The post How Understanding Sampling Can Help You Conquer the GMAT appeared first on Veritas Prep Blog.

]]>For example:

In a large population, say all the people in a state, it is difficult to find the number of people with a certain trait, such as red hair. So you pick up 100 people at random (from different families, different areas, different backgrounds) and find the number of people who have red hair in this selection of 100.

Let’s say 12 have red hair. You can then generalize that approximately 12% of the whole population has red hair. The more unbiased your sample, the better the approximation.

In this example, you found something about the entire population (12% has red hair) based on a small sample and hence, using few resources. To find the actual percentage of people who have red hair in the entire population, you would need far more effort, time and money. Usually the use of fewer resources justifies the use of sampling even though it comes with some error.

So that is a bit of background on sampling. It will help you make sense of the official question given below:

*In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?*

*A) 400*

*B) 625*

*C) 1,250*

*D) 2,500*

*E) 10,000*

This is what took place: From a pond, 50 fish were caught, tagged and returned to the pond. Then 50 were caught again and 2 of those were found to be tagged.

Why was this done?

The total number of fish in the pond is the population of the pond. It is unknown. Since counting the total number of fish in the pond was hard, they tagged 50 of them and let them disperse evenly in the population. This means they gave a certain trait to a known number of fish in the pond – they tagged 50 fish.

Then they caught 50 fish again and these fish became the sample. Out of these 50, 2 were found to be tagged. So 2 of the 50 fish caught were found to have the trait given (tagged) – 4% of our sample was tagged.

The question tells us that “… the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond …” that is, the question tells us that the sample is representative of the population. This implies that 50 (the number of fish we tagged) is 4% of the entire fish population of the pond.

50 = 4% of Total Fish Population, therefore, we can calculate that the Total Fish Population = 50 * 100/4 = 1250. Our answer is then C.

Using sampling, we were able to calculate the total population of the pond without actually counting each fish. For increased accuracy, often the exercise of taking samples is repeated many times and then some kind of average is used to get the best approximation.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on 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 How to Solve Probability Problems on the GMAT appeared first on Veritas Prep Blog.

]]>I suspect there are two reasons for the concern. First, is simply that the human brain isn’t naturally wired to do probability very well. Whereas many branches of mathematics are thousands of years old and have their roots in ancient civilizations, there was no working theory of probability until the 16^{th} century.

This is pretty surprising. The ancient Greeks, for example, possessed the rudiments of integral calculus, but when it came to probability, they were clueless. Moreover, there is plenty of research demonstrating that, even now, well-educated adults struggle with probability even when the question touches on material within their field of expertise.

Secondly, GMAC seems to be realizing that probability is such an elastic concept that other question types can be incorporated into a probability question. Consequently, probability questions have been showing up a bit more frequently on some of the newer material released by GMAC. If we’re not wired to do probability very well, and these questions are showing up more frequently, some anxiety about the topic is inevitable.

The reason that probability can encompass other categories so easily is that the probability of an event occurring is, at heart, a simple ratio: the number of desired outcomes/the number of total possible outcomes. To simplify matters, it can be helpful to break this ratio into its component parts. First find the total possible number of outcomes. Then find the number of desired outcomes. When we think about the issue this way, it seems much more manageable. Take this newer official question, for example:

*If an integer n to be chosen randomly between 1 and 96 inclusive, what is the probability that n(n+1)(n+2) is divisible by 8 ? *

*A) 1/4 *

*B) 3/8
*

*C) 1/2
*

*D) 5/8
*

*E) 3/4 *

On the surface, this is a probability question, but because we’re talking about divisibility, it’s also testing our knowledge of number properties. So let’s start by thinking about our total possible outcomes. There are 96 numbers between 1 and 96 inclusive, so clearly, there are 96 total possible outcomes when we select a number at random. We have the denominator of our fraction.

