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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A. 2/5

B. 3/5

C. 7/10

D. 4/5

E. 9/10

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

Probability will tell you that

Required probability = Favorable cases/Total cases

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

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

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

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

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

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

5 = 3.5 + 1.5

2 = 3.5 – 1.5

So a = 3.5, b = 1.5.

a and b are not integers.

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

5 = 4 + 1

3 = 4 – 1

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

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

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

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

4*5 = 20

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

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

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

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

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

Let’s go back to our question:

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

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

3 Odd numbers: 1, 3, 5

2 Even numbers: 2, 4

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

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

Total number of favorable cases = 3 + 4 = 7

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

Required Probability = 7/10

Answer (C)

Takeaway:

When can we write a number as difference of squares?

- When the number is odd

or

- When the number has 4 as a factor

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

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

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

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

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

**TRAIL** running.

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

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

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

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

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

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

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

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

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

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

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

*(A) **1:5*

*(B) **625 : 3125*

*(C) **100 : 105*

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

*(E) **725 : 3225*

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

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

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

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

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

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

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

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

“I am glad that you brought this up! *This is an official question, and the answer choice is the official answer. *I do not understand why you need to be “convinced.” You can trust the official answer to an official question!

In fact, when you saw that your answer was not the correct answer you started looking for ways that you could be right and the official answer wrong. This is not a particularly helpful mindset.

Let’s compare the verbal and the quantitative sections. What do you do when you see that the official answer to a Quant problem is 27 and you thought it was 42? Be honest. You know what you do, you say “27, huh, I must have made a mistake. How did I end up with 42, let me see what I did wrong here so that I do not do it again.”

Right?

You do NOT you say, “I bet it is really is 42 and I am going to think of reasons why it is 42 and not 27.” That would seem strange right? I mean a *Quant* problem only has one correct answer and if you get a different answer you made a mistake and need to figure out why you missed it right?

Okay well here is something that it takes students a long time to learn - **A verbal question only has one correct answer as well. And if you got a different answer you need to say “what did I do wrong and how can I not make this mistake in the future.” **Just as you would on a Quant problem.

I have had tutoring students who wanted to argue the answers on verbal questions, particularly CR and RC, but SC sometimes as well. Eventually I say something along the lines of “This is not the kind of test where you should be debating against the answer key. If you want to get a high GMAT score you need to focus on why you did not get the correct answer and how you can get it right next time.”

Now unofficial questions can often be improved. In fact, when I write original questions of my own I welcome it when students debate the merits of each question. I then edit it to make it better. Every edit makes it a question better. Yet even most unofficial questions are well written and really do have just one correct answer.

What I am saying is that your mind set should be “Why did I get this wrong?” “What can I do better next time?” Rather than “I am not convinced with this official answer to this official question.”

It may seem like a slight difference, but it is the difference between a 600 and a 700.

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

*David Newland* has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here.

When two items are sold at the same selling price, one at a profit of x% and the other at a loss of x%, there is an overall loss. The loss% = (x^2/100)%

We will see how this formula is derived but the algebra involved is tedious. You can skip it if you wish.

Say two items are sold at $S each. On one, a profit of x% is made and on the other a loss of x% is made.

Say, cost price of the article on which profit was made = Ct

Ct (1 + x/100) = S

Ct = S/(1 + x/100)

Cost Price of the article on which loss was made = Cs

Cs (1 – x/100) = S

Cs = S/(1 – x/100)

Total Cost Price of both articles together = Ct + Cs = S/(1 + x/100) + S/(1 – x/100)

Ct + Cs = S[1/(1 + x/100) + 1/(1 - x/100)]

Ct + Cs = 2S/(1 – (x/100)^2)

Total Selling Price of both articles together = 2S

Overall Profit/Loss = 2S – (Ct + Cs)

Overall Profit/Loss % = [2S – (Ct + Cs)]/[Ct + Cs] * 100

= [2S/(Ct + Cs) – 1] * 100

= [2S/[2S/(1 – (x/100)^2)] – 1] * 100

= (x/100)^2 * 100

= x^2/100

Overall there is a loss of (x^2/100)%.

Let’ see how this formula works on a GMAT Prep question.

**Question**: John bought 2 shares and sold them for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had

(A) a profit of $10

(B) a profit of $8

(C) a loss of $8

(D) a loss of $10

(E) neither a profit nor a loss

**Solution**:

Note that the question would have been straight forward had the COST price been the same, say $100. A 20% profit would mean a gain of $20 and a 20% loss would mean a loss of $20. Overall, there would have been no profit no loss.

Here the two shares are sold at the same SALE price. One at a profit of 20% on cost price which must be lower than the sale price (to get a profit) and the other at a loss of 20% on cost price which must be higher than the sale price (to get a loss). 20% of a lower amount will be less in dollar terms and hence overall, there will be a loss.

