So if geometry isn’t useful in your studies, why would the GMAT regularly contain 46 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 345 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!
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.
]]>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 nonGMAT 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 surefire 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!
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.
]]>Now, some numbers are spelled out down to the decimals, but other numbers, such as 11!, seem unnecessarily abstract. 11 factorial is a big number, but wouldn’t it be simpler if I had a concrete number in front of me instead of a shorthand notation for 10 multiplications. The answer is: not really. If you wanted to expand 11! To get a longhand answer, you’ll end up with a large concrete number that is no easier to manipulate than the shorthand you had before. For example, 11! is actually 39,916,800. Does that make it any easier to use? Again, the answer is: not really.
In essence, every time you see a big number like this, the GMAT is baiting you into performing tedious calculations that don’t help you in any way. Having a cumbersome number is the GMAT’s way of saying “Don’t try and solve this with brute force, there’s a concept here you should recognize”. While it’s uncommon for the GMAT to actually speak, given that it’s an admissions exam, it actually is telling you loud and clear that concentrating on the number is a trap. There will always be some element that will help highlight the underlying issue without performing tedious math.
There are many concepts that may come into play, and it’s hard to approach these questions with a single standard approach, but some elements repeat more frequently than others. One of the first things to look for is the units digit. The units digit gives away many properties of a number. As an example, 39,916,800 ends with a 0, indicating that it is even, and that it is divisible by 10. Different units digits can yield different number properties, so you can learn a lot from one simple digit. The factors of the number in question can often unlock clues as to which numbers to look for among the answer choices. Finally the order of magnitude can also play a pivotal role in determining how to approach a question.
Since we don’t have one definitive strategy, let’s test our mental agility on an actual GMAT question:
For integers x, y and z, if ((2^x)^(y))^(z) = 131,072, which of the following must be true:
(A) The product xyz is even
(B) The product xyz is odd
(C) The product xy is even
(D) The product yz is prime
(E) The product yz is positive
This question is significantly easier if you recognize which power of two 131,072 is off the bat (I knew that Computer Science degree would be good for something). However, let’s approach this knowing that 131,072 is a multiple of two, but that calculating which one would require more time than the two minutes we have earmarked for this question. Furthermore, simply knowing that 131,072 is a power of 2 gives us all the information we really need to solve this question.
We know x, y and z will combine to form some integer, but we’re not sure which. Let’s call it integer R (as in Ron) for simplicity’s sake. Moreover, the way the equation is set up, the powers will all be multiplied by one another, meaning that their exact order won’t matter. As such, the commutative law of mathematics confirms that if ((2^5)^(3))^(2) is the exact same thing as ((2^3)^(2))^(5). If the order doesn’t matter, then there are a lot of potential situations that could occur. So R will equal x + y + z, but the order won’t change anything. Let’s look at the answer choices, and start from the end because they’re easier to eliminate.
Answer choice E asks us whether y*z must be positive. If y*z gives us some positive number, then x would just be whatever is left over to form R. It doesn’t matter is y*z is positive or negative, as x can just come and make up the difference. Let’s say y*z = 4, then x would just be R – 4. If, instead, y*z = 4, then x would just be R – 12 and there would be no difference. In other words, as long as one variable is unrestricted, it will always be able to make up for the restriction on the other two. If you recognize this, you can eliminate C, D and E for the same reason. Two out of three ain’t bad, but in this case, it ain’t enough.
This brings us down to answer choices A and B, which are complimentary. Either the product of the three numbers is even, or it is odd. One of these, logically, must be true. Unfortunately, the best way to verify this appears to be doing the calculation longhand (like the petals of a flower: she loves me, she loves me not). Herein lays a potential shortcut: the units digit. Since the number is a power of two, we can simply follow the pattern of multiples of two and see what we get. Considering primarily the units digit (underlined for emphasis):
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
2^9 = 512
You probably don’t have to go this far to notice the pattern, but it doesn’t hurt to confirm if you’re not sure after 2^5. Essentially, the unit digit oscillates in a fixed pattern: 2, 4, 8, 6, and then repeats. This is helpful, because the number in question ends with a 2, and every power of two that ends with a 2 is either 2^1, 2^5, 2^9, etc. All of these numbers are odd powers of 2, repeating every fourth element. With this pattern clearly laid out, it becomes apparent that the answer must be that the product of these three variables must be odd. As such, answer choice B is correct here. We can also probably deduce from order of magnitude that 131,072 is 2^17.
