The other answer we can give you? Sarah Koenig would do pretty darned well on Data Sufficiency questions, where often it’s just as important to determine what you don’t know as it is to determine what you do. While the internet buzzed with theories certain that Adnan did it, that Jay did it, that a recently-released serial killer did it, Koenig was often ridiculed for being so noncommittal in her assessment of whether Adnan is guilty or not. But that’s an important mentality on Data Sufficiency questions, as one of the common ways that the GMAT will bait you is giving you information that seems overwhelmingly sufficient (The Nisha call! The phone was in Leakin Park!) but that leaves just enough doubt (Why did Jay’s story change so much?) that you can’t prove a definitive answer. And like the jury in the Serial case, we all have that tendency to jump to conclusions (“well if he didn’t kill her, who did?”) and filter out information that we don’t like (Christina Gutierrez’s performance…). This Serial-themed Data Sufficiency problem should exemplify (forgive the lack of subscript formatting, but a sequence problem in a Serial blog post seemed fitting):

The infinite (serial) sequence a1, a2, …, an, … is such that a1 = x, a2 = y, a3 = z,a4 = 3 and an = a(n-4) for n > 4. What is the sum of the first 98 terms of the sequence?

(1) x = 5

(2) y + z = 2

As people unpack the mystery in this problem, they start to see what’s going on. If an = a(n-4), then each term equals the term that came four prior. So the sequence really goes:

x, y, z, 3, x, y, z, 3, x, y, z, 3…

So although it looks like a pretty massive mystery, really you’re trying to figure out x, y, and z because 3 is just 3. And here’s a common way of thinking:

Statement 1 is not sufficient, but it gets you one of the terms. And Statement 2 is not sufficient but it gets you two more. So when you put them together, you know that the sum of one trip through the 4-term sequence is 5 + 2 + 3 = 10, so you should be able to extrapolate that to the whole thing, right? Just figure out how many trips through will get you to term 98 and you have it; like the Syed jury, you have the motive and the timeline and the cell phone records and Jay’s testimony, so the answer has to be C. Right?

But let’s interview Sarah Koenig here:

Sarah: The pieces all seem to fit but I’m just not so sure. Statement 2 looks really bad for him. If we can connect those dots for y and z, and we already have x, we should have all variables converted to numbers. Literally it all adds up. But I feel like I’m missing something. I can definitely get the sum of the first 4 terms and of the first 8 terms and of the first 12 terms; those are 10, and 20, and 30. But what about the number 98?

And that’s where Sarah Koenig’s trademark thoughtfulness-over-opinionatedry comes in. There is a giant hole in “Answer choice C’s case” against this problem. You can get the sequence in blocks of 4, but 98 is two past the last multiple of 4 (which is 96). The 97th term is easy: that’s x = 5. But the 98th term is tricky: it’s y, and we don’t know y unless we have z with it ( we just have the sum of the two). So we can’t solve for the 98th term. The answer has to be E – we just don’t know.

Now if you’ve heard yesterday’s episode, think about Dana’s “think of all the things that would have to have gone wrong, all the bad luck” rundown. “He lent his car and his phone to the guy who pointed the finger at him. That sucks for him. On the day that his girlfriend went missing. That’s awful luck…” And in real life she may be right – that’s a lot of probability to overcome. But on the GMAT they hand pick the questions. On this problem you can solve for the 97th term (up to 96 there are just blocks of 4 terms, and you know that each block sums to 10, and the 97th term is known as 5) or the 99th term (same thing, but add the sum of the 98th and 99th terms which you know is 2). But the GMAT hand-selected the tricky question just like Koenig hand-selected the Adnan Syed case for its mystery. GMAT Data Sufficiency questions are like Serial…it pays to be skeptical as you examine the evidence. It pays to think like Sarah Koenig. Unlike Jay, the statements will always be true and they’ll always be consistent, but like Serial in general you’ll sometimes find that you just don’t have enough information to definitively answer the question on everyone’s lips. So do your journalistic due diligence and look for alternative explanations (Don did it!). Next thing you know you’ll be “Stepping Out!!!” of the test center with a high GMAT score.

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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*

One reason people spend a lot of time on these questions is that they try to read the entire passage thoroughly. This is normal because this is how most reading is done, be it in newspapers or periodicals or novels. However, on the GMAT, speed is the name of the game. If I were doing a book report on Shakespeare’s works, then I would read the text multiple times, looking for nuance and symbolism. The goal on the GMAT is quite different: you have roughly eight minutes to read a passage and then answer four questions about it. That isn’t much time, but it can work if you’re question-focused.

Why be question focused? (Rhetorical question) A typical passage may have 300-400 words, and you could be asked 20-30 different questions about the information contained within it. In reality, you will only be asked 3-4-5 questions about this text, so becoming an expert on the minutiae contained within seems like a complete waste of time. In fact, considering that you only have ~2 minutes per question, it is not only a waste of time but a distraction that will waste precious time and lower your score. The vast majority of questions will require you to go back to the passage and reread the relevant portion, so your initial read is only there to give you a general sense of the text. After the initial read, you should be able to answer broad, universal questions. However, for questions that deal in specifics, you’ll have to go back to the text.

