The post GMAT Tip of the Week: Make J. Cole One of Your Critical Reasoning Role Modelz appeared first on Veritas Prep Blog.

]]>One of the most common misconceptions that GMAT examinees have about the exam is that, while on quantitative questions, only one answer can be correct and everything else is wrong, on verbal questions “my wrong answer was good, but maybe not the best.” It is critical to realize that **on GMAT verbal questions, exactly one answer is right and the other four are fatally flawed and 100% wrong!** Visit a GMAT classroom or a GMAT Club forum thread discussing a Critical Reasoning problem, and you’re almost certain to see/hear students protesting for why their wrong answer could be right. “Well but what if the argument said X, would I be right?” “Well but what if instead of “some” it said “most” would it be right then?”

But students love trying to save an incorrect answer to verbal questions, and in particular Critical Reasoning questions. And to an extent that’s understandable: in high school and college, math was always black and white but in “verbal” classes (literature and the arts, history, philosophy…) as long as you could defend your stance or opinion you could be considered “right” even if that opinion differed from that of your professor. You could “save” an incorrect or unpopular position on an issue by finding a way to justify your stance, and in some cases you were even rewarded for proposing and defending an unorthodox, contrarian viewpoint. But on Critical Reasoning problems, remember this important mantra about incorrect answers:

*Don’t save her; she don’t want to be saved.*

Your job is to attack answer choices, looking for the flaw instead of looking for ways to defend. Each incorrect answer choice is specifically written so that **someone** will see **something** redeeming about part of it – otherwise no one would ever pick it and it would be a waste of an answer – so looking for ways to save an answer choice is a fool’s errand. If you’re looking for little things to like about answer choices you should find that in just about every answer choice you see. The operative word in “Critical Reasoning” is critical – you want to be as critical as you can, much like J. Cole is when he discusses his relationships in *No Role Modelz*.

Consider an example from the Veritas Prep Question Bank:

*According to a recent study, employees who bring their own lunches to work take fewer sick days and and are, on average, more productive per hour spent at work than those who eat at the workplace cafeteria. In order to minimize the number of sick days taken by its staff, Boltech Industries plans to eliminate its cafeteria.*

*Which of the following, if true, provides the most reason to believe that Boltech Industries’ strategy will not accomplish its objective?*

*A) Boltech’s cafeteria is known for serving a diverse array of healthy lunch options.*

* B) Because of Boltech’s location, employees who choose to visit a nearby restaurant for lunch will seldom be able to return within an hour.*

* C) Employees have expressed concern about the cost of dining at nearby restaurants compared with the affordability of the Boltech cafeteria.*

* D) Employees who bring their lunch from home tend to lead generally healthier lifestyles than those of employees who purchase lunch.*

* E) Many Boltech employees chose to work for the company in large part because of the generous benefits, such as an on-site cafeteria and fitness center, that Boltech offers.*

Less than half of all test-takers get this problem right, in large part because they try to “save” wrong answer choices. The goal of this plan is very clearly stated as “to minimize the number of sick days” but students very frequently pick choices B and E. With B, they try to save it by thinking “but isn’t being away from your desk a long time for a lunch really bad, too?” And the answer may very well be “yes” but the question specifically asks for a reason to think that the strategy will not achieve its objective, and that objective is very clearly stated as pertaining only to sick days.

“Well what if the plan was to minimize time away from employees’s desks?” students love to ask, committed to saving the bad answer choice. While that answer might be “yes,” the even bigger answer is “train yourself to stop trying to save wrong answers!” The study time you expend trying to create a situation in which your wrong answer would be right (“well with E, if the goal were employee retention then it would probably be right”) is time you spend reinforcing a habit that can get you in trouble on test day. Trying to save answers leads you both to wrong answers and to extra time spent on a hard decision, because, again, if your mindset is to look for the good in every answer choice those choices are written to give you something good to find!

So as you study, and especially on test day, heed the wisdom of J. Cole. If you fall into the trap of saving answers, tell the GMAT “fool me one time, shame on you; fool me twice can’t put the blame on you.” But most importantly, as you look at Critical Reasoning answer choices, don’t save her. She don’t want to be saved.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: The Song Remains the Same appeared first on Veritas Prep Blog.

]]>Biggie’s “Hypnotize” samples directly from “La Di Da Di” (originally by Doug E. Fresh – yep, he’s the one who inspired “The Dougie” that Cali Swag District wants to teach you – and Slick Rick). “Biggie Biggie Biggie, can’t you see, sometimes your words just hypnotize me…” was originally “Ricky, Ricky, Ricky…” And right around the same time, Snoop Dogg and 2Pac just redid the entire song just about verbatim, save for a few brand names.

The “East Coast edit” of Chris Brown’s “Loyal”? French Montana starts his verse straight quoting Jay-Z’s “I Just Wanna Love U” (“I’m a pimp by blood, not relation, I don’t chase ’em, I replace ’em…”), which (probably) borrowed the line “I don’t chase ’em I replace ’em” from a Biggie track, which probably got it from something else. And these are just songs we heard on the radio this morning driving to work…

The point? Hip hop is a constant variation on the same themes, one of the greatest recycling centers the world has ever known.