Now we just have to figure out how many ways we can multiply three consecutive numbers, n(n+1)(n+2), to get a multiple of 8. Put another way, any multiple of 8, or 2^3, must contain three 2’s. One way this can happen is if the middle number, n+1, is odd, because every odd number must be sandwiched between a multiple of 2 and a multiple of 4.

If n+1 is 3, for example, you’d have 2*3*4, which is a multiple of 8. (We need three 2’s in all. The 2 gives us one, and the 4 donates the other 2’s.) If n+1 is 5, you’d have 4*5*6, which is also a multiple of 8. (The 4 donates two 2’s and the 6 donates one. So long as we have three 2’s, we have a multiple of 8.) Between 1 and 96, we’ve got 48 odd numbers.

The other way we can get a multiple of 8, when we multiply n(n+1)(n+2) is if n + 1 is itself a multiple of 8. Clearly 7*8*9 will be a multiple of 8. As will 15*16*17. We can either count the multiples of 8 between 1 and 96, or we can use the trusty formula: [(High-Low)/Interval] + 1. The first multiple of 8 between 1 and 96 is 8. The largest is 96. And the interval will be 8. So we get [(96-8)/8] + 1 = 11 + 1 = 12 multiples of 8.

So we have two categories of desired outcomes: there are 48 ways that n+1 can be odd, and there are 12 ways that n+1 can be a multiple of 8, giving us a total of 48 + 12 = 60 desired outcomes.

We’re done! The number of desired outcomes/number of total possible outcomes is 60/96, which will reduce to 5/8. The correct answer is D.

Takeaway: There’s no reason to be intimidated by probability questions, particularly when we remember that a probability calculation can be viewed as a ratio of two numbers. If we break the problem into its constituent parts, the question is often revealed to be quite a bit easier than it seems at first glance, a realization that proves true for almost any challenging GMAT problem.

**GMATPrep question courtesy of the Graduate Management Admissions Council.*

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

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

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]]>The post Advanced Exponent Properties for the GMAT appeared first on Veritas Prep Blog.

]]>We know what the graph of 2^x looks like:

It shows that when x is positive, with increasing value of x, 2^x increases very quickly (look at the first quadrant), but we don’t know exactly how it increases.

It also shows that when x is negative, 2^x stays very close to 0. As x decreases, the value of 2^x decreases by a very small amount.

Now note the spacing of the powers of 2 on the number line:

2^0 = 1

2^1 = 2

2^2 = 4

2^3 = 8

and so on…

2^1 = 2 * 2^0 = 2^0 + 2^0

2^2 = 2 * 2^1 = 2^1 + 2^1

2^3 = 2 * 2^2 = 2^2 + 2^2

2^4 = 2 * 2^3 = 2^3 + 2^3

So every power of 2 is equidistant from 0 and the next power. This means that a power of 2 would be much closer to 0 than the next higher powers. For example, 2^2 is at the same distance from 0 as it is from 2^3.

But 2^2 is much closer to 0 than it is to 2^4, 2^5 etc.

Let’s look at a question based on this concept. Most people find it a bit tough if they do not understand this concept:

*Given that x = 2^b – (8^30 + 16^5), which of the following values for b yields the lowest value for |x|?*

*A) 35*

*B) 90*

*C) 91*

*D) 95*

*E) 105*

We need the lowest value of |x|. We know that the smallest value any absolute value function can take is 0. So 2^b should be as close as possible to (8^30 + 16^5) to get the lowest value of |x|.

Let’s try to simplify:

(8^30 + 16^5)

= (2^3)^30 + (2^4)^5

= 2^90 + 2^20

Which value should b take such that 2^b is as close as possible to 2^90 + 2^20?

2^90 + 2^20 is obviously larger than 2^90. But is it closer to 2^90 or 2^91 or higher powers of 2?

Let’s use the concept we have learned today – let’s compare 2^90 + 2^20 with 2^90 and 2^91.

2^90 = 2^90 + 0

2^91 = 2^90 + 2^90

So now if we compare these two with 2^90 + 2^20, we need to know whether 2^20 is closer to 0 or closer to 2^90.