Specific questions deal with (drum roll please) specific elements of the passage. At first glance, you wouldn’t necessarily recall such minute details, but if you know where to go back in the text, it becomes a trivial case of rereading until you find it. As an example, you might not remember what Luke Skywalker was wearing on Tatooine when he first meets Obi-Wan Kenobi, but you could just rewatch the first act of Star Wars and see for yourself. There is no need to memorize every minor detail, as long as you know where to find the answer, you can just look it up.

Let’s look at a GMAT passage and answer a question that deals with a specific element of the passage (note: this is the same passage I used in October for a function question).

Nearly all the workers of the Lowell textile mills of Massachusetts were unmarried daughters from farm families. Some of the workers were as young as ten. Since many people in the 1820s were disturbed by the idea of working females, the company provided well-kept dormitories and boarding-houses. The meals were decent and church attendance was mandatory. Compared to other factories of the time, the Lowell mills were clean and safe, and there was even a journal, The Lowell Offering, which contained poems and other material written by the workers, and which became known beyond New England. Ironically, it was at the Lowell Mills that dissatisfaction with working conditions brought about the first organization of working women.

The mills were highly mechanized, and were in fact considered a model of efficiency by others in the textile industry. The work was difficult, however, and the high level of standardization made it tedious. When wages were cut, the workers organized the Factory Girls Association. 15,000 women decided to “turn out”, or walk off the job. The Offering, meant as a pleasant creative outlet, gave the women a voice that could be heard by sympathetic people elsewhere in the country, and even in Europe. However, the ability of the women to demand changes was severely circumscribed by an inability to go for long without wages with which to support themselves and help support their families. The same limitation hampered the effectiveness of the Lowell Female Labor Reform Association (LFLRA), organized in 1844.

No specific reform can be directly attributed to the Lowell workers, but their legacy is unquestionable. The LFLRA’s founder, Sarah Bagley, became a national figure, testifying before the Massachusetts House of Representatives. When the New England Labor Reform League was formed, three of the eight board members were women. Other mill workers took note of the Lowell strikes, and were successful in getting better pay, shorter hours, and safer working conditions. Even some existing child labor laws can be traced back to efforts first set in motion by the Lowell Mill Women.

According to the passage, which of the following contributed to the inability of the workers at Lowell to have their demands met?

(A) The very young age of some of the workers made political organization impractical.

(B) Social attitudes of the time pressured women into not making demands.

(C) The Lowell Female Labor Reform Association was not organized until 1844.

(D) Their families depended on the workers to send some of their wages home.

(E) The people who were most sympathetic to the workers lived outside of New England.

If you’ve been following the Veritas technique on Reading Comprehension, then you should have spent about two minutes reading through the passage and summarizing each paragraph in a couple of words. If you didn’t do this, feel free to go back and do it now. Once completed, your summaries of each paragraph should be something like:

1) Lowell Mills and context

2) Labor strife and consequences

3) Legacy of Lowell Mills

Your exact wording may vary, but you want to keep it at about 3-5 words or so. This should give enough of a framework so you know where to go in every question. If we look at the question at hand, it asks why were the workers at Lowell unable to have their demands met. This has to be in the second paragraph, as that was the part that dealt with the actual worker strife.

Rereading this paragraph, we go through a description of what prompted the strike and then how many people participated. Directly following this is the line: “However, the ability of the women to demand changes was severely circumscribed by an inability to go for long without wages with which to support themselves and help support their families”. This was their downfall: they needed money to support themselves and their loved ones (unsurprisingly the downfall of most strikes). The wording used may be somewhat obtuse, but the context makes it quite clear that the issue was money. Going through the answer choices, D is the only option that is remotely close to what we want, and is therefore the correct answer.

On Reading Comprehension questions, it’s very easy to experience information overload (TL;DR for the new generation). A lot of information is contained in each passage, and this is not an accident. The test is designed to try and waste your time with frivolous sentences, so your goal is to read for overarching intent and know that you’ll have to revisit the text on most questions. Specific questions tend to ask about something minor, or possibly tangential, and therefore usually require you to reread the passage. Practice Reading Comprehension timing and you will find that you can answer these specific questions faster.

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.*

Last Digit of Base:

0 – Last digit of expression with any power will be 0.

1 – Last digit of expression with any power will be 1.

2 – 2, 4, 8, 6, 2, 4, 8, 6… Cyclicity is 4.

3 – 3, 9, 7, 1, 3, 9, 7, 1… Cyclicity is 4.

4 – 4, 6, 4, 6, 4, 6, 4, 6… Cyclicity is 2.

5 - Last digit of expression with any power will be 5.

6 – Last digit of expression with any power will be 6.

7 – 7, 9, 3, 1, 7, 9, 3, 1… Cyclicity is 4.