When it comes to large numbers on the GMAT, you should never try to use brute force to solve the problem. The numbers are arbitrarily large to dissuade you from trying to actually calculate the numbers, and they can be made arbitrarily larger on the next question to waste even more of your time. The GMAT is a test of how you think, so thinking in terms of constantly calculating the same numbers over and over limits you to being an ineffective calculator. Your smart phone currently has at least 100 times your computational power (but not the ability to use it independently… yet…). Brute force may break some doors down, but mental agility is a skeleton key.
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.
]]>What motivates you to be a GMAT instructor?
“I have been teaching the GMAT for 10 years because I absolutely love what the test is designed to assess and how it makes you learn and think. This is not a content regurgitation test, but rather it is one that assesses who is good at taking basic content and using that to solve very difficult problems and reasoning puzzles. I believe that the skills and thinking processes the GMAT assesses are invaluable not only in business but in all walks of life. I really enjoy unlocking this way of thinking for students and teaching them to love a test that they may have at first despised!”
If you could give three pieces of advice to future GMAT test takers, what would they be?
“1) Do not waste 3 months preparing on your own, receive a low score, and THEN sign up for a high quality GMAT prep course. Take our full GMAT course before you even open a book or read about the GMAT. It will save you so much time, energy, and frustration.
Click here for Chris’ other two points of advice.
Is there a common misconception of the GMAT or of what is a realistic GMAT score?
“I think there are many important misconceptions about the test as a whole and the scoring system in particular. As I have intimated earlier, the biggest misconception about the GMAT is that it is a content test in which memorizing all the rules and the underlying content will allow you to do well. This is certainly not the case and it is why so many students get frustrated when they prepare on their own. The GMAT is so different from the tests that you were able to ace in college with memorization ‘allnighters.’ Also, I think people underestimate how competitive and difficult the GMAT really is. Remember that you are competing against a highly selective group of college graduates from around the world who are very hungry to attend a top US business school. This test is no joke and requires an intensive preparation geared toward success in higher order thinking and problem solving.”
Read the rest of the interview here!
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!
]]>Now, at a restaurant, you may be particularly hungry and decide to order both the soup and the salad (and the frog legs while we’re at it). Similarly, on forms, someone who selects both options is being confusing. Perhaps you’ve smoked once and didn’t like it. Perhaps you smoke only on long weekends when the Philadelphia Eagles have a winning record. Sometimes people decide they don’t want to pick between the two choices given. However, if the question were changed to “have you ever smoked a cigarette?” and then given yes or no options, the decision becomes much easier. You have to be in one camp or the other, there is no sitting on the fence (like Humpty Dumpty).
For questions that set up this kind of duality, the entire spectrum of possibilities is essentially covered in these two options. There is no third option; there is no “It’s Complicated” selection. There isn’t even a section for you to explain yourself in the comments below. On these questions, you have to either be on one side or the other, you cannot be in both. Equally, you cannot be in the “neither” camp either. Necessarily, to this point in your life, you have either smoked a cigarette or you have not. Since one of them must be true, this certainty offers some insight on inference questions in critical reasoning.
As you probably recall, inference questions require that an answer choice must be true at all times. This isn’t always easy to see as many answer choices seem likely, but simply are not guaranteed. Sometimes, on inference questions, you get two answer choices that are compliments of one another. You get two choices that say something to the effect of “Ron is always awesome” and “Ron is not always awesome”. Even I would go for the latter here, but clearly one of these must be correct. They cannot both be correct, but they also cannot both be false. Having two answer choices like this guarantees that one of them must be the correct answer, and makes your task considerably easier.
Let’s look at an example:
A few people who are bad writers simply cannot improve their writing, whether or not they receive instruction. Still, most bad writers can at least be taught to improve their writing enough so that they are no longer bad writers. However, no one can become a great writer simply by being taught how to be a better writer, since great writers must have not only skill but also talent.
Which one of the following can be properly inferred from the passage above?
(A) All bad writers can become better writers
