p, giving us 3(20) = p, or 60 = p. Then, with p, we can plug into 1/2 p = m, giving us 1/2 (60) = m, or 30 = m.

So, now we know p, r, and m. We can plug them into our big equation, n + p + r + m = u, to get:

n + 60 + 20 + 30 = u

or,

n + 110 = u

Since we have another equation with just n and u, we should be able to solve:

n + 110 = u

1/3 u = n

If we substitute 1/3 u for n in the first equation, we get:

1/3 u + 110 = u

110 = 2/3 u

(3/2) 110 = u

165 = u

We could also solve for n, which would be a third of u, so 55. But u is what we want, because with it we can find t and answer the question:

1/2 t = u

1/2 t = 165

t = 330

***

Unrelated to solving this problem, a statue of Chuck Norris also fell off the loading dock. The ground broke and the loading dock sank down, with the statue landing on top of the loading dock again. Even statues of Chuck Norris don’t fall.

(Also, Chuck Norris knows who would win in a fight of ninjas, pirates, and robots. The answer: Chuck Norris.)

]]>GMAT success depends not only on getting the right answer–but on getting it fast. Time management is key to conquering the GMAT: After all, test-takers only have an average of two minutes to spend on each question. Saving time isn’t just about answering the hard questions in less time–it’s also about answering easier questions faster. Every second you save is a second you can use on a hard problem. Taking only 30 seconds instead of 60 on one question means you’ll have 25% more time for a hard question later on. And believe it or not, there ARE easy ways to save time on many types of questions–without sacrificing accuracy.

Knewton’s course covers many strategies that will help you get the right answer, and faster. Our content developers and teachers are time-saving experts. Some of the tactics we rely on are commonly known (and too-commonly forgotten!), while others are much less widely utilized. The following is a list of Knewton’s top 10 great time management tactics. The list is a combination of the physical and the psychological, everything from test strategies to typing tips. All of these guidelines will help you bank time early, give you more time to concentrate on hard questions, and ultimately increase your score.

10. **Don’t untangle complicated language unless you have to**. If you come upon a few lines in a reading passage that are all “tied up,” don’t waste time untying them. Just get the gist and keep reading. If a question asks about those lines, you can always go back and figure out what is going on then; but if no question deals with them, untangling would have been a waste of time. Like all the time savers in this list, the idea is to keep moving–and go back only if you absolutely have to.

9. **Look at the verb.** When a Reading Comprehension question asks for the primary/main purpose of a question, that purpose is often expressed by infinitives in the answer choices. For example, possible answers might include, a) to explain a complicated scientific concept, b) to suggest a new application of a scientific theory, and c) to advocate for a new application of a scientific theory. Before considering the complete answer choice, try to eliminate choices just by looking at the verbs. Verbs like encourage, argue, suggest, support, advocate, etc. represent a strong agenda on the author’s part. If the passage is only presenting information, you can immediately eliminate choices with those verbs. A choice with a verb like summarize or report could be the correct choice.

8.** Learn keyboard shortcuts. **If you don’t know what CTRL-X means, learn! Some particularly important shortcuts to know: Copy by pressing CONTROL and C (CTRL-C) at the same time; paste by pressing CTRL-V. CTRL-X cuts. CTRL-Z is undo, and CTRL-Y is redo. If you are used to using keyboard shortcuts, note that not all of them will work. (I like to use CTRL-Up/Down Arrow to jump between paragraphs, but that won’t work on the GMAT.) So whether you are used to using the keyboard in this way or not, download the official GMAT practice test at mba.com and practice keyboard shortcuts as you write your AWA essays. You’ll definitely be moving things around in your essay. These shortcuts can help you do that faster, leaving more time to hone your diction and develop your ideas.

7. **Guess and move on**. Sometimes you just don’t know the answer. Or you know you would get it if you spent five minutes on the problem, but five minutes is too long. Staring at a problem you aren’t solving is a huge waste of time. If you’ve been working (really working) on a problem for 3 minutes, stop and ask if you will be done in 30 seconds. If the answer is no, guess and move on. And if you have been staring at a question for 60-90 seconds and still don’t know what to do, the same is true: It’s time to guess and move on.

6. **Zoom out** **from reading comprehension passages.** If a question asks about the “occipital lobe,” try literally drawing back the focus of your eyes to see the whole passage, registering each place the phrase “occipital lobe” appears. This is a skill that can be improved with practice. RC passages an take up a lot of time if you have to read through them again and again — this skill can help you find what you need without rereading.

5. **Compare answer choices**. Answer choices are often grouped together. Look at what makes the choices similar and what makes them different. So, if on a sentence correction question, two choices begin with “its” and three begin with “their,” you have a 2/3 split. The antecedent of the pronoun will either be singular or plural, and once you know which one is correct, you can eliminate the incorrect choices right away.

4. **Pick a strategy**. Sometimes there will be multiple ways to solve a problem. You can tell that testing cases will get you there, with a little work; and so will solving algebraically, although that doesn’t seem super quick either. Rather than wasting time debating the relative efficiency, just pick a strategy and stick to it.

3. **Don’t solve**. This one is obvious but often overlooked. Data Sufficiency problems ask you to say when you have enough information to answer the question in the prompt, not to actually compute the answer. Sometimes you need to work all the way to a solution, but often, all you need to know is *how* to get the solution–and whether you could do so with the information provided. In these cases, actually solving is a waste of valuable time.

2. **Be confident. **If you know the right answer, stick with it. Often on, say, a Problem Solving question, you’ll need to figure out the right answer before you even get to the choices. Don’t waste time second guessing yourself when you see a different answer that looks appealing; you studied for this, you did the question properly. Select your answer and proceed to the next question.

1. **Know your s#!&**. This one is on the obvious side, but too important to leave off the list. The most important things you can do to prepare for the GMAT is to understand all the concepts tested and to be familiar with all the question types. There is no magic formula–the best strategy is to spend a lot of time beforehand practicing and familiarizing yourself with the various concepts and question formats.