8 – 8, 4, 2, 6, 8, 4, 2, 6… Cyclicity is 4.

9 – 9, 1, 9, 1, 9, 1, 9, 1… Cyclicity is 2.

Cyclicity is nothing but pattern recognition. You see that when you multiply 2 by itself, there is a pattern of last digit which goes 2, 4, 8, 6, 2, 4, 8, 6 and so on. We can use the same principle for when a question asks us for the last two digits of the expression. Let me remind you first that here at QWQW, we sometimes flirt with the lines that define GMAT scope. Obviously, we do point out whenever we are indulging and that’s exactly what we are going to do in this post. We are carrying on for the love of Math and the Q51 score.

The last two digits of the base decide the last two digits of the expression. For example,

**Example 1: **Let’s look at powers of 11.

11^1 = 11

11^2 = 121

11^3 = 1331

11^4 = …41 (we should just multiply the last two digits together and ignore the rest)

11^5 = …51

11^6 = …61

11^7 = …71

Note that the last two digits are displaying a pattern depending on the power. So we expect the cyclicity here to be 10.

11^8 = …81

11^9 = …91

11^(10) = …01

11^(11) = …11

11^(12) = …21

and so on. So the last two digits should go from 11, 21 to 91, 01 and then go to 11 again. The cycle of 10 starts from power of 1, 11, 21 etc. This means that 11^(46) should have last two digits as 61, 11^(92) should have last two digits as 21 and 11^(168) should have last two digits as 81.

Let’s look at some other numbers now:

**Example 2:** Say, we need the last two digits of 6^{58}

6^1 = 6 (No second last digit)

6^2 = 36

6^3 = 216

6^4 = …96 (Just multiply the last two digits)

6^5 = …76

6^6 = …56

6^7 = …36

and hence starts the cycle again:

3, 1, 9, 7, 5, 3, 1, 9, 7, 5 and so on.

The new cycle with tens digit of 3 begins at the powers of 2, 7, 12, 17, 22, 27 etc. So the new cycle will also begin at power of 57 and 6^58 will have 1 as the tens digit.

**Example 3:** How about the last two digits of 7^102?

7^1 = 7 (No second last digit)

7^2 = 49

7^3 = 343

7^4 = …01

7^5 = …07

7^6 = …49

7^7 = …43

We see a cyclicity of 4 here: 49, 43, 01, 07, 49, 43, 01, 07 … and so on. The new cycle begins at 2, 6, 10, 14 i.e. even powers which are not multiples of 4. So a new cycle will begin at 102 too. So the last two digits of 7^(102) will be 49.

Now there can be many variations in the questions asking us to find the last two digits. We will use different concepts for different question types. Today we saw how to use pattern recognition. We will look at some other methods next week.

*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!*

However…

There are three knee-jerk questions that you should plug (if not chug) into your brain to ask yourself every time you see a Min/Max problem before you ask that fourth question “What’s my strategy?”:

- Do the numbers have to be integers?
- Is zero a possible value?
- Are repeat numbers possible?

In the Veritas Prep Word Problems lesson we refer to these problems as “scenario-driven” Min/Max problems precisely because of the above questions. The scenario created by the problem drives the whole thing, related mainly to those three above questions. Consider these four prompts and ask yourself which ones can definitively be answered:

*#1: “Four friends go fishing and catch a total of 10 fish. How many fish did the friend with the highest total catch?”*

*#2: “Four friends go fishing and catch a total of 10 fish. If no two friends caught the same number of fish, how many fish did the friend with the highest total catch?”*

*#3: “Four friends go fishing and catch a total of 10 fish. If each friend caught at least one fish but no two friends caught the same number, how many fish did the friend with the highest total catch?”*

*#4: “Four friends go fishing and catch a total of 10 pounds of fish. If each friend caught at least one fish but no two friends caught the same number, how many pounds of fish did the friend with the highest total catch?”*

Hopefully you can see the progression as this set builds. In the first problem, there’s clearly no way to tell. Did one friend catch all ten? Did everyone catch at least two and two friends tied with 3? You just don’t know. But then it gets interesting, based on the questions you need to ask yourself on all of these.

With #2, two big restrictions are in play. Fish must be integers, so you’re only dealing with the 11 integers 0 through 10. And if no two friends caught the same number there’s a limited number of unique values that can add up to 10. But the catch on this one should be evident after you’ve read #3. Zero *IS* possible in this case, so while the totals could be 1, 2, 3, and 4 (guaranteeing the answer of 4), if the lowest person could have caught 0 (that’s where “min/max” comes in – to maximize the top value you want to minimize the other values) there’s also the possibility for 0, 1, 2, and 7. Because the zero possibility was still lurking out there, there’s not quite enough information to solve this one. And that’s why you always have to ask yourself “is 0 possible?”.

#3 should showcase that. If 0 is no longer a possibility *AND* the numbers have to be integers *AND* the numbers can’t repeat, then the only option is 1 (the new min value since 0 is gone), 2 (because you can’t match 1), 3, and 4. The highest total is 4.