And so is the GMAT.

Good test-takers – like veteran hip hop heads – train themselves to see the familiar within what looks (or sounds) unique. A hip hop fan often says, “Wait, where I have heard that before?” and similarly, a good test-taker sees a unique, challenging problem and says, “Wait, where have I seen that before?”

And just like you might recite a lyric back and forth in your mind trying to determine where you’ve heard it before, on test day you should recite the operative parts of the problem or the rule to jog your memory and to remind yourself that you’ve seen this concept before.

Is it a remainder problem? Flip through the concepts that you’ve seen during your GMAT prep about working with remainders (“the remainder divided by the divisor gives you the decimals; when the numerator is smaller then the denominator the whole numerator is the remainder…”).

Is it a geometry problem? Think of the rules and relationships that showed up on tricky geometry problems you have studied (“I can always draw a diagonal of a rectangle and create a right triangle; I can calculate arc length from an inscribed angle on a circle by doubling the measure of that angle and treating it like a central angle…”).

Is it a problem that asks for a seemingly-incalculable number? Run through the strategies you’ve used to perform estimates or determine strange number properties on similar practice problems in the past.

The GMAT is a lot like hip hop – just when you think they’ve created something incredibly unique and innovative, you dig back into your memory bank (or click to a jazz or funk station) and realize that they’ve basically re-released the same thing a few times a decade, just under a slightly different name or with a slightly different rhythm.

The lesson?

You won’t see anything truly unique on the GMAT. So when you find yourself stumped, act like the old guy at work when you tell him to listen to a new hip hop song: “Oh I’ve heard this before…and actually when I heard it before in the ’90s, my neighbor told me that she had heard it before in the ’80s…” As you study, train yourself to see the similarities in seemingly-unique problems and see though the GMAT’s rampant plagiarism of itself.

The repetitive nature of the GMAT and of hip hop will likely mean that you’re no longer so impressed by Tyga, but you can use that recognition to be much more impressive to Fuqua.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: Big Sean Says Your GMAT Score Will Bounce Back appeared first on Veritas Prep Blog.

]]>If you have a car stereo or Pandora account, you’ve undoubtedly heard Big Sean talking about bouncing back this month. “Bounce Back” is a great anthem for anyone hitting a rough patch – at work, in a relationship, after a rough day for your brackets during next week’s NCAA tournament – but this isn’t a self-help, “it’s always darkest before dawn,” feel-good article. Big Sean has some direct insight into the GMAT scoring algorithm with Bounce Back, and if you pay attention, you can leverage Bounce Back (off the album “I Decided” – that’ll be important, too) to game-plan your test day strategy and increase your score.

So, what’s Big Sean’s big insight?

The GMAT scoring (and question delivery) algorithm is designed specifically so that you can “take an L” and bounce back. And if you understand that, you can budget your time and focus appropriately. The test is designed so that just about everybody misses multiple questions – the adaptive system serves you problems that should test your upper threshold of ability, and can also test your lower limit if you’re not careful.

What does that mean? Say you, as Big Sean would say, “take an L” (or a loss) on a question. That’s perfectly fine…everyone does it. The next question should be a bit easier, providing you with a chance to bounce back. The delivery system is designed to use the test’s current estimate of your ability to deliver you questions that will help it refine that estimate, meaning that it’s serving you questions that lie in a difficulty range within a few percentile points of where it thinks you’re scoring.

If you “take an L” on a problem that’s even a bit below your true ability, missing a question or two there is fine as long as it’s an outlier. No one question is a perfect predictor of ability, so any single missed question isn’t that big of a deal…if you bounce back and get another few questions right in and around that range, the system will continue to test your upper threshold of ability and give you chances to prove that the outlier was a fluke.

The problem comes when you don’t bounce back. This doesn’t mean that you have to get the next question right, but it does mean that you can’t afford big rough patches – a run of 3 out of 4 wrong or 4 out of 5 wrong, for example. At that point, the system’s estimate of you has to change (your occasional miss isn’t an outlier anymore) and while you can still bounce back, you now run the risk of running out of problems to prove yourself. As the test serves you questions closer to its new estimate of you, you’re not using the problems to “prove how good you are,” but instead having to spend a few problems proving you’re “not that bad, I promise!”

So, okay. Great advice – “don’t get a lot of problems wrong.” Where’s the real insight? It can be found in the lyrics to “Bounce Back”:

*Everything I do is righteous
Betting on me is the right risk
Even in a ***** crisis…*

During the test you have to manage your time and effort wisely, and that means looking at hard questions and determining whether betting on that question is the right risk. You **will** get questions wrong, but you also control how much you let any one question affect your ability to answer the others correctly. A single question can hurt your chances at the others if you:

- Spend too much time on a problem that you weren’t going to get right, anyway
- Let a problem get in your head and distract you from giving the next one your full attention and confidence

Most test-takers would be comfortable on section pacing if they had something like 3-5 fewer questions to answer, but when they’re faced with the full 37 Quant and 41 Verbal problems they feel the need to rush, and rushing leads to silly mistakes (or just blindly guessing on the last few problems). And when those silly mistakes pile up and become closer to the norm than to the outlier, that’s when your score is in trouble.