(B) All great writers had to be taught to become better writers.
(C) Some bad writers can never become great writers.
(D) Some bad writers can become great writers.
(E) Some great writers can be taught to be even better writers.
Since this is an inference question, we must read through the answer choices because there are many possible answers that could be inferred from this passage. When reading through the passage, you probably note that answers C and D are somewhat complimentary. Either the bad writers can become great writers, or they can’t. However, some people might be miffed by the fact that “some writers” is vague and could mean different people in different contexts. However, while the term “some writers” is undoubtedly abstract, it can refer to any subset of writers one or greater (and up to the entire group). Any group of bad writers is thus conceivable in this passage, but the answer choice must be true at all times, so the groups comprised of “some writers” can mean anyone, and these two groups can be considered equivalent.
If you recognize that either answer choice C or answer choice D must be the answer, then you can easily skip over the other three choices. For completeness’ sake, let’s run through them quickly here. Answer choice A directly contradicts the first sentence of this passage: Some bad writers simply cannot improve their writing. Answer choice B contradicts the major point of this passage, which is that great writers have a combination of skill and talent, and you cannot teach talent. Answer choice E makes sense as an option, but it doesn’t necessarily have to be true. This is a classic example of something that’s likely true in the real world, but not necessarily guaranteed by this particular passage.
This leaves us with two options to consider. Can bad writers become great writers, or can they never become great writers? As mentioned above, great writers are born with some level of talent that cannot be mimicked by practice alone. The passage explicitly states “no one can one can become a great writer simply by being taught how to be a better writer”. Even though some bad writers can improve their writing with some help (perhaps even writing a Twilight Saga), some cannot improve their writing at all. If these bad writers cannot improve their writing, they necessarily will never become great writers. Answer choice C must be true based on the passage.
Looking at answer choice D in contrast, it states: “some bad writers can become great writers”. Perhaps some can, but this cannot be guaranteed in any way from the passage. It’s possible that all the writers are terrible even after year of practice. In fact, since we know that some will never improve (the opposite), this conclusion is certainly is not guaranteed. Answer choice C is supported by the passage, answer choice D seems conceivable in the real world, but it is certainly not assured.
On the GMAT, as in life, when confronted with two complimentary choices, you have to end up making a choice. In this instance, because you typically have five choices to consider, whittling the competition down to two choices already saves you time and gives you confidence. Recognizing which option must always be true is all that’s left to do, and that often comes down to playing Devil’s Advocate. When you’re tackling a decision such as this, consider what has to be true, and you’ll make the right choice.
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.
]]>A common strategy in puzzles is to build the outsides or the corners first, as these pieces are more easily identifiable than a typical piece, and then try and connect them wherever possible. Indeed, you are unlikely to have ever solved a puzzle without needing to jump around (except for puzzles with 4 pieces or so).
Similarly, you are often faced with GMAT questions that seem like intricate puzzles, and this same strategy of jumping around can be applied. If you start at the beginning of a question and make some strides, you may find your progress has been jammed somewhere along the way and you must devise a new strategy to overcome this roadblock. Jumping around to another part of the problem is a good strategy to get your creative juices flowing.
Let’s say a math question is asking you about the sum of a certain series. A simplistic approach (possibly one used by a Turing machine) would sequentially count each item and keep a running tally. However, a more strategic approach might involve jumping to the end of the series, investigating how the series is constructed, and finding the average. This average can then be multiplied by the number of terms to correctly find the sum of a series in a couple of steps, whereas the brute force approach would take much longer. Since the GMAT is an exam of how you think, the questions asked will often reward your use of logical thinking and your understanding of the underlying math concepts.
Let’s look at a sequence and see how thinking out of order can actually get our thinking straight:
In the sequence a1, a2, a3, an, an is determined for all values n > 2 by taking the average of all terms a1 through an1. If a1 = 1 and a3 = 5, then what is the value of a20?
(A) 1
(B) 4.5
(C) 5
(D) 6
(E) 9