We already know that 2^20 is equidistant from 0 and 2^21, so obviously it will be much closer to 0 than it will be to 2^90.

Hence, 2^90 + 2^20 is much closer to 2^90 than it is to 2^91 or any other higher powers.

We should take the value 90 to minimize |x|, therefore the answer is B.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on 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 5 Tips for Being Efficient with Data Sufficiency Problems appeared first on Veritas Prep Blog.

]]>Data Sufficiency questions are inherently more difficult than Problem Solving questions because they are more conceptual in nature. Take for example the following problem:

*Is xy > 0?*

*1) x < 6*

*2) 0 ≤ y < x*

Right off the bat, we see that there are 2 variables, so to answer the question we need to know the values of x and y. However, this problem is better viewed conceptually – instead of determining the actual values of x and y, if we recognize that this problem is really testing us on the Properties of Numbers, we realize that what is actually being asked is if x and y are either both positive or both negative. Once we re-phrase the question this way, the problem is much easier to deal with. Statement 1 says that x is less than 6, but this does not tell us definitively whether x is positive or negative. Nor, does Statement 1 give us any information about y. Thus, Statement 1 is not sufficient.

Statement 2 gives us information about both x and y. We now know that y is less than or equal to 0, and x is greater than y. This looks promising. But, since y could be 0 (or greater than 0), we cannot say that xy is greater than 0. Statement 2 is not sufficient. Taking both Statements together provides no more information about y, so we still cannot answer the question (although some might be tempted to overlook the less than or equal to portion).

Here are some tips to efficiently and strategically approach these unique problems:

**Memorize the answer choices!**They are the same for every Data Sufficiency question on the GMAT, so you can save valuable time by knowing them and knowing that if Statement 1 is sufficient, your answer choices are either A or D.- Before reading the statements, try to
**verbalize what information you need to answer the question**. This will help you to determine whether the statements provide the information you need. **Leverage as much information as you can from the prompt**. Often times, important information is included in the prompt but not readily apparent.**Be very wary of statements that provide information that blatantly and obviously answers the question**. If a question asks what the value of x is and one statement tells you x = 6, take a very close look at the other statement. Many times, the other statement will contain information that is difficult to decipher and the test makers are baiting you to select the obvious answer and move on.**Be on the lookout for statements that give no new information**. The circumference of a circle, for instance, contains just as much information as the length of the radius. If you know the circumference, you can find the radius; conversely, if you know the radius, you can find the circumference. Often on Data Sufficiency questions, Statement 2 will just be a repackaging of the same information provided by Statement 1.

Even though GMAT Data Sufficiency problems require some different thinking, with some strategic practice, you will master them. Start with becoming familiar with the structure of the questions and the concepts they most commonly test.

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

By Dennis Cashion, a Veritas Prep instructor based in Denver.

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]]>The post The GMAT Quant Decimal Trend You NEED to Know appeared first on Veritas Prep Blog.

]]>But then you see a question like this:

*Which of the following fractions has a decimal equivalent that is a terminating decimal?*

*A) 10/189*

*B) 15/196*

*C) 16/225*

*D) 25/144*

*E) 39/128*

Once you spend a little time trying to divide 10 by 189, you realize that the question is going to be incredibly painful and time-consuming if you have to keep applying this approach until you find a fraction that results in a terminating decimal. So let’s be mindful of the fact that the purpose of the GMAT is not to test one’s facility for engaging in tedious arithmetic, but rather to assess our ability to recognize patterns under pressure.