You can avoid that spiral by determining when a question is not the right risk! If you recognize in 30-40 seconds (or less) that you’re probably going to take an L, then take that L quickly (put in a guess and move on) and bank the time so that you can guarantee you’ll bounce back. You know you’re taking at least 5 Ls on each section (for most test-takers, even in the 700s that number is probably closer to 10) so let yourself be comfortable with choosing to take 3-4 Ls consciously, and strategically bank the time to ensure that you can thoroughly get right the problems that you know you should get right.

Guessing on the GMAT doesn’t have to be a panic move – when you know that the name of the game is giving yourself the time and patience to bounce back, a guess can summon Big Sean’s album title, “I Decided,” as opposed to “I screwed up.” (And if you need proof that even statistics PhDs who wrote the GMAT scoring algorithm need some coaching with regard to taking the L and bouncing back, watch the last ~90 seconds of this video.)

So, what action items can you take to maximize your opportunity to bounce back?

**Right now:** pay attention to the concepts, question types, and common problem setups that you tend to waste time on and get wrong. Have a plan in mind for test day that “if it’s *this* type of problem and I don’t see a path to the finish line quickly, I’m better off taking the L and making sure I bounce back on the next one.”

Also, as you review those types of problems in your homework and practice tests, look for techniques you can use to guess intelligently. For many, combinatorics with restrictions is one of those categories for which they often cannot see a path to a correct answer. Those problems are easy to guess on, however! Often you can eliminate a choice or two by looking at the number of possibilities that would exist without the restriction (e.g. if Remy and Nicki would just patch up their beef and stand next to each other, there would be 120 ways to arrange the photo, but since they won’t the number has to be less than 120…). And you can also use that total to ask yourself, “Does the restriction take away a lot of possibilities or just a few?” and get a better estimate of the remaining choices.

**On test day:** Give yourself 3-4 “I Decided” guesses and don’t feel bad about them. If your experience tells you that betting your time and energy on a question is not the right risk, take the L and use the extra time to make sure you bounce back.

The GMAT, like life, guarantees that you’ll get knocked down a few times, but what you can control is how you respond. Accept the fact that you’re going to take your fair share of Ls, but if you’re a real one you know how to bounce back.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: Keep Your GMAT Score Safe from the Bowling Green Massacre appeared first on Veritas Prep Blog.

]]>Whatever Ms. Conway’s intentions (or lack thereof; again we’ll let you decide) with the quote, she is certainly guilty of inadvertently doing one thing: she didn’t likely intend to help you avoid a disaster on the GMAT, but if you’re paying attention she did.

Your GMAT test day does not have to be a Bowling Green Massacre!

Here’s the thing about the Bowling Green Massacre: it never happened. But by now, it’s lodged deeply enough in the psyche of millions of Americans that, to them, it did. And the same thing happens to GMAT test-takers all the time. They think they’ve seen something on the test that isn’t there, and then they act on something that never happened in the first place. And then, sadly, their GMAT hopes and dreams suffer the same fate as those poor souls at Bowling Green (#thoughtsandprayers).

Here’s how it works:

**The Quant Section’s Bowling Green Massacre**

On the Quant section, particularly with Data Sufficiency, your mind will quickly leap to conclusions or jump to use a rule that seems relevant. Consider the example:

*What is the perimeter of isosceles triangle LMN?*

*(1) Side LM = 4*

* (2) Side LN = 4√2*

*A. Statement (1) ALONE is sufficient, but statement (2) alone is insufficient*

* B. Statement (2) ALONE is sufficient, but statement (1) alone is insufficient*

* C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient*

* D. EACH statement ALONE is sufficient*

* E. Statements (1) and (2) TOGETHER are NOT sufficient*

When people see that square root of 2, their minds quickly drift back to all those flash cards they studied – flash cards that include the side ratio for an isosceles right triangle: x, x, x√2. And so they then leap to use that rule, inferring that if one side is 4 and the other is 4√2, the other side must also be 4 to fit the ratio and they can then calculate the perimeter. With both statements together, they figure, they can derive that perimeter and select choice C.

But think about where that side ratio comes from: an isosceles **right** triangle. You’re told in the given information that this triangle is, indeed, isosceles. But you’re never told that it’s a right triangle. Much like the Bowling Green Massacre, “right” never happened. But the mere suggestion of it – the appearance of the √2 term that is directly associated with an isosceles, right triangle – baits approximately half of all test-takers to choose C here instead of the correct E (explanation: “isosceles” means only that two sides match, so the third side could be either 4, matching side LM, or 4√2, matching side LN).

Your mind does this to you often on Data Sufficiency problems: you’ll limit the realm of possible numbers to integers, when that wasn’t defined, or to positive numbers, when that wasn’t defined either. You’ll see symptoms of a rule or concept (like √2 leads to the isosceles right triangle side ratio) and assume that the entire rule is in play. The GMAT preys on your mind’s propensity for creating its own story when in reality, only part of that story really exists.