The loss % = (20)^2/100 % = 4%.

But we need the amount of loss, not the percentage of loss.

Total Sale price of the two shares = 2*96 = $192

Since there is a loss of 4%, the 96% of the total cost price must be the total sale price

(96/100)*Cost Price = Sale Price

Cost Price = $200

Loss = $200 – $192 = $8

Answer (C)

*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!*

Test-takers struggle mightily with the concept of “Rate of Change” vs. “Actual Number”.

Consider this quick data table, which displays the average monthly temperature in Chicago, Illinois:

Month…….Average High Temperature

February……..34.7

March………46.1

April………58

May………69.9

June………79.2

July………83.5

August……..81.2

Now, from a quick glance you should see that the temperature increases every month from February through July. But there’s another angle to this data, too, and challenging Integrated Reasoning questions can hinge on that exact point. The temperature INCREASES every month, but the GROWTH RATE declines – from February to March the temperature increases by 11.4 degrees, but from June to July it only goes up 4.3 degrees as summer temperatures level off. So while the data table above might clearly demonstrate that the temperature is rising (we promise, Chicago – although we know it hasn’t been too noticeable just yet!), an Integrated Reasoning question might show you this graph:

Based on this graph, most students would incorrectly answer the question: “From March through August, how many months did the average temperature decrease?”, as most would look at the graph and see several months of decline. But the important thing to keep in mind is “WHAT declined?”. And in this case it’s “the growth rate in the temperature” not “the temperature itself”. In this graph, any time the data point is above 0, that means the temperature increased. Only one month (August) was colder than the month prior.

This next graph will plot both “average temperature” and temperature growth” together to highlight this concept.

So what is the lesson? Make sure that you’re aware of the difference between the “actual number” and the “rate of change” and that you look for that concept to be tested on Graphics Interpretation questions. When newscasters say that “Apple’s earnings growth dropped 5% this quarter” that doesn’t necessarily mean that Apple lost money or didn’t improve upon the last quarter; it just means that it grew slower. Think back to physics classes and the difference between acceleration and velocity – “percent change” is the acceleration component, but people often mistake it for the velocity. And based on Question Bank data, every time this concept has been tested more than half of users missed this concept!

So remember – the rate of change can decline while the actual number still increases…just not as quickly. Understanding and recognizing this concept can keep both metrics positive for your Integrated Reasoning score.

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

*By Brian Galvin*

Reading comprehension is a category of questions on the GMAT designed to test whether you can read a long (and often pointless, bloated and sleep-inducing) passage and understand the major points covered. This exercise is designed to emulate the various reports and papers you’re likely to read throughout school and work for the next 40 years or so (or until we’re replaced by robots). The passage is presented, and then a series of 3 to 6 questions about the passage will be asked. Ideally, you understood the passage well enough to answer the questions about what you just read. If you grasp the major point the author was trying to get at, you’re likely to get the questions right.

Not every passage you read will ask you about the primary purpose of the passage (say that three times fast!) Sometimes the questions will ask about the author’s tone, the scope of the subject or the organization of the text. However, every passage can potentially ask you about the primary purpose, and at least one will ask you on test day. To avoid losing easy points on this type of relatively straight forward question, it’s important to ascertain which elements are important, and which details are superfluous.

A very good method to ensure you’re following along with the passage is to summarize each paragraph in 3-5 words after you finish reading it. This summary might not have all the details included in the paragraph, but it will succinctly recap the important element(s) of what you have just finished reading. Ideally, you don’t even have to spend time writing these words down, just forming them in your mind’s eye is enough to keep them in your memory for a few minutes. Of course, if you prefer to write this down, or if you want to expand to 6 or 7 words, that’s perfectly acceptable as well. It is important to be mindful of the time constraint, though.

Let’s look at a GMAT passage and answer a question using the organization of the passage (note: this is the same passage I used throughout 2013 for scope, tone and organization.)

*Young Enterprise Services (YES) is a federal program created to encourage entrepreneurship in 14-18 year olds who have already shown a clear aptitude for starting business ventures. The program, started in 2002, has provided loans, grants, and counseling – in the form of workshops and individual meetings with established entrepreneurs – to over 7,500 young people. The future of YES, however, is now in jeopardy. A number of damaging criticisms have been leveled at the program, and members of the Congressional agency that provides the funding have suggested that YES may be scaled down or even dismantled entirely.*

*One complaint is that the funds that YES distributes have disproportionally gone to young people from economically disadvantaged families, despite the program’s stated goal of being blind to any criteria besides merit. Though no one has claimed that any of the recipients of YES funds have been undeserving, several families have brought lawsuits claiming that their requests for funding were rejected because of the families’ relatively high levels of income. The resulting publicity was an embarrassment to the YES administrators, one of whom resigned.*