This question is designed to make you waste time trying to decipher it. A certain pattern is established for this sequence, and then the twentieth term is being asked of us. If the sequence has a pattern for all numbers greater than two, and it gave you the first two numbers, then you could deduce the subsequent terms to infinity (and beyond!). However, only the first and third terms are given, so there is at least an extra element of determining the value of the second term. After that, we may need to calculate 16 intermittent items before getting to the 20th value, so it seems like it might be a time consuming affair. As is often the case on the GMAT, once we get going this may be easier than it initially appears.
If a1 is 1 and a3 is 5, we actually have enough information to solve a2. The third term of the sequence is defined as the average of the first two terms, thus a3 = (a1 + a2) / 2. This one equation has three variables, but two of them are given in the premise of the question, leading to 5 = (1 + a2) /2. Multiplying both sides by 2, we get 10 = 1 + a2, and thus a2 has to be 9. The first three terms of this sequence are therefore {1, 9, 5}. Now that we have the first three terms and the general case, we should be able to solve a4, a5 and beyond until the requisite a20.
The fourth term, a4 is defined as the average of the first three terms. Since the first three terms are {1, 9, 5}, the fourth term will be a4 = (1 + 9 + 5) / 3. This gives us 15/3, which simplifies to 5. A4 is thus equal to 5. Let’s now solve for a5. The same equation must hold for all an, so a5 = (1 + 9 + 5 + 5) /4, which is 20/4, or again, 5. The third, fourth and fifth terms of this sequence are all 5. Perhaps we can decode a pattern without having to calculate the next fourteen numbers (hint: yes you can!).
A3 is 5 because that is the average of 1 and 9. Once we found a3, we set off to find subsequent elements, but all of these elements will follow the same pattern. We take the elements 1 and 9, and then find the average of these two numbers, and then average out all three terms. Since a3 was already the average of a1 and a2, adding it to the equation and finding the average will change nothing. A4 will similarly be 5, and adding it into the equation and taking the average will again change nothing. Indeed all of the terms from A3 to A∞ will be equal to exactly 5, and they will have no effect on the average of the sequence.
You may have noticed this pattern earlier than element a5, but it can nonetheless be beneficial to find a few concrete terms in order to cement your hypothesis. You can stop whenever you feel comfortable that you’ve cracked the code (there are no style points for calculating all twenty elements). Indeed, it doesn’t matter how many terms you actually calculate before you discover the pattern. The important part is that you look through the answer choices and understand that term a20, like any other term bigger than a3, must necessarily be 5, answer choice C.
While understanding the exact relationship between each term on test day is not necessary, it’s important to try and see a few pattern questions during your test prep and understand the concepts being applied. You may not be able to recognize all the common GMAT traps, but if you recognize a few you can save yourself valuable time on questions. If you find yourself faced with a confusing or convoluted question, remember that you don’t have to tackle the problem in a linear fashion. If you’re stuck, try to establish what the key items are, or determine the end and go backwards. When in doubt, don’t be afraid to skip around (figuratively, literal skipping is frowned upon at the test center).
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.
]]>The advantage of the matrix box is that it highlights the innate relationships that must be true, but that are not always easy to keep track of. For instance, if a box contains 100 paperclips, some of which are metallic and some of which are plastic, then if we find 40 paperclips made of metal, there must necessarily be 60 that are made of plastic. The binary nature of the information guarantees that all the elements will fall into one of the predetermined categories, so knowing about one gives you information about the other.
The matrix box allows you to catalogue information before it becomes overwhelming. Anyone who’s studied the GMAT for any length of time (five minutes is usually enough) knows that the exam is designed to be tricky. As such, questions always give you enough information to solve the problem, but rarely give you the information in a convenient manner. Setting up a proper matrix box essentially sets you up to solve the problem automatically, as long as you know what to do with the data provided.
Let’s look at an example and what clues us into the fact that we should use a matrix box.
Of 200 students taking the GMAT, all of them have college degrees, 120 have been out of college for at least 3 years, 70 have business degrees, and 60 have been out of college for less than 3 years and do not have business degrees. How many of them have been out of college for at least 3 years and have business degrees.
A) 40
B) 50
C) 60
D) 70
E) 80
The principle determinant on whether we should use Venn diagrams or matrix boxes is whether the data has any overlap. In this example, it’s very hard to believe that a student could both have a business degree and not have a business degree, so it looks like the information can’t overlap and a matrix box approach should be used. Before we set up the matrix box, it’s important to know that the axes are arbitrary and you could put the data on either axis and end up with essentially the same box. We can thus proceed with whichever method we prefer. The box may look like what we have below:
Business Degree 
No Business Degree 
Total 