**The Verbal Section’s Bowling Green Massacre**

This same phenomenon appears on the Verbal section, too – most notably in Critical Reasoning. Much like what many allege that Kellyanne Conway did, your mind wants to ascribe particular significance to events or declarations, and it will often exaggerate on you. Consider the example:

*About two million years ago, lava dammed up a river in western Asia and caused a small lake to form. The lake existed for about half a million years. Bones of an early human ancestor were recently found in the ancient lake-bottom sediments that lie on top of the layer of lava. Therefore, ancestors of modern humans lived in Western Asia between two million and one-and-a-half million years ago.*

*Which one of the following is an assumption required by the argument?*

*A. There were not other lakes in the immediate area before the lava dammed up the river.*

* B. The lake contained fish that the human ancestors could have used for food.*

* C. The lava that lay under the lake-bottom sediments did not contain any human fossil remains.*

* D. The lake was deep enough that a person could drown in it.*

* E. The bones were already in the sediments by the time the lake disappeared.*

The key to most Critical Reasoning problems is finding the conclusion and knowing EXACTLY what the conclusion says – nothing more and nothing less. Here the conclusion is the last sentence, that “ancestors of modern humans lived” in this region at this time. When people answer this problem incorrectly, however, it’s almost always for the same reason. They read the conclusion as “the FIRST/EARLIEST ancestors of modern humans lived…” And in doing so, they choose choice C, which protects against humans having come before the ones related to the bones we have.

“First/earliest” is a classic Bowling Green Massacre – it’s a much more noteworthy event (“scientists have discovered human ancestors” is pretty tame, but “scientists have discovered the FIRST human ancestors” is a big deal) that your brain wants to see. But it’s not actually there! It’s just that, in day to day life, you’d rarely ever read about a run-of-the-mill archaeological discovery; it would only pop up in your social media stream if it were particularly noteworthy, so your mind may very well assume that that notoriety is present even when it’s not.

In order to succeed on the GMAT, you need to become aware of those leaps that your mind likes to take. We’re all susceptible to:

- Assuming that variables represent integers, and that they represent positive numbers
- Seeing the symptoms of a rule and then jumping to apply it
- Applying our own extra superlatives or limits to conclusions

So when you make these mistakes, commit them to memory – they’re not one-off, silly mistakes. Our minds are vulnerable to Bowling Green Massacres, so on test day #staywoke so that your score isn’t among those that are, sadly, massacred.

**free online GMAT seminars **running all the time. And as always, be sure to follow us on **Facebook**, **YouTube**, **Google+** and **Twitter**!

*By Brian Galvin.*

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]]>The post Quarter Wit, Quarter Wisdom: Solving the Hourglass Puzzle appeared first on Veritas Prep Blog.

]]>First, understand what an hourglass is – it is a mechanical device used to measure the passage of time. It is comprised of two glass bulbs connected vertically by a narrow neck that allows a regulated trickle of sand from the upper bulb to fall into the lower one. The sand also takes a fixed amount of time to fall from the upper bulb to the lower bulb. Hourglasses may be reused indefinitely by inverting the bulbs once the upper bulb is empty.

This is what they look like:

Say a 10-minute hourglass will let us measure time in intervals of 10 minutes. This means all of the sand will flow from the upper bulb to the lower bulb in exactly 10 minutes. We can then flip the hourglass over – now sand will start flowing again for the next 10 minutes, and so on. We cannot measure, say, 12 minutes using just a 10-minute hourglass, but we can measure more time intervals when we have two hourglasses of different times. Let’s look at this practice problem to see how this can be done:

*A teacher of mathematics used an unconventional method to measure a 15-minute time limit for a test. He used a 7-minute and an 11-minute hourglass. During the whole time, he turned the hourglasses only 3 times (turning both hourglasses at once counts as one flip). **Explain how the teacher measured out 15 minutes.*

Here, we have a 7-minute hourglass and an 11-minute hourglass. This means we can measure time in intervals of 7 minutes as well as in intervals of 11 minutes. But consider this: if both hourglasses start together, at the end of 7 minutes, we will have 4 minutes of sand leftover in the top bulb of the 11-minute hourglass. So we can also measure out 4 minutes of time.

Furthermore, if we flip the 7-minute hourglass over at this time and let it flow for that 4 minutes (until the sand runs out of the top bulb of the 11-minute hourglass), we will have 3 minutes’ worth of sand leftover in the 7-minute hourglass. Hence, we can measure a 3 minute time interval, too, and so on…

Now, let’s see how we can measure out 15 minutes of time using our 7-minute and 11-minute hourglasses.

First, start both hourglasses at the same time. After the top bulb of the 7-minute hourglass is empty, flip it over again. At this time, we have 4 minutes’ worth of sand still in the top bulb of the 11-minute hourglass. When the top bulb of the 11-minute hourglass is empty, the *bottom bulb* of 7-minute hourglass will have 4 minutes’ worth of sand in it. At this point, 11 minutes have passed

Now simply flip the 7-minute hourglass over again and wait until the sand runs to the bottom bulb, which will be in 4 minutes.

This is how we measure out 11 + 4 = 15 minutes of time using a 7-minute hourglass and an 11-minute hourglass.