Generally speaking, the best way to uncover a pattern is to use simple numbers first and then extrapolate our results to the more complex scenario we’re tasked with evaluating. We already established above that ½ is a terminating decimal and 1/3 is not. Let’s continue in that vein and see what we find (terminating decimals are in bold):

**½ = .5**

1/3 = .3333…

**¼ = .25**

**1/5 = .2**

1/6 = .166666…

1/7= .142857…

**1/8 = .125**

1/9 = .1111

**1/10 = .1**

Next, let’s examine our terminating decimal expressions and see if these numbers have any elements in common. Each of these fractions, it turns out, has a denominator whose prime factorization is composed solely of two prime bases, 2 or 5 or both. This turns out to be a general principle: if a fraction has been simplified, and the prime factorization of the denominator can be expressed in the form of 2^x * 5^y where x and y are non-negative integers, the fraction can be expressed as a terminating decimal.

Now back to our question. We can rephrase the question to be, “Which of the following denominators has a prime factorization that consists solely of 2’s or 5’s or both?”

Not bad. That certainly makes life a little easier. But before we dive in and begin taking prime factorizations with reckless abandon, let’s think like the test-maker. There is no way to do this question without working with the answer choices. Most test-takers will begin with A and work their way down. If you’re trying to create a difficult time-consuming question, where would you bury the correct answer? Probably towards D or E. So when we encounter this kind of scenario, we’re better off if we start at the bottom and work our way up.

E) 39/128. The denominator is 128, which has a prime factorization of 2^7. Because the denominator consists solely of 2’s, this fraction, when expressed as a decimal, must terminate. We’re done. E is the answer. (Intuitively, this makes sense, as all we’re really doing is cutting our numerator in half seven times.) Much easier than doing long division.

Before we commit this principle to memory, let’s make sure that it will be helpful in other contexts. After all, the rule that unlocks a single question won’t be terribly useful to us. So here is the same concept utilized in a Data Sufficiency question:

*Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal? *

*(1) 90 < r < 100 *

*(2) s = 4 *

Notice how much easier this question is if we rephrase it as “if r/s is in its most simplified form, does the prime factorization of the denominator consist entirely of 2’s or 5’s?”

Statement 1 can’t be sufficient on its own, as it tells us nothing about the denominator. 91/2 is a terminating decimal, for example, but 91/3 is not.

Statement 2 tells us that the denominator is 4, or 2^2. If we’ve internalized our terminating decimal rule, we see right away that this must be sufficient, as *anything* dividing by 4 will result in a terminating decimal. The answer is B, Statement 2 alone is sufficient to answer the question.

Takeaway: When studying for the GMAT, it can feel as though there are an infinite number of rules, axioms, and formulas to memorize. Our job, when preparing, is to find the rules that are applicable in multiple contexts and internalize those. If we encounter a problem that seems unusually time-consuming, and no rule springs to mind, we can derive the necessary pattern on the spot by working with simple numbers.

**GMATPrep question courtesy of the Graduate Management Admissions Council.*

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

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

The post The GMAT Quant Decimal Trend You NEED to Know appeared first on Veritas Prep Blog.

]]>The post GMAT Tip of the Week: Yogi Berra Teaches GMAT Sentence Correction appeared first on Veritas Prep Blog.

]]>As news of his passing turned into news reports summarizing his life, many were stunned by just how illustrious his career was: 18 All-Star game appearances (in 19 pro seasons), 10 World Series championships as a player, 3 American League MVP awards, part of the Normandy campaign on D-Day… To much of the world, he was “the quote guy” who also had been a really good baseball player. His wordsmithery is what we all remembered:

- Never answer an anonymous letter.
- It ain’t over ’til it’s over.
- It gets late early out here.
- Pair up in threes.

And his command (or butchering) of the English language is what you should remember as you take the GMAT. Yogi Berra famously “didn’t say some of the things I said” but he did, however inadvertently, have a lot to say about GMAT Sentence Correction:

**Pronouns Matter**

What’s funny about his quote, “*Always go to other people’s funerals, otherwise they won’t come to yours”*?

It’s the pronoun “they.” You know what Yogi means – go to other people’s funerals so that other people will come to yours. But in that sentence, the logical referent for “they” is “other people(‘s)”, and those other people have already been designated in the sentence as people who have already died. So the meaning is illogical: those same people cannot logically attend a funeral in the future. When you use a pronoun, it has to refer back to a specific noun. If that noun cannot logically do what the pronoun is said to be doing, that’s a Sentence Correction, illogical meaning problem.