At least 3 years 

Less than 3 years 

Total 
Without filling out any information, it’s important to note that the “Total” column and row will be the most important parts. They allow us to determine missing information using simple subtraction. If we have the total figures, as little as one piece of information in the inside squares would be enough to solve every missing square (like the world’s simplest Sudoku). Let’s populate the total numbers provided in the question:
Business Degree 
No Business Degree 
Total 

At least 3 years 
120 

Less than 3 years 

Total 
70 
200 
With these three pieces of information, we can fill out the remaining “Total” squares by simply subtracting the given totals.
Business Degree 
No Business Degree 
Total 

At least 3 years 
120 

Less than 3 years 
80 

Total 
70 
130 
200 
Now all we would need to reach the correct answer is one piece of information: any of the remaining four squares. Luckily the question stem will always provide at least one of these, as the problem is unsolvable otherwise. Problems may be tricky and convoluted on the GMAT, but they will never be impossible. Looking back at the question, there are 60 students who have been out of college for less than 3 years and do not have business degrees. Plugging in this value we get:
Business Degree 
No Business Degree 
Total 

At least 3 years 
120 

Less than 3 years 
60 
80 

Total 
70 
130 
200 
Using a little bit of basic math we can turn this into:
Business Degree 
No Business Degree 
Total 

At least 3 years 
70 
120 

Less than 3 years 
20 
60 
80 
Total 
70 
130 
200 
And finally the completed:
Business Degree 
No Business Degree 
Total 