Let’s look at another problem:

*Having two hourglasses, a 7-minute one and a 4-minute one, how can you correctly time out 9 minutes?*

Now we need to measure out 9 minutes using a 7-minute hourglass and a 4-minute hourglass. Like we did for the last problem, begin by starting both hourglasses at the same time. After 4 minutes pass, all of the sand in the 4-minute hourglass will be in the lower bulb. Now flip this 4-minute hourglass back over again. In the 7-minute hourglass, there will be 3 minutes’ worth of sand still in the upper bulb.

After 3 minutes, all of the sand from the 7-minute hourglass will be in the lower bulb and 1 minute’s worth of sand will be in the upper bulb of the 4-minute hourglass.

This is when we will start our 9-minute interval.

The 1 minute’s worth of sand will flow to the bottom bulb of the 4-minute hourglass. Then we just need to flip the 4-minute hourglass over and let all of the sand flow out (which will take 4 minutes), and then flip the hourglass over to let all of the sand flow out again (which will take another 4 minutes).

In all, we have measured out a 1 + 4 + 4 = 9-minute interval, which is what the problem has asked us to find.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube, Google+, and Twitter!*

*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!*

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]]>The post Quarter Wit, Quarter Wisdom: Solving the Pouring Water Puzzle appeared first on Veritas Prep Blog.

]]>Today, we will look at the popular “pouring water puzzle”. You may remember a similar puzzle from the movie *Die Hard with a Vengeance*, where Bruce Willis and Samuel L. Jackson had to diffuse a bomb by placing a 4 gallon jug of water on a set of scales.

Here is the puzzle:

*You have a 3- and a 5-liter water container – each container has no markings except for that which gives us its total volume. We also have a running tap. We must use the containers and the tap in such a way that we measure out exactly 4 liters of water. How can this be done?*

Don’t worry that this question is not written in a traditional GMAT format! We need to worry only about the logic behind the puzzle – we can then answer any question about it that is given in any GMAT format.

Let’s break down what we are given. We have only two containers – one of 3-liter and the other of 5-liter capacity. The containers have absolutely no markings on them other than those which give us the total volumes, i.e. the markings for 3 liters and 5 liters respectively. There is no other container. We also have a tap/faucet of running water, so basically, we have an unlimited supply of water. Environmentalists may not like my saying this, but this fact means we can throw out water when we need to and just refill again.

Now think about it:

**STEP 1:** Let’s fill up the 5-liter container with water from the tap. Now we are at (5, 0), with 5 being the liters of water in the 5-liter container, and 0 being the liters of water in the 3-liter container.

**STEP 2:** Now, there is nothing we can do with this water except transfer it to the 3-liter container (there is no other container and throwing out the water will bring us back to where we started). After we fill up the 3-liter container, we are left with 2 liters of water in the 5-liter container. This brings us to (2, 3).

**STEP 3:** We gain nothing from transferring the 3 liters of water back to 5-liter container, so let’s throw out the 3 liters that are in the 3-liter container. Because we just threw out the water from the 3-liter container, we will gain nothing by simply refilling it with 3 liters of water again. So now we are at (2, 0).

**STEP 4:** The next logical step is to transfer the 2 liters of water we have from the 5-liter container to the 3-liter container. This means the 3-liter container has space for 1 liter more until it reaches its maximum volume mark. This brings us to (0, 2).

**STEP 5:** Now fill up the 5-liter container with water from the tap and transfer 1 liter to the 3-liter container (which previously had 2 liters of water in it). This means we are left with 4 liters of water in the 5-liter container. Now we are at (4, 3).

This is how we are able to separate out exactly 4 liters of water without having any markings on the two containers. We hope you understand the logic behind solving this puzzle. Let’s take a look at another question to help us practice:

*We are given three bowls of 7-, 4- and 3-liter capacity. Only the 7-liter bowl is full of water. Pouring the water the fewest number of times, separate out the 7 liters into 2, 2, and 3 liters (in the three bowls).*

This question is a little different in that we are not given an unlimited supply of water. We have only 7 liters of water and we need to split it into 2, 2 and 3 liters. This means we can neither throw away any water, nor can we add any water. We just need to work with what we have.

We start off with (7, 0, 0) – with 7 being the liters of water in the 7-liter bowl, the first 0 being the liters of water in the 4-liter bowl, and the second 0 being the liters of water in the 3-liter bowl – and we need to go to (2, 2, 3). Let’s break this down:

**STEP 1:** The first step would obviously be to pour water from the 7-liter bowl into the 4-liter bowl. Now you will have 3 liters of water left in the 7-liter bowl. We are now at (3, 4, 0).

**STEP 2:** From the 4-liter bowl, we can now pour water into the 3-liter bowl. Now we have 1 liter in the 4-liter bowl, bringing us to (3, 1, 3).

**STEP 3:** Empty out the 3-liter bowl, which is full, into the 7-liter bowl for a total of 6 liters – no other transfer makes sense [if we transfer 1 liter of water to the 7-liter bowl, we will be back at the (4, 0, 3) split, which gives us nothing new]. This brings us to (6, 1, 0).