*Another challenge has been the admittedly difficult task of ensuring that a young person, not his or her family, is truly the driving force behind the venture. The rules state that the business plan must be created by the youth, and that any profits in excess of $1,000 be placed in an escrow account that can only be used for education, investment in the venture, and little else, for a period that is determined by the age of the recipient. Despite this, several grants had to be returned after it was discovered that parents – or in one case, a neighbor – were misusing YES funds to promote their own business ideas. To make matters worse, the story of the returned monies was at first denied by a YES spokesperson who then had to retract the denial, leading to more bad press.*

*In truth, YES has had some real success stories. A 14-year old girl in Texas used the knowledge and funding she received through the program to connect with a distributor who now carries her line of custom-designed cell phone covers. Two brothers in Alaska have developed an online travel advisory service for young people vacationing with their families. Both of these ventures are profitable, and both companies have gained a striking amount of brand recognition in a very short time. However, YES has been pitifully lax in trumpeting these encouraging stories. Local press notwithstanding, these and other successes have received little media coverage. This is a shame, but one that can be remedied. The administrators of YES should heed the advice given in one of the program’s own publications: “No business venture, whatever its appeal, will succeed for long without an active approach to public relations.”*

*The primary purpose of the passage is to _______*

*(A) **detail the approach that should be taken in remedying YES’s public relations problems*

*(B) **defend YES from the various criticisms that have been leveled against it*

*(C) **suggest a way to improve the program*

*(D) **detail several criticisms and problems of the YES program*

*(E) **make the case that YES, despite some difficulties, has been quite successful for some people who have taken part in the program*

If you summarized each paragraph as you read through them, your summary should look something like:

1^{st} paragraph: YES program

2^{nd} paragraph: Problem w/ program

3^{rd} paragraph: Another problem w/ program

4^{th} paragraph: Successes & next steps

With a summary like this, which is all of 13 words, you follow the main point of the story and you’re less likely to get sidetracked by tempting answer choices. Let’s look through the choices and see if any of them encapsulate the main purpose of this passage.

Answer choice A indicates that the goal is to detail the approach in remedying the program’s problems. This answer choice initially makes a lot of sense, as the passage is all about the problems and how to solve them. However, the use of the word “detail” should be sufficient to recognize that this is not what the passage is really doing. The author gives their overarching suggesting of using more PR, but does not detail anything at any point. The choice of words precludes this answer from being considered further.

Answer choice B is about defending YES from criticisms, which is not even something that happens in the text. The author makes no effort to defend the program from the justified criticisms, and merely suggests a course of action moving forward. Answer choice B is thus incorrect.

Answer choice C concisely indicates that the author is suggesting a way to improve the program. This is essentially correct since the author lists a couple of issues with the program, and then outlines a very general way to improve things going forward. We should check the other answer choices, but this choice appears correct and is general enough that it will be hard to eliminate.

Answer choice D stops short at mentioning only the problems and criticisms of the program. This would be correct if the fourth paragraph did not exist, but as it is this choice is summing up the first three paragraphs and ignoring the author’s conclusion. This choice is incorrect as well.

Answer choice E stresses the successes of a few people while acknowledging the managerial incompetence at YES, so it is also a tempting answer choice. However the author mentions one or two success stories mostly for anecdotal reasons, and not to promote the status quo. The program must still be overhauled, despite a couple of feel-good stories. Again this answer choice does not adequately represent the primary purpose of the passage.

As answer choice C is the correct selection here, it is important to note that the answer does not need to recap the entire passage. Such an exercise would be inherently difficult in only a few words, but more so, it is unnecessary. Summarizing something does not necessarily require reiterating every detail, but rather understanding the underlying reason for the writing of the passage. The purpose of this article is to demonstrate that concept (Inception style), and help you save time and maximize your GMAT score on test day.

My friends from the television show *The* *Big Bang Theory* are fond of super heroes. Okay Sheldon and Leonard are not really my friends (unfortunately) but they are certainly fond of super heroes. They love Superman and Batman and the entire Justice League.

What they fail to understand is that they are super heroes themselves…with super powers that translate extremely well to the GMAT. Their biggest super power? Making equations of course!!!

You don’t think that making equations is a super power…did you not hear that music while Sheldon and (Raj) Koothrappali were working on that equation? That was super hero music for sure!

While making equations may not be as cool as flying; on the GMAT the ability to see an equation where others may not is indeed a super power. *A super power that you may already possess.*

All that you need to do in order to create an equation is to set two things equal. Moreover, if any two things are equal to a third then they can be set equal to each other and you have another equation!