At least 3 years 
50 
70 
120 
Less than 3 years 
20 
60 
80 
Total 
70 
130 
200 
The question was asking for how many students have been out of college for at least 3 years and have business degrees, but using this method we could solve any potential question (Other than “What is the meaning of life”?). Since the number of students with business degrees who have been out of college three years or more is 50, the correct answer will be answer choice B.
In matrix box problems, setting up the question is more than half the battle. Correctly setting up the parameters will ensure that the rest of the problem gets solved almost automatically, and all you have to do is avoid silly arithmetic mistakes or getting ahead of yourself too quickly. Remember that if the information doesn’t overlap, it will likely make for a good matrix box problem. On these types of questions, don’t be afraid to think inside the box.
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.
]]>Needless to say, many people opted to cancel their scores out of fear that a disappointing result would reflect badly on them and hinder their chances of being accepted into the school of their choice. The overall takeaway of my article was that most people felt that they did badly on the GMAT, and therefore tended to cancel their scores more often than they should have.
Lo and behold, in the summer of 2014 the GMAC (the FIFA of the GMAT) decided to change this policy and allow students to see their scores before deciding whether or not to cancel them. This decision was met with jubilation and applause (by me) from most prospective students, as this situation was entirely preferable to the previous circumstances. However, some students still are unclear when they should cancel their scores and when they shouldn’t. As such, I figured this would be a golden opportunity to revisit this topic and discuss cancelling your scores under the new world order.
First, let’s begin with the bad news. If you cancel your score, you are not refunded your 250$ fee for taking the exam. Nor can you retake the exam the next day; the same 31 day waiting period applies. Perhaps most jarringly, your record will still indicate that a score was cancelled, meaning that there will still be some record of the GMAT having been taken, just no accompanying score. Finally, if you do decide to cancel your score, you can subsequently change your mind and ask for the score to be reinstated, although this will incur an additional cost of 100$, and must be done within 60 days of the test date.
Let’s begin with some valid reasons why someone would consider cancelling their scores. Firstly, if you sleep very badly the night before or something goes very wrong in your personal life (worse than Menudo breaking up), you may be incapable of concentrating properly and your score will consequently suffer. In these situations, when you know you can do significantly better, it may be a good idea to cancel your score. Another instance would be if you took the exam and got some score, perhaps a 600, and then retook it and scored 450, a considerably worse result. Since the goal is to try and show improvement from one GMAT to the next, a marked decline could send the wrong message to the schools of your choice. This is another instance where cancelling your score may be a legitimate option.
If we explore some of the situations where it may be less advisable to cancel your score, we can start with a good rule of thumb: If it’s your first GMAT, you should (practically) never cancel your score. Why? Because if you cancel your score, you remove your baseline GMAT score. The best case scenario may be to take the exam once, ace it, and never look back (or possibly go back to teach it years later), but the reality is most people end up taking this exam more than once. The current average number of times someone takes the GMAT is about 2.7, meaning that many people take the exam two or three times before getting the score they want. If you’re aiming for a 650, and only get a 550 on the first try, then subsequent scores will demonstrate perseverance and determination, two skills sought after in business professionals. Cancelling your first score will only raise questions as to how badly it went (210?) and why you elected to remove the only thing on an otherwise blank canvas.
Sometimes, you score a 600 the first time, decide you want a 650, and retake the exam and only get a 610 or 620. This shows some improvement, but many people become depressed that it doesn’t show enough improvement, especially if they studied for several months to achieve this moderate increase. Again, cancelling this updated score will only raise questions as to how badly the test went, and a small improvement is still an improvement. Most GMAT schools take the best GMAT score as their reference, so even a 10 point progress from 600 to 610 could be enough to make a difference in your application. The same principle applies if your score went down slightly, say to 580. While a slight decline isn’t cause for a celebration, it’s a minor hiccup that demonstrates that you can consistently stay within the same range. Also, cancelling a slight drop opens the possibility that you did very badly on this second attempt and opted to cancel the score, artificially exaggerating how poorly the test actually went.
Sometimes, the idea of cancelling your score will come up before you’re even done with the test. Halfway through the verbal section, when you’re wallowing in the fact that you guessed the last three questions, your brain may take solace in the idea of cancelling the exam score. Sometimes you’ll contemplate it during a difficult stretch in the quantitative section (sometimes even on question 1!). The fact that you can now see your score before deciding whether to cancel it is a huge benefit in your choice as it removes the guesswork from the equation. No matter how badly you think you’re doing, at least you can see the score, make a decision, and even potentially reverse that decision within a couple of months.