**STEP 4:** Shift the 1 liter of water from the 4-liter bowl to the 3-liter bowl. We are now at (6, 0, 1).

**STEP 5:** From the 7-liter bowl, we can now shift 4 liters of water into the 4-liter bowl. This leaves us with with 2 liters of water in the 7-liter bowl. Again, no other transfer makes sense – pouring 1 liter of water into some other bowl takes us back to a previous step. This gives us (2, 4, 1).

**STEP 6:** Finally, pour water from the 4-liter bowl into the 3-liter bowl to fill it up. 2 liters will be shifted, bringing us to (2, 2, 3). This is what we wanted.

We took a total of 6 steps to solve this problem. At each step, the point is to look for what helps us advance forward. If our next step takes us back to a place at which we have already been, then we shouldn’t take it.

Keeping these tips in mind, we should be able to solve most of these pouring water puzzles in the future!

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube, Google+, and Twitter!*

*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!*

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]]>The post GMAT Tip of the Week: Taking the Least Amount of Time to Solve “At Least” Probability Problems appeared first on Veritas Prep Blog.

]]>Fortunately, and contrary to popular belief, the GMAT isn’t “pure evil.” Wherever it provides opportunities for less-savvy examinees to waste their time, it also provides a shortcut for those who have put in the study time to learn it or who have the patience to look for the elevator, so to speak, before slogging up the stairs. And one classic example of that comes with the “at least one” type of probability question.

To illustrate, let’s consider an example:

*In a bowl of marbles, 8 are yellow, 6 are blue, and 4 are black. If Michelle picks 2 marbles out of the bowl at random and at the same time, what is the probability that at least one of the marbles will be yellow?*

*(A) 5/17*

* (B) 12/17*

* (C) 25/81*

* (D) 56/81*

* (E) 4/9*

Here, you can first streamline the process along the lines of one of those “There are two types of people in the world: those who _______ and those who don’t _______” memes. Your goal is to determine whether you get a yellow marble, so you don’t care as much about “blue” and “black”…those can be grouped into “not yellow,” thereby giving you only two groups: 8 yellow marbles and 10 not-yellow marbles. Fewer groups means less ugly math!

But even so, trying to calculate the probability of every sequence that gives you one or two yellow marbles is labor intensive. You could accomplish that “not yellow” goal several ways:

First marble: Yellow; Second: Not Yellow

First: Not Yellow; Second: Yellow

First: Yellow; Second: Yellow

That’s three different math problems each involving fractions and requiring attention to detail. There ought to be an easier way…and there is. When a probability problem asks you for the probability of “at least one,” consider the only situation in which you WOULDN’T get at least one: if you got none. That’s a single calculation, and helpful because if the probability of drawing two marbles is 100% (that’s what the problem says you’re doing), then 100% minus the probability of the unfavorable outcome (no yellow) has to equal the probability of the favorable outcome. So if you determine “the probability of no yellow” and subtract from 1, you’re finished. That means that your problem should actually look like:

PROBABILITY OF NO YELLOW, FIRST DRAW: 10 non-yellow / 18 total

PROBABILITY OF NO YELLOW, SECOND DRAW: 9 remaining non-yellow / 17 remaining total

10/18 * 9/17 reduces to 10/2 * 1/17 = 5/17. Now here’s the only tricky part of using this technique: 5/17 is the probability of what you DON’T want, so you need to subtract that from 1 to get the probability you do want. So the answer then is 12/17, or B.

More important than this problem is the lesson: when you see an “at least one” probability problem, recognize that the probability of “at least one” equals 100% minus the probability of “none.” Since “none” is always a single calculation, you’ll always be able to save time with this technique. Had the question asked about three marbles, the number of favorable sequences for “at least one yellow” would be:

Yellow Yellow Yellow

Yellow Not-Yellow Not-Yellow

Yellow Not-Yellow Yellow

Yellow Yellow Not-Yellow

Not-Yellow Yellow Yellow

…

(And note here – this list is not yet exhaustive, so under time pressure you may very well forget one sequence entirely and then still get the problem wrong even if you’ve done the math right.)

Whereas the probability of No Yellow is much more straightforward: Not-Yellow, Not-Yellow, Not-Yellow would be 10/18 * 9/17 * 8/16 (and look how nicely that last fraction slots in, reducing quickly to 1/2). What would otherwise be a terrifying slog, the “long way” becomes quite quick the shorter way.

So, remember, when you see “at least one” probability on the GMAT, employ the “100% minus probability of none” strategy and you’ll save valuable time on at least one Quant problem on test day.

**free online GMAT seminars **running all the time. And as always, be sure to follow us on **Facebook**, **YouTube**, **Google+** and **Twitter**!

*By Brian Galvin.*

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]]>The post Investing in Success: The Best In-Person or Online GMAT Tutors Can Make a Difference appeared first on Veritas Prep Blog.

]]>**Knowledge of All Aspects of the GMAT**

The best private GMAT tutor has more than just general advice regarding the GMAT. The person has thorough knowledge of the exam and its contents. There are several parts to the GMAT, including the Verbal, Quantitative, Integrated Reasoning, and Analytical Writing sections. A qualified tutor will have plenty of tips to share that can help you to navigate all of the sections on the GMAT. Plus, an experienced tutor will be able to evaluate the results of your practice GMAT to determine where you need to focus most of your study efforts. This puts the element of efficiency into your test prep.