What’s funny about his quote, “*When you come to a fork in the road, take it”*?

Again, it’s the pronoun, this time “it.” Since a fork in the road is a place where the road diverges into two paths, you can’t take “it” – you have to pick one path. And this is a good example of another sentence correction theme. In order to fix this thought (and the one above), there’s really not a pronoun that will work. “Them” has no logical referent (there’s only one fork) so the meaning is extremely important.

The only way to fix it is to change something prior in the sentence. Perhaps, “When you come to a turnoff on the road, take it,” or, “when the road presents a turn, take it.” On the GMAT, a pronoun error isn’t always fixed by fixing the pronoun – often the correct answer will change the logic that precedes the pronoun so that in the correct answer the previously-incorrect pronoun is correct.

**Modifiers Matter**

What’s funny about his quote, “*Congratulations. I knew the record would stand until it was broken”*?

Of course records stand until they’re broken, but in a grammatical sense Yogi’s primary mistake was his placement of the modifier “until it was broken.” What he likely meant to say is, “Until the record was broken, I thought it might stand forever.” That’s a perfectly logical thought, but we all laugh at the statement he actually made because the placement of the modifier creates a laughable meaning. So learn to spot similarly-misplaced modifiers by checking to make sure the language means exactly what it should.

**Redundancy Is Funny (but sometimes has its place)**

What’s funny about, “*We made too many wrong mistakes,” *and *“It’s like déjà vu all over again”*?

They’re redundant. A mistake is, by nature, something that went wrong. And déjà vu is the feeling that something happened before, so of course it’s “all over again.” Redundancy does come up on the GMAT, but as Yogi himself would point out, there’s a fine line between “redundant (and wrong)” and “a useful literary device”.

Take, for example, his famed, *“It ain’t over ’til it’s over” *quote. In a sports context, even though the word “over” is repeated, that sentence carries a lot of useful meaning: “when someone might say that the game is over, if there is still time (or outs) remaining there’s always a chance to change the result.” The world chuckles at this particular Yogi quote, but in actuality it’s arguably his most famous because, in its own way, it’s quite poignant.

What does that mean for you on the GMAT? Don’t prioritize redundancy as a primary decision point! GMAT Sentence Correction, by nature, involves plenty of different literary devices and sentence structures, and it’s extremely unlikely that you’ll feel like an expert on all of them.

Students often eliminate correct answers because they perceive redundancy, but a phrase like “not unlike” (a “not” next to an “un-“? That’s a redundant double-negative!) actually has a logical and important meaning (“not unlike” means “it’s not totally different from…there are at least some similarities,” whereas “like” conveys significantly more similarity). Rules for modifiers and pronouns are much more absolute, and you can get plenty of practice with those. Be careful with redundancy because, as Yogi might say, sometimes saying it twice is twice as good as saying it once.

**It’s all in your head.**

*“Baseball is ninety percent mental and the other half is physical.”*

To paraphrase the great Yogi Berra, 90% of Sentence Correction is mental and the other half is grammatical. When he talked about baseball, he was talking about the physical tools – the ability to hit, run, throw, catch – as meaning substantially less than people thought, but the mental part of the game – strategy, mental toughness, stamina, etc. – being more important than people thought. The exact percentages, as his quote so ineloquently suggests, are harder to pin down and less important than the takeaway.

So heed Yogi’s advice as it pertains to Sentence Correction. Memorizing and knowing hundreds of grammar rules is “the other half” (or maybe 10%) of the game – employing good strategy (prioritizing primary Decision Points, paying attention to logical meaning, etc.) is the more-important-but-often-overlooked part of success. However eloquently or inelegantly Yogi Berra may have articulated his lessons, at least he made them memorable.

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

*By Brian Galvin.*

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]]>The post 6 Simple Steps to Attack Critical Reasoning Questions on the GMAT appeared first on Veritas Prep Blog.