And #4 shows why the seemingly-irrelevant backstory of “friends going fishing” is so important. Pounds of fish can be nonintegers, but fish themselves have to be integers. So even though this prompt looks very similar to #3, because we’re no longer limited to integers it’s very easy for the values to not repeat and still give wildly different max values (1, 2, 3, and 4 or 1.5, 2, 3, and 3.5 for example).

As you can see, the scenario really drives the answer, although the fourth question “What is my strategy?” will almost always require some real work. Let’s take a look at a couple questions from the Veritas Prep Question Bank to illustrate.

**Question 1:**

Four workers from an international charity were selling shirts at a local event yesterday. Did one of the workers sell at least three shirts yesterday at the event?

(1) Together they sold 8 shirts yesterday at the event.

(2) No two workers sold the same number of shirts.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

(C) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

(D) EACH statement ALONE is sufficient to answer the question asked

(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Before you begin strategizing, ask yourself the three major questions:

1) Do the values have to be integers? YES – that’s why the problem chose shirts.

2) Is zero possible? YES – it’s not prohibited, so that means you have to consider zero as a min value.

3) Can the numbers repeat? That’s why statement 2 is there. With the given information and with statement 1, numbers can repeat. That allows you to come up with the setup 2, 2, 2, and 2 for statement 1 (giving the answer “NO”) or 1, 2, 2, and 3 (giving the answer “YES” and proving this insufficient).

But when statement 2 says on its own that, NO, the numbers cannot repeat, that’s a much more impactful statement than most test-takers realize. Taking statement 2 alone, you have four integers that cannot repeat (and cannot be negative), so the smallest setup you can find is 0, 1, 2, and 3 – and with that someone definitely sold at least three shirts. Statement 2 is sufficient with really no calculations whatsoever, but with careful attention to the ever-important questions.

**Question 2:**

Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000

(B) $41,667

(C) $42,000

(D) $50,000

(E) $60,000

Here ask yourself the same questions:

1) The numbers do not have to be integers.

2) Zero is theoretically possible (but probably constrained by the 20% difference restriction)

3) Numbers absolutely can repeat (which will be very important)

4) What’s your strategy? If you want the LOWEST possible single salary, then use your answer to #3 (they can repeat) and give the other 20 salaries the maximum. That way your calculation looks like:

x + 20(1.2x) = 1,050,000

Which breaks out to 25x = 1,050,000, and x = 42000. And notice how important the answer to #3 was – by knowing that numbers could repeat, you were able to quickly put together a smart strategy to minimize one single value.

The larger lesson is crucial here, though – these problems are often (but not always) fairly basic mathematically, but derive their difficulty from a situation that limits some options or allows for more than you’d think via integer restrictions, the possibility of zero, and the possibility of repeat values. Ask yourself these four questions, and your answer to the first three especially will maximize your efficiency on the strategic portion of the problem.

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*

So if geometry isn’t useful in your studies, why would the GMAT regularly contain 4-6 questions that deal specifically with geometry? The answer is: the people making the exam want to know how you think. That’s all. The GMAT is a test designed to measure your critical thinking skills and your ability to reason out conclusions. The fact that geometry is being used as a vehicle to accomplish these goals is only because geometry is a key part of the high school curriculum. Similar questions could easily be formulated about linear algebra, calculus or other mathematical disciplines (please no one tell the GMAC about manifolds). However, the fact that not everyone has seen these disciplines before would give some people an unfair advantage. The GMAT may be many things, but unfair is not usually one of the qualities mentioned (cruel comes up a lot, though).

The other issue about geometry is it seems that it’s a subject that requires a lot of memorization. While it’s true that many formulae (or formulas) need to be committed to memory before taking the test, most questions revolve around how to use that information. On occasion, it may seem that there’s a different formula for every situation, the majority of questions will require you to apply a simple concept or formula in an unfamiliar situation.

Let’s look at an example of a geometry question that doesn’t require any special formula, but stumps a lot of students:

If the radius of a circle that centers at the origin is 5, how many points on the circle have integer coordinates?

(A) 4

(B) 8

(C) 12

(D) 15

(E) 20

There is a necessity to understand some of the verbiage in this question in order to be able to answer it properly. Firstly, a circle that is centered at the origin is centered at point {0,0}. The radius is 5, which means we know the diameter (2*r), the circumference (2*π*r) and the area (π * r^2). However, none of that information really helps us to answer this question. We are interested in how many points on the circle have integer coordinates. Quite simply, a circle has an infinite number of discrete points, so it’s easier to answer this question in the reverse: For each integer coordinate, is that point on the circle?