This is something that is easiest to illustrate in Geometry. In fact, this is the essence of geometry. If you know that the area of a triangle is Base * Height / 2, and you also know that the area of the triangle is 30, then you drop the thing that they have in common (in this case the area) and create the equation from the other two pieces: Base * Height / 2 = 30, or Base * Height = 60.

You are so used to having this super power at your disposal that you probably do not even think about it when you are using it. The previous example probably did not even impress you. You are like Super Man: when he is rescuing a jumbo jet full of passengers he never seems to stop and think, “Oh, wow! I am actually flying.” He is so focused on using his powers that he never stops to think how awesome they really are.

Try this example from the Veritas Prep Word Problems book. Use your Super Power and create an equation. (If you are having trouble making the equation just remember to find two things that are each equal to a third thing. Drop the thing they have in common and set the other two parts equal to each other).

“Machines A and B always operate independently at their respective constant rates. When working alone machine A can fill the production lot in 5 hours, and machine B can fill the production lot in X hours. Together they can fill the production lot in 2 hours. What is the value of X?

A) 3 1/3

B) 3

C) 2 1/2

D) 2 1/3

E) 1 1/2”

What are the two things that you can set equal to each other? Let’s start with what you know. You know that the rate of A is 1 / 5 (of the job per hour). The rate of B is 1 / X (of the job per hour) and the rate of the two together (the rate of A + B) = 1 / 2 (of the job per hour).

Do you see it now? You know that the rate of A + B is 1 / 2. You can also add the individual rates of A and B, so that (the rate of A) + (rate of B) = 1 / 5 + 1/ X. You now have two different values that is each equal to the rate of A + B. Now you can set them equal to each other. So that “**1 / 5 + 1 / X = 1 / 2**” (the rate of A) + (the rate of B) = the rate of (A + B).

Now you have an equation that you can solve and the rest is Algebra. Find a common denominator for 5 and 2 so that the equation becomes “2 / 10 + 1 / X = 5 / 10.” 1 / X must equal 3 / 10. That means 3X = 10 and X = 3 1/3. The correct answer is A.

You and I might not be quite up to the status of theoretical physicists Sheldon and Koothrappali, but we do have something in common with them. We have the Power to create equations, meaning that we are super heroes, too!

*David Newland* has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here.

There are some triplets that you should know out cold: (3, 4, 5), (5, 12, 13) and (8, 15, 17). Usually you will find one of these three or their multiples on GMAT. Given a right triangle and two sides, say the two legs, of length 20 and 48, we need to immediately bring them down to the lowest form 20:48 = 5:12. So we know that we are talking about the 5, 12, 13 triplet and the hypotenuse will be 13*4 = 52. These little things help us save a lot of time. Why is it that some people get done with the Quant section in less than an hour while others fall short on time? It is these little things that an adept test taker has mastered which make all the difference.

Anyway, let us go on to the question we have in mind.

Question: In the figure given below, the length of PQ is 12 and the length of PR is 15. The area of right triangle STU is equal to the area of the shaded region. If the ratio of the length of ST to the length of TU is equal to the ratio of the length of PQ to the length of QR, what is the length of TU?

(A) (9√2)/4

(B) 9/2

(C) (9√2)/2

(D) 6√2

(E) 12

Solution: The information given in the question seems to overwhelm us but let’s take it a bit at a time.

“length of PQ is 12 and the length of PR is 15”

PQR is a right triangle such that PQ = 12 and PR = 15. So PQ:PR = 4:5. Recall the 3-4-5 triplet. A multiple triplet of 3-4-5 is 9-12-15. This means QR = 9.

“ratio of the length of ST to the length of TU is equal to the ratio of the length of PQ to the length of QR”

ST/TU = PQ/QR

The ratio of two sides of PQR is equal to the ratio of two sides of STU and the included angle between the sides is same ( = 90). Using SAS, triangles PQR and STU are similar.

“The area of right triangle STU is equal to the area of the shaded region”

Area of triangle PQR = Area of triangle STU + Area of Shaded Region

Since area of triangle STU = area of shaded region, (area of triangle PQR) = 2*(area of triangle STU)

In similar triangles, if the sides are in the ratio k, the areas of the triangles are in the ratio k^2. If the ratio of the areas is given as 2 (i.e. k^2 is 2), the sides must be in the ratio √2 (i.e. k must be √2).

Since QR = 9, TU must be 9/√2. But there is no 9/√2 in the options – in the options the denominators are rationalized. TU = 9/√2 = (9*√2)/(√2*√2) = (9*√2)/2.

Answer (C)

The question could take a long time if we do not remember the Pythagorean triplets and the area of similar triangles property.

Takeaways:

- Pythagorean triplets you should know: (3, 4, 5), (5, 12, 13) and (8, 15, 17) and their multiples.
- In similar triangles, if the sides are in the ratio k, the areas of the triangles are in the ratio k^2.

*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!*