]]>This can be difficult because several of the answers can appear attractive. Keep in mind, however, that for Inference questions, the correct answer **must be true**. Answers that are “likely to be true” or “could be true” based on the information provided in the stimulus seem attractive at first, but if they are not true 100% of the time, in every situation, then they are not the correct answer.

Another difficulty in approaching Inference questions is that with the many of the other question types (Strengthen, Weaken, etc.), your job is to select the answer that includes new information that either undermines or supports the conclusion. For Inference questions, you do not want to bring in information that is not in the stimulus. All of the information required to answer the question will be included in the stimulus.

Here is a 6-step approach that can help you to efficiently attack GMAT Critical Reasoning Inference questions:

**1) Read the question stem first**.

This will allow you quickly categorize the type of Critical Reasoning question (Strengthen, Weaken, Inference, etc.) and let you focus on identifying the premises in the stimulus. Questions such as, “Which of the following can be correctly inferred from the statements above?” and, “If the statements above are true, which of the following must also be true?” signify that you are dealing with an Inference question.

**2) Speculate what you think the correct conclusion is**.

Sometimes this may be difficult to verbalize, but having an outline or framework of what the “must be true” answer should include will help to eliminate some answer choices.

**3) Evaluate the answer choices using your speculated answer**.

You want to carefully read all 5 answer choices. As you read the answers, compare them to the answer, or the outline of the answer, you speculated. Some answers are obviously incorrect – either they are too narrow in scope, too extreme to be always be true, or do not follow the criteria laid out in the stimulus. Eliminate these answers. For other answer choices that seem attractive, keep them as possibilities. Once you have read all of the answer choices, you can then compare your list of possible answers using the criteria that the correct answer must be always be true.

**4) Become a Defense Lawyer**.

When comparing your list of possible answers, try to come up with plausible scenarios that would prove the answer being considered not true. Just because the stimulus says that “everyone sitting in the dentist’s office waiting room at 9:00 a.m. was a patient” does not necessarily mean that they were waiting for an appointment. Some could have already finished their appointment, and some could have been there dropping off another patient. Like a defense lawyer, you need to find every every scenario in which an answer choice might not be true in order to eliminate it from your options.

**5) Be aware of exaggerated or extreme answers**.

Because the correct answer must always be true, modifiers that exaggerate an element of the premise or make an extreme claim usually signify an incorrect answer. If the stimulus says, “Some of the widgets produced by Company X were defective,” an attractive, yet incorrect answer choice may exaggerate this statement with a modifier such as “most” by claiming, “Most of Company X’s widgets were found to be defective.” Furthermore, answers that include the terms “always”, “never”, “none” and the like are good indicators that the answer will not be true 100% of the time.

**6) Be aware of answers that change the scope of the stimulus**.

On more difficult Inference questions (as if they were not difficult enough), the test makers will tempt you to select an answer choice that slightly changes an element of the facts laid out in the stimulus. For example, the stimulus might discuss the decrease in the violent crime rate in City A over a certain time period.

The attractive answer that follows all of the elements of having to be true 100% of the time, but is still incorrect might discuss decrease in the murder rate of City A over that time period. While the answer would seem to fit the bill, the murder rate is not the same as the rate of violent crime – this changes the scope of the initial stimulus and we can therefore rule that answer out.

The correct inference or conclusion on Critical Reasoning Inference questions is very close to what is stated explicitly in the stimulus. Remember, the right answer choice on these question types must be true 100% of the time.

By Dennis Cashion, a Veritas Prep instructor based in Denver.

The post 6 Simple Steps to Attack Critical Reasoning Questions on the GMAT appeared first on Veritas Prep Blog.

]]>The post How to Use the Answer Choices to Solve GMAT Quant Problems appeared first on Veritas Prep Blog.