Let’s start with the obvious ones. The point {5,0} has to necessarily be on the circle. If the origin is {0,0} and the radius is 5, then not only must point {5,0} be on the circle, but so must point {-5,0}. The circle extends in all four directions, so we cannot forget the negative values. Similarly, the points {0,5} and {0,-5} will also be on the points, effectively covering the four cardinal points from the original circle. The circle could look something like this:

After solving for these four points, we must evaluate whether other integer coordinates could be on the circle. One thing should be clear: if the radius is 5, then any integer point above 5 will necessarily not be on the circle, as it is beyond the reach of our radius. We’ve already covered zero, so the only options we have left are one, two, three and four. Of course all of these numbers have negatives and can be considered on either the x or y axis, but still we have a finite number of possibilities to consider.

Another important thing that might not be as obvious is that the answer to this question will necessarily be a multiple of four. Given that a circle extends in all directions by the same distance, it is impossible for point {x, y} to be on the circle and for points {x,-y}, {-x,y} and {-x,-y} to not also be on the circle. This is an important property of all circles and one of the reasons they’re so common in everything from architecture to cooking (and to alien crop circles, if you believe in that). This rule also guarantees that any answer choice that’s not a multiple of four can be eliminated. We can thus eliminate answer choice D (15).

How do we go about finding other points on the circle? (Why am I asking rhetorical questions?) By using the Pythagorean Theorem, of course! Any point on the circle naturally forms a right angle triangle with the radius as the hypotenuse, and the radius is always five. Therefore, if the two other sides can be formed out of integers, we have a point on the circle with integer coordinates. The graph below will highlight this principle:

Since the Pythagorean Theorem states that the squares of the sides will be equal to the square of the hypotenuse, we only need to look for numbers that satisfy the equation a^2 +b^2 = r^2. And given that r is 5, r^2 must always be 25. So if we plug in a as one, we find that 1 + b^2 = 25. This gives us b^2 = 24, or b = √24, which is not an integer. We only have to plug this in three more times, so there’s no reason not to try all the possibilities. If a = 2, then we get 4 + b^2 = 25. The value of b would be √21, which again is not an integer value.

If a = 3, however, we quickly recognize the vaunted 3-4-5 triangle, as 9 + b^2 = 25, meaning b^2 is 16 and therefore b is 4. This means that the points {3,4}, {-3,4}, {3,-4} and {-3,-4} are all on the circle. We’ve brought the total up to 8, but we’re not done. The final value is when a equals four, which will again work and bring in the converse of the last iteration: {4,3}, {-4,3}, {4,-3} and {-4,-3}. These values are distinct from the previous ones, so we now have a total of 12 points. We’ve already checked five, so we can stop here. The answer to this question is answer choice C. There will be 12 distinct values with integer coordinates, as crudely demonstrated below (or on any analog clock).

In geometry, even if it feels like you have to constantly commit more rules to memory, remember that the rules are not nearly as important as knowing how to apply them. This problem can be solved with just the Pythagorean Theorem and a little elbow grease (or a graphing calculator). The GMAT is very much a test of how you think, not of what you know. If you think about geometry problems as cases that must be solved, or obstacles to be overcome, you’ll be in good shape to solve them.

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!

Mark is playing poker at a casino. Mark starts playing with 140 chips, 20% of which are $100 chips and 80% of which are $20 chips. For his first bet, Mark places chips, 10% of which are $100 chips, in the center of the table. If 70% of Mark’s remaining chips are $20 chips, how much money did Mark bet?

You can view this as a word problem where you assume the number of chips and then go splitting them up or you can view this as a mixtures problem even though it doesn’t use words such as ‘mixture’, ‘solution’, ‘combined’ etc. As we have seen enough number of times, our mixture problems are solved in seconds using the weighted average concept.

The question discussed here also belongs to the same category – looks super tricky but can be easily solved with weighted averages formula. But we have seen plenty and more of such questions in our blog posts. Today we will take a look at a different type of sinister question and I suggest you to think about the concept being tested in that before trying to solve it.

**Question**: Mark owns four low quality watches. Watch1 loses 15 minutes every hour. Watch2 gains 15 minutes every hour relative to watch1 (that is, as watch1 moves from 12:00 to 1:00, watch2 moves from 12:00 to 1:15). Watch3 loses 20 minutes every hour relative to watch2. Finally, watch4 gains 20 minutes every hour relative to watch3. If Mark resets all four watches to the correct time at 12 noon, what time will watch4 show at 12 midnight that day?

(A)10:00

(B)10:34

(C)11:02

(D)11:48

(E)12:20

Before we look at the solution, think about the concept being tested here – clocks? Circular motion?

Neither!

**Solution**: Note that when giving data about watch1, you are told how it varies with the actual time. Data about all other watches tells us about the time they show relative to the incorrect watches. The concept being tested here is Relative Speed!

What do we mean by “gains 15 mins” or “loses 20 mins” etc? When a watch gains 15 mins every hour, it means that even though it should show that one hour has passed, it shows that 1 hr 15 mins have passed. So the watch runs faster than it should. Hence the speed of the watch is more than the speed of a correct watch. Now the question is how much more? The minute hand of the correct watch travels one full circle in one hour. The minute hand of the incorrect watch travels one full circle and then a quarter circle in one hour (to show that 1 hour 15 mins have passed even when only an hour has passed). So it is 5/4 times the speed of a correct watch. On the same lines, let’s analyze each watch.