The GMAT instructors at Veritas Prep achieved scores on the exam that placed them in the 99th percentile, so if you work with a Veritas Prep tutor, you know you’re studying with someone who has practical experience with the exam. Our tutors are experts at describing the subtle points of the GMAT to their students.

**Access to Quality Study Resources**

If you want to thoroughly prepare for the GMAT, you must use quality study materials. At Veritas Prep, we have a GMAT curriculum that guides you through each section of the test. Your instructor will show you the types of questions on the test and reveal proven strategies you can use to answer them correctly. Of course, our curriculum teaches you the facts you need to know for the test. But just as importantly, we show you how to apply those facts to the questions on the exam. We do this in an effort to help you think like a business executive as you complete the GMAT. Private tutoring services from Veritas Prep give you the tools you need to perform your best on the exam.

**Selecting Your Method of Learning**

The best GMAT tutors can offer you several options when it comes to preparing for the exam. Perhaps you work full-time as a business professional. You want to prepare for the GMAT but don’t have the time to attend traditional courses. In that case, you should search for an online GMAT tutor. As a result, you can prep for the GMAT without disrupting your busy work schedule. At Veritas Prep, we provide you with the option of online tutoring as well as in-person classes. We recognize that flexibility is important when it comes to preparing for the GMAT, and we want you to get the instruction you need to earn a high score on this important test.

**An Encouraging Instructor**

Naturally, when you take advantage of GMAT private tutoring services, you will learn information you need to know for the test. But a tutor should also take the time to encourage you as you progress in your studies. It’s likely that you’ll face some stumbling blocks as you prepare for the different sections of the GMAT. A good instructor must be ready with encouraging words when you’re trying to master difficult skills.

Encouraging words from a tutor can give you the push you need to conquer especially puzzling questions on the test. The understanding tutors at Veritas Prep have been through preparation for the GMAT as well as the actual test, so we understand the tremendous effort it takes to master all of its sections.

If you want to partner with the best GMAT tutor as you prep for the test, we have you covered at Veritas Prep! When you sign up to study for the GMAT with Veritas Prep, you are investing in your own success. Give us a call or write us an email today to let us know when you want to start gearing up for excellence on the GMAT!

*Getting ready to take the GMAT? We have **free online GMAT seminars** **running all the time. And, be sure to follow us on **Facebook**, **YouTube**, **Google+**, and **Twitter**!*

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]]>The post GMAT Writing Tips: Analytical Writing for the GMAT appeared first on Veritas Prep Blog.

]]>**Take a Few Minutes to Plan Your Essay**

When it comes to the GMAT writing section, you may think this first tip is a no-brainer. Unfortunately, some students become nervous or anxious about this part of the exam and forget to plan out their essay before diving into the task. This can result in a poorly organized essay or one that is missing important points.

Take the time to carefully read the directions and the argument. Then, create a rough outline of what points you want to include in the essay as well as where you want to include them. If you lose your train of thought while you’re writing, simply look at your outline to regain your focus.

**Determine the Flaws in the Argument**

Your essay’s plan should include the flaws in the author’s argument. Faulty comparisons and mistaken assumptions as well as vague words are all things to point out when critiquing the argument. Writing a quick note about each flaw you find can be helpful when it comes time to elaborate on them in your essay. Plus, making note of them helps you to remember to include all of them in the final piece.

**Use Specific Examples in Your Essay**

The use of specific examples is a key element for Analytical Writing. GMAT graders will be looking for specific examples as they score your essay. It’s not enough to state that a piece of the given argument is inaccurate – you have to use the information within the argument to prove your point. Also, using specific examples helps you to demonstrate that you understand the argument.

**Read and Evaluate High-Scoring Analytical Essays**

When preparing for the GMAT Analytical Writing section, it’s a good idea to read and evaluate essays that received high scores. This can help you see what needs to be adjusted in your own writing to create an essay that earns a high score. In fact, you can break each essay down and highlight the individual elements that earned it a high score.

**Study the Scoring System for the GMAT Analytical Writing Section**

Studying the scoring rubric for the analytical essay is very helpful in your quest to craft a high-scoring piece. After writing a practice essay, you can compare its contents to the criteria on the rubric. If your essay is missing an element, you can go back and do a rewrite. This sort of practice takes a bit of time, but will prove beneficial on test day.

**Study with a GMAT Tutor**

A professional tutor can assist you in preparing for the section on Analytical Writing. GMAT tutors at Veritas Prep have taken the exam and earned a score in the 99th percentile. This means that when you prep for the Analytical Writing section with one of our tutors, you’re learning from a teacher with practical experience! Your tutor can help you boost your writing skills by reviewing the outline of your practice essay and giving you tips on how to improve it. Also, your tutor can provide strategies for what you can do to make your analytical essay more convincing.

We have a variety of tutoring options for those who want help preparing for the analytical essay section on the GMAT. At Veritas Prep, we know that you have a busy schedule, and we want to make it convenient to prep for this test. We also offer resources such as the opportunity for you to take a free GMAT test. This is an excellent way to find out how your skills measure up on each section of the exam. Call or contact us online today and let us give you a hand with your essay-writing skills!