]]>Take for example, the following question:

**If 3 ^{x}4^{y }= 177,147 and x – y = 11, then x =?**

A) Undefined

B) 0

C) 11

D) 177,136

E) 177,158

Where do we begin here? 177,147 is a large (not familiar) number and there are not one, but two exponents in the equation. Looking at the answer choices, we can see that D and E cannot be the answer as they are too large, so at least now we have a starting point. Additionally, we can see that our choices come down to some mixture of x and y, all y, or all x.

If x = 0, then we can say that 177, 147 is not divisible by 3 and is divisible by 4, so checking the divisibility rule is the ticket! Knowing that to be divisible by 4, the last two digits must be divisible by 4, we can see that 177,147 is not divisible by 4, so 4^{y}** ^{ }**becomes irrelevant and we realize y must equal 0. The sum of the digits of 177, 147 is 27, which is divisible by 3, so we can see that the 3

Answer choices are little used resources by GMAT test takers. In the heat of battle, we become so focused on solving the problems in front of us that we forget to utilize all of the information at our disposal. Another way the answer choices can help you is by plugging them back into the problem to see if they work.

This “back-plugging” is useful when the problem to be solved is algebraic in nature and the answer choices are numbers (not variables). You may find it is easier on a certain problem to arithmetically calculate 2, 3 or even 5 answers by plugging in the answer choices, than in creating and manipulating a complex algebraic equation. In these cases, plugging in answer choice C first will help you to eliminate up to 60% of the answers on the first calculation.

Many times, just understanding what the correct answer should “look like” by employing some reasoning on the front end will allow you to eliminate some, if not all of the incorrect answers. Consider this problem:

**((-1.9)(o.6) – (2.6)(1.2))/6.0 = ?**

A) -0.71

B) 1.00

C) 1.07

D) 1.71

E) 2.71

This is not a difficult problem by any measure, and some test takers will not hesitate to jump in and begin multiplying and dividing decimals. However, by spending a little bit of time looking at the big picture of this problem, an astute test taker would see that the answer must be negative. The first term is negative and we are subtracting a larger number from it. Therefore, the correct answer must be A.

So, instead of jumping in and crunching numbers on the GMAT, you can save yourself some time and brain power by using the answer choices to assist you in reasoning your way to the correct answer – or at least in eliminating several of the incorrect answers.

By Dennis Cashion, a Veritas Prep instructor based in Denver.

The post How to Use the Answer Choices to Solve GMAT Quant Problems appeared first on Veritas Prep Blog.

]]>The post 99th GMAT Score or Bust! Lesson 9: Talk Like a Lawyer appeared first on Veritas Prep Blog.

]]>First, take a look at the previous lessons in this series: **1**, **2**, **3**, **4**, **5**, **6,** **7 **and** 8**!

__Lesson Nine: __

Talk Like a Lawyer. When you click “Agree” on a user contract (think iTunes) or read through a GMAT question, you may just see an overkill of words. But thanks to lawyers, every word on that user agreement is carefully chosen – and that GMAT question is written the same exact way. In this final “9 for 99th” video, Ravi (a member of the bar himself) shows you how to talk and read like a lawyer, noticing those subtle word choices that can make or break your answer to those carefully-written GMAT problems you see on test day.

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

Want to learn more from Ravi? He’s taking his show on the road for a one-week Immersion Course in New York this summer, and he teaches frequently in our new Live Online classroom.

*By Brian Galvin*

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]]>The post Beat the GMAT Verbal Section by Personalizing Questions appeared first on Veritas Prep Blog.

]]>Moreover, the questions themselves aren’t exactly known for their dazzling wit and soaring narrative verve. They’re boring. Reading Comp. passages are often tedious and technical, while Critical Reasoning arguments can feel so abstract as to be ungraspable. So how do we, as test-takers, combat this?

One answer, when it comes to those abstract Critical Reasoning questions, is to personalize the argument. I’ve blogged in the past about how our reading comprehension improves dramatically when we’re emotionally invested in what we’re reading, so why not attempt to trick ourselves into this state of heightened concentration?