Say the speed of a correct watch is s.

- “Watch1 loses 15 minutes every hour. “

Watch1 covers only three quarters of the circle in an hour.

Speed of watch1 = (3/4)*s

- “Watch2 gains 15 minutes every hour relative to watch1 (that is, as watch1 moves from 12:00 to 1:00, watch2 moves from 12:00 to 1:15).”

Now we have the speed of watch2 relative to speed of watch1. Speed of watch2 is (5/4) times the speed of watch1.

Speed of watch2 = (5/4)*(3/4)s = (15/16)*s

- “Watch3 loses 20 minutes every hour relative to watch2.”

Watch3 loses 20 mins every hour means its speed is (2/3)rd the speed of watch2

Speed of watch3 = (2/3)*(15/16)*s = (5/8)*s

- “Finally, watch4 gains 20 minutes every hour relative to watch3.”

Speed of watch4 = (4/3)*Speed of watch3 = (4/3)*(5/8)*s = (5/6)*s

So the speed of watch4 is (5/6)th the speed of a correct watch. So if a correct watch shows that 6 hours have passed, watch4 will show that 5 hours have passed. If a correct watch shows that 12 hours have passed, watch4 will show that 10 hours have passed. From 12 noon to 12 midnight, a correct watch would have covered 12 hours. Watch4 will cover 10 hours and will show the time as 10:00.

Answer (A)

*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!*

Why?

There are certain combinations of numbers that just have to be top of mind when you take the GMAT. The quantitative section goes quickly for almost everyone, and so if you know the following combinations you can save extremely valuable time.

Based on Pythagorean Theorem, a^2 + b^2 = c^2, these four ratios come up frequently with right triangles:

a_______b________c

3_______4________5

5______12_______13

x_______x______x*(sqrt 2)___(in an isosceles right triangle)

x____x*(sqrt3)___2x________(in a 30-60-90 triangle)

These four ratios come up frequently when right triangles are present, so they’re about as high as you can get on the “should I memorize this?” scale. But just as important is using these ratios wisely and appropriately, so make sure that when you see the opportunity for them you keep in mind these two important considerations:

1) **These “Pythagorean Triplets” are RATIOS, not just exact numbers.**

So a 3-4-5 right triangle could also be a 6-8-10 or 15-20-25, and an isosceles right triangle could very well have dimensions a = 4(sqrt 2), b = 4(sqrt 2), and c = 8 (which would be one of the short sides 4(sqrt 2) multiplied by (sqrt 2) ). An average level question might pair 5 and 12 with you and reward you for quickly seeing 13, while a harder question could make the ratio 15, 36, 39 to reward you for seeing the ratio and not just the exact numbers you memorized.

Similarly, people often memorize the 45-45-90 and 30-60-90 triangles so specifically that the test can completely destroy them by making the “wrong” side carry the radical. If the short sides are 4 and 4, you’ll naturally see the hypotenuse as 4(sqrt 2). But if they were to ask you for the length of the hypotenuse and tell you that the area of the triangle is 4 (so 1/2 * a * b = 4, and with a equal to b you’d have 1/2 a^2 = 4, so a^2 = 8 and the short side then measures 2(sqrt 2)), it’s difficult for many to recognize that the hypotenuse could be an integer. So be careful and know that the above chart gives you *RATIOS* and not fixed numbers or fixed placements for the radical sign that denotes square root.

2) **In order to apply these ratios, you MUST know which side is the hypotenuse.**

In a classic GMAT trap, they could easily ask you:

What is the perimeter of triangle ABC?

(1) Side AB measures 5 meters.

(2) Side AC measures 12 meters.

And it’s common (in fact a similar problem shows that about 55% of people make this exact mistake) to think “oh well this is a 5-12-13, so both statements together prove that side BC is 13 and I can calculate that the perimeter is 30 meters.” But wait – 5 and 12 only lead to a third side of 13 when you know that 5 and 12 are the short sides. If you don’t know that, the triangle could fit the Pythagorean Theorem with 12 as the hypotenuse, meaning that you’re solving for side b:

5^2 + b^2 = 12^2, so 25 + b^2 = 144, and b then equals the square root of 119.

So while it’s critical that you memorize these four right triangle ratios, it’s just as important that you don’t fall so in love with them that you use them even when they don’t apply.

Important caveats aside, knowing these ratios is crucial for your ability to work quickly on the quant section. For example, a problem that says something like:

In triangle XYZ, side XY, which runs perpendicular to side YZ, measures 24 inches in length. If the longest side of the the triangle is 26 inches, what is the area, in square inches, of triangle XYZ?