*Getting ready to take the GMAT? We have **free online GMAT seminars** **running all the time. And, be sure to follow us on **Facebook**, **YouTube**, **Google+**, and **Twitter**!*

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]]>The post The Patterns to Solve GMAT Questions with Reversed-Digit Numbers – Part II appeared first on Veritas Prep Blog.

]]>The biggest takeaways from that post were:

- Anytime we add two two-digit numbers whose tens and units digits have been reversed, we will get a multiple of 11.
- Anytime we take the difference of two two-digit numbers whose tens and units digits have been reversed, we will get a multiple of 9.

For the hardest GMAT questions, we’re typically mixing and matching different types of number properties and strategies, so it can be instructive to see how the above axioms might be incorporated into such problems.

Take this challenging Data Sufficiency question, for instance:

*When the digits of two-digit, positive integer M are reversed, the result is the two-digit, positive integer N. If M > N, what is the value of M?*

*(1) The integer (M –N) has 12 unique factors.*

*(2) The integer (M –N) is a multiple of 9.*

The average test-taker looks at Statement 1, sees that it will be very difficult to simply pick numbers that satisfy this condition, and concludes that this can’t possibly be enough information. Well, the average test-taker also scores in the mid-500’s, so that’s not how we want to think.

First, let’s concede that Statement 1 is a challenging one to evaluate and look at Statement 2 first. Notice that Statement 2 tells us something we already know – as we saw above, *anytime* you have two two-digit numbers whose tens and units digits are reversed, the difference will be a multiple of 9. If Statement 2 is useless, we can immediately prune our decision tree of possible correct answers. Either Statement 1 alone is sufficient, or the statements together are not sufficient, as Statement 2 will contribute nothing. So right off the bat, the only possible correct answers are A and E.

If we had to guess, and we recognize that the average test-taker would likely conclude that Statement 1 couldn’t be sufficient, we’d want to go in the opposite direction – this question is significantly more difficult (and interesting) if it turns out that Statement 1 gives us considerably more information than it initially seems.

In order to evaluate Statement 1, it’s helpful to understand the following shortcut for how to determine the total number of factors for a given number. Say, for example, that we wished to determine how many factors 1000 has. We could, if we were sufficiently masochistic, simply list them out (1 and 1000, 2 and 500, etc.). But you can see that this process would be very difficult and time-consuming.

Alternatively, we could do the following. First, take the prime factorization of 1000. 1000 = 10^3, so the prime factorization is 2^3 * 5^3. Next, we take the exponent of each prime base and add one to it. Last, we multiply the results. (3+1)*(3+1) = 16, so 1000 has 16 total factors. More abstractly, if your number is x^a * y^b, where x and y are prime numbers, you can find the total number of factors by multiplying (a+1)(b+1).

Now let’s apply this process to Statement 1. Imagine that the difference of M and N comes out to some two-digit number that can be expressed as x^a * y^b. If we have a total of 12 factors, then we know that (a+1)(b+1) = 12. So, for example, it would work if a = 3 and b = 2, as a + 1 = 4 and b + 1 = 3, and 4*3 =12. But it would also work if, say, a = 5 and b = 1, as a + 1 = 6 and b + 1 = 2, and 6*2 = 12. So, let’s list out some numbers that have 12 factors:

- 2^
**3*** 3^**2**(3+1)(2+1) = 12 - 2^
**5*** 3^**1**(5+1)(1+1) = 12 - 2^
**2*** 3^**3**(2+1)(3+1) = 12

Now remember that M – N, by definition, is a multiple of 9, which will have at least 3^2 in its prime factorization. So the second option is no longer a candidate, as its prime factorization contains only one 3. Also recall that we’re talking about the difference of two two-digit numbers. 2^2 * 3^3 is 4*27 or 108. But the difference between two positive two-digit numbers can’t possibly be a three-digit number! So the third option is also out.

The only possibility is the first option. If we know that the difference of the two numbers is 2^3 * 3^2, or 8*9 = 72, then only 91 and 19 will work. So Statement 1 alone is sufficient to answer this question, and the answer is A.

Algebraically, if M = 10x + y, then N = 10y + x.

M – N = (10x + y) – (10y + x) = 9x – 9y = 9(x – y).

If 9(x – y) = 72, then x – y = 8. If the difference between the tens and units digits is 8, the numbers must be 91 and 19.

Takeaway: the hardest GMAT questions will require a balance of strategy and knowledge. In this case, we want to remember the following:

- Anytime we take the difference of two two-digit numbers whose tens and units digits have been reversed, we will get a multiple of 9.

- If one statement is easier to evaluate than the other, tackle the easier one first. If it’s the case that one statement gives you absolutely nothing, and the other is complex, there is a general tendency for the complex statement alone to be sufficient.

- For the number x^a * y^b, where x and y are prime numbers, you can find the total number of factors by multiplying (a+1)(b+1).

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

*By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles written by him here.*

The post The Patterns to Solve GMAT Questions with Reversed-Digit Numbers – Part II appeared first on Veritas Prep Blog.

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