If the CR question is about the impact of pesticide use on crop yields, I imagine I’m the farmer, and the well-being of my family is at stake. If the question is about how overtime pay will impact employee incentives, I imagine I own the business and that the consequence of my company’s compensation structure will impact not only me, but dozens of workers whose livelihood I’m responsible for. By creating these artificial stakes, I find that my brain is able to lock in on the minutia of the question in a way it can’t if the question is about some airy fictional farmer, whom I know exists only in the mind of some bureaucratic question writer.

Take an official question, for example:

*In the past the country of Malvernia has relied heavily on imported oil. Malvernia recently implemented a program to convert heating systems from oil to natural gas. Malvernia currently produces more natural gas each year than it uses, and oil production in Malvernian oil fields is increasing at a steady pace. If these trends in fuel production and usage continue, therefore, Malvernian reliance on foreign sources for fuel is likely to decline soon. *

*Which of the following would it be most useful to establish in evaluating the argument?*

(A) When, if ever, will production of oil in Malvernia outstrip production of natural gas?

(B) Is Malvernia among the countries that rely most on imported oil?

(C) What proportion of Malvernia’s total energy needs is met by hydroelectric, solar, and nuclear power?

(D) Is the amount of oil used each year in Malvernia for generating electricity and fuel for transportation increasing?

(E) Have any existing oil-burning heating systems in Malvernia already been converted to natural-gas-burning heating systems?

If you’re anything like most test-takers, your eyes glaze over a bit. You know that Malvernia is not a real country, that it’s been invented for the sake of the problem. Consequently, the details of energy consumption in this non-existent country are not going to be terribly compelling to, well, anyone. This is by design. So let’s create some artificial stakes. Let’s say you’re the President of Malvernia. The economic well-being of your country, and, therefore, the prospects of your reelection, are going to be impacted by your country’s energy policy. Now let’s break down the facts:

- Historically, you’ve relied on oil imports.
- A new program converts heating systems from oil to gas.
- You produce more gas than you use.
- Oil production is increasing.

Based on this, you’ve concluded that your reliance on foreign oil will soon decrease. The question is what do you, as President, need to know to determine whether this prediction is valid?

Let’s break down each answer choice:

(A) The question of when production of oil will outstrip production of gas isn’t really relevant. In fact, if you’re using less oil as a result of the change in heating systems, and oil production is up, it’s possible that you can reduce your dependence on foreign oil without having to produce more oil than gas. A is out.

(B) Whether you are among the most dependent countries on foreign oil doesn’t matter. You are now, and we’re trying to determine if you will be in the future. This doesn’t help. Eliminate B.

(C) Hydroelectric, solar, and nuclear power aren’t relevant for this argument. We know that you’re dependent on foreign oil now, irrespective of other energy sources. It’s increased oil production and switching to gas that will, according to the argument, reduce this dependence. C is out of scope.

(D) Let’s say your oil consumption for electricity and transportation is increasing. Suddenly, the fact that you’re switching heating systems from oil to gas might not help – if your oil needs are going up in other areas, you may remain dependent on foreign oil. But if your oil consumption in these other areas is *not *increasing, that would reduce your dependence on foreign oil because your heating systems are switching to gas. D looks good.

(E) This doesn’t matter at all. We know that the systems are going to switch from oil to gas, so the question of whether some systems have already made the switch sheds no light on whether you will remain dependent on foreign oil.

D is the answer. Once you have the answer to whether your oil consumption for electricity and transportation is increasing, you’ll be better able to assess whether you will remain dependent on foreign oil, and, consequently, whether your reign as supreme ruler of Malvernia will continue.

Takeaway: There is plenty of research indicating that our comprehension improves drastically when we’re reading something we care about. When we put ourselves into the position of the agents having to make decisions in these arguments, we can transform a tedious abstraction into something that has a bit of emotional resonance, which will, in turn, result in a higher GMAT score.

**Official Guide question courtesy of the Graduate Management Admissions Council.*

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

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