(A) 100

(B) 120

(C) 140

(D) 150

(E) 165

Those employing Pythagorean Theorem are in for a fight, calculating a^2 + 24^2 = 26^2, then finding the length of a and calculating the area. But those who know the trusty 5-12-13 triplet can quickly see that if 24 = 12*2 and 26 = 13*2, then the other short side is 5*2 which is 10, and the area then is 1/2 * 10 * 24, which is 120. Knowing these ratios, this is a 30 second problem; without them it could be a slog of over 2 minutes, easily, with a higher degree of difficulty due to the extensive calculations. So on today of all days, Friday, the 5th day of the 12th month, keep that 13th in there as a lucky charm.

On the GMAT, these ratios will get you out of lots of trouble.

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*By Brian Galvin*

The most common constructs that come in pairs are idioms, which are accepted turns of phrase, and elements requiring parallel structure. Both of these concepts can come up in sentence correction questions, and both play into whether a sentence has been properly constructed. Idioms often come up in pairs because one part of a sentence necessitates a parallel structure down the road. Similarly, parallel structure needs to have consistent elements or the sentence loses efficacy and becomes hard to read (like reading the word efficacy in a non-GMAT context).

A common example of the duality of idioms is the “Not only… but also…” idiom, whereby something will be described as “not only this… but also that”. If you don’t have the second part of the idiom, the first part doesn’t make much sense. You can say: “Ron is eating turkey”, but if you say “Not only is Ron eating turkey.” There must be some logical conclusion to that sentence, or you’re committing a sentence construction error. As an example: “Not only is Ron eating turkey, but he’s also eating yams.” Now the sentence is complete, as the idiom requires a second portion to complete the entire thought.

A common example of the importance of parallel structure is when making lists (and checking them twice). As an example, consider: “Ron likes eating turkey, watching football and to spend time with family”. The parallel structure is not maintained in this sentence because the first two are participial verbs and the third is an infinitive. You could rewrite this example as “Ron likes eating turkey, watching football and spending time with family” and it would be fine. However, that is not the only option. You could also rewrite this as “Ron likes to eat turkey, to watch football and to spend time with family”, or even “Ron likes to eat turkey, watch football and spend time with family”. Any of these constructions would be acceptable, because they all maintain the consistency required in parallel structures.

Now that we’ve seen how important it is to stick together, let’s look at an example that highlights these concepts in sentence correction:

In a plan to stop the erosion of East Coast beaches, the Army Corps of Engineers proposed building parallel to shore a breakwater of rocks that would rise six feet above the waterline and act as a buffer, so that it absorbs the energy of crashing waves and protecting the beaches.

(A) act as a buffer, so that it absorbs

(B) act like a buffer, so as to absorb

(C) act as a buffer, absorbing

(D) acting as a buffer, absorbing

(E) acting like a buffer, absorb

One ongoing difficulty in sentence correction is that a problem is rarely about only one concept. Frequently multiple issues must be addressed, such as agreement, awkwardness and antecedents of pronouns (and that’s just the letter A!) As such, it’s paramount to identify the decision points and see which types of errors could potentially occur in this sentence. It may not be as obvious on test day as it is now to note that this sentence has some issues with parallelism, but the fact that some verbs are underlined while others are not can help guide your approach here.

There is a verb (rise) before the underlined portion, and another verb (protecting) after the underlined portion. (Rise and protect make me think this sentence is about Batman). The correct answer choice will have to work with both verbs effortlessly, so let’s evaluate them one at a time. The first decision point we have in the underlined portion is deciding between “act” and “acting”, and this verb must match up with the previous verb “rise” as both are being commanded by the wall of rocks that is their shared subject. Since “rise” is an infinitive, and it is not underlined, the correct match must be with “act”. This parallel structure eliminates answer choices D and E, as both have the verb in its participle form. As an aside, please note that you don’t need to know the grammatical terms; they’re listed primarily for clarity.

The second decision point is the other verb, which comes in three different forms (absorbs, absorb, absorbing) in the three answer choices. Since the verb at the end of the sentence is in its participle (protecting), the parallel structure dictates that the answer choice must be answer choice C, as it is the only remaining choice with “absorbing”. We have thus eliminated four answer choices using only parallel structure. While answer choice C is indeed the correct answer, we can also note the idiom “act as a buffer”, which is used correctly, as opposed to “act like a buffer” in answer choice B. This decision point could be sufficient on its own, but you can often knock out a single incorrect answer choice for multiple reasons. Answer choice C is the only choice that does not contain any sentence construction errors.

Often, I compare the concept of parallelism to the banal notion of wearing socks. Any two socks are acceptable as long as they match, but wearing unmatched socks is a sure-fire way to get mocked (by me). Similarly, parallel structure only requires that you remain consistent within the same sentence, not that lists must be constructed exclusively in a certain way. Parallelism is very important in sentence correction, as it’s often the only reason to eliminate an answer choice that otherwise makes grammatical sense.

If you’re studying for the GMAT during the holidays this year, I wish you the best of luck, and remember that studying well and succeeding on the GMAT go hand in hand.

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!

This, of course, makes applying to business school much more competitive for international students (since there are simply more applicants in the pool competing for slots), but it also makes things tougher for American applicants, mostly because the scores of these international applicants is considerably higher as well. It has long been established through grade-school and high-school statistics that the Asian population dominates over the U.S. in mathematic performance. Since business schools discovered a strong connection between GMAT quantitative scores and business school success, this translates into a distinct advantage for Asian applicants who perform well on the GMAT.

Again, the numbers are impressive (or depressing if you are from the U.S.). Asian test takers average 45 raw score on the quant portion of the GMAT, whereas U.S. test takers average just 33. This is a significant difference, and one that has sent U.S. students scrambling to catch up. The boom in test-prep services is a stark indicator of this, and there is much ground still to cover. Asian students, for example, put about twice as many hours into preparing for the GMAT as U.S. students do.

There is talk of bifurcating the test results from GMAT so the business schools in the U.S. can separate out scores by region. This would help U.S. students be more favorably compared to other students with a similar background and culture. While it would not be fair to have two different scoring systems, it seems that GMAC is at least trying to help b-schools make better assessments on which students in the U.S. will be (comparatively) decent performers in their curriculum.

Of course the headline here, is twofold. If you are an international applicant, you must have more than just a good GMAT score to differentiate yourself. If you are an American applicant, you need to do whatever you can to press out a decent GMAT score in order to be competitive. The extra hours you put in will more than pay off if you end up being invited to join the school of your dreams, vs. being left out in the cold because your paper qualifications didn’t measure up.

Learn about top MBA programs by downloading our Essential Guides! Call us at 1-800-925-7737 and speak with an MBA admissions expert today, or click here to take our Free MBA Admissions Profile Evaluation! As always, be sure to find us on Facebook and Google+, and follow us on Twitter.

*Bryant Michaels has over 25 years of professional post undergraduate experience in the entertainment industry as well as on Wall Street with Goldman Sachs. He served on the admissions committee at the Fuqua School of Business where he received his MBA and now works part time in retirement for a top tier business school. He has been consulting with Veritas Prep clients for the past six admissions seasons. See more of his articles here.*

**How did you hear about Veritas Prep?**

* I signed on with Veritas Prep via Service to School, a non-profit that helps veterans make the transition from the military to both undergraduate and graduate school. Veritas Prep has teamed up with Service to School and is awarding free GMAT prep scholarships to select candidates. My Service to School Ambassador, a fellow veteran who is an MBA candidate at the Booth School of Business, thought I was a good fit for the Veritas Prep program and that’s how the process started! I ended up using Veritas Prep and only Veritas Prep to prepare for the GMAT.*

**What was your initial experience with the GMAT? How did you first feel going in?**

*I took the diagnostic CAT a week before starting the Veritas Prep course and walked away with a 580 and a bruised ego. Not that I expected a great score on my first test, but it was still a good reality check, and it let me know how much work I had ahead of me. I know I’m definitely not alone when I say this, but finding study time with a busy work schedule is tough, even more so if you have a family. It took me a few weeks to nail down my rhythm. I also took a little longer than I should have to schedule the official test, so by the time my appointment came around I feared that I had forgotten a bunch of material I’d learned in the Veritas Prep course. Regardless, my CAT scores were right around my target range (710-730) and this gave me enough confidence going into the actual test. Even though I’m still a ways off from beginning the school application process, I honestly wanted to be “one and done” with the GMAT as I’m about to take a job with a significantly higher demand on my time.*

**How did the Veritas Prep course help prepare you?**

*In my opinion, one of the most devilish aspects of the GMAT is that it stresses thought processes more than concept mastery. The Veritas Prep course hammered that fact home within the first five minutes of study and continued to stress it in each of the lessons. I feel that the value in prep courses lies in the foundation of fundamental concepts for future individual study that they establish. In that regard, the Veritas Prep course (and instructor) did a great job in developing my ability to think through questions so that when I eventually moved to self-study I could look at all the math and verbal concepts through a more logical lens. I should also mention the quality of Veritas Prep’s materials – the lesson books, online problem sets (with solutions), and CATs are all extremely easy to use. In particular, the CATs were pretty spot-on in terms of difficulty and content when compared to the actual GMAT.*

**Tell us about your test day experience and how you felt throughout the experience?**

*I had a healthy mix of nerves and confidence. I’d already scouted the test location so I didn’t have to worry about finding the place in the beehive that is downtown Honolulu. Once the test got started I felt like I was back at my house doing another Veritas Prep practice test: equal amounts of “I’ve got this” reactions and “I’m screwed” reactions to the questions that came up on the screen. I didn’t notice too much test fatigue – I did a few full practices on the Veritas Prep site – although about halfway through the verbal section I really wanted nothing more than to finish and see my score. When I clicked past the last page of admin data verification and saw the 750 on the screen I was so excited that I couldn’t get out of my chair for almost three minutes.*

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*Compiled by Colleen Hill*