When it comes to cancelling scores on the GMAT, the rule of thumb is that you shouldn’t cancel your score unless some “force majeure” or act of God came into the equation. The rule change allows us more flexibility in our decision making process, but the same factors must still be considered. If this is the first time you take the exam, your score is higher than any of your previous scores or if you just feel like you’re stinking up the exam (figuratively, not literally), you probably shouldn’t cancel your score. If your score truly is abysmal, then you can take a page from Pacific Rim and say “We are cancelling the apocalypse!” and be confident in your decision. The GMAT is designed to be tricky, but at least all the guesswork about cancelling your score has been removed for 2014 and beyond.
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.
]]>My response is, “This is a clearly a problem, not just for study sessions but also for the GMAT itself which requires 4 straight hours of focus.
Luckily, there are simple ways to improve your focus, and these techniques will not only allow you to focus as you study for longer periods of time, but will also have other benefits throughout your life. I have been doing a lot of research into brain science and the GMAT recently, and one thing that comes up in even book or article that I read is meditation/mindfulness. The latest scientific research supports the conclusion that the number one way to increase your ability to focus is to begin a simple meditation and mindfulness practice.
When I mention “meditation” people think that I am talking about sitting in an uncomfortable position and meditating for hours at a time. They assume that it has something to do with adopting a particular religion or belief. Nothing could be further from the truth. Meditation and mindfulness basically mean being present wherever you are and not letting your mind wander. In other words, focusing!
In the last several years I have read many books and articles on topics like the ability to focus and how to be more productive and happy – The crazy thing is that every author researching these topics has mentioned meditation and mindfulness. You cannot be focused, you cannot be productive, and it turns out that you cannot even be happy if you do not learn to pay attention to where you are and what you are doing.
How to practice mindfulness? The bestseller author Tich Naht Han talks about brushing your teeth as a chance to focus on the ritual of brushing. Washing the dishes is a chance for you to be present and focus on the dishes – rather than basically ignoring the washing or brushing as your mind races everywhere (this is what we normally do)!
Mindfulness really just means that you are paying attention to where you are and what you are doing (yes, it does sound a little like Yoda from Star Wars). So if you are walking your dog that is what you are focused on, not the things at work you failed to complete today. And if you are at work then give your full attention there and do not worry about the fact that you need to walk the dog later!
“Meditation” simply means that you are taking mindfulness to another level. You are focusing on one thing and noticing when your mind wanders. It is a simple as that. You can meditate on the sunset and really notice the colors as they change. You can meditate on a song and really hear the notes. And as mentioned above you can meditate on your toothbrush or your dish scrubber, too.
One of the most common meditations is to sit quietly in a comfortable chair (or walk slowly if you prefer a walking meditation) and focus on your breathing. Simply say “IN” as you breathe in and “OUT” as you exhale. Do not try to prevent yourself from thinking about other things. Just notice when your mind does wander and bring it back to the breath again. So you are sitting in a chair and softly saying “IN” and “OUT” and suddenly a thought comes into your mind “I should be studying for the GMAT!” Just notice the thought and bring your focus back to the breathing. Then a thought pops up “I am wasting my time sitting here” again just acknowledge it and bring your attention back the breathing. Do this for just 5 minutes and believe it or not you will probably have better focus throughout the rest of the day.
In her groundbreaking work “The Willpower Instinct” Kelly McGonigal, Ph.D. writes of a student who had LOTS of trouble focusing. He was concerned that meditation would be impossible for him – this is because he thought that meditation required an empty mind for long periods of time. His meditation was really bad! He was constantly having thoughts pop up and had to keep bringing himself back to the breathing. He felt like he was “failing” at meditation!
Yet this student found that just 5 minutes of what anyone would consider very bad meditation had great results for him. The rest of the day he was much more focused. You can try five minutes of meditating each day right? Maybe first thing in the morning?
The scientific research shows the impacts that small amounts of meditation actually have on the brain. From “The Willpower Instinct” (page 25)
And one more thing – your happiness depends on your ability to focus on what you are doing! A recent study by Harvard psychologists found that a wandering mind was correlated with unhappiness. In fact, the actual activity that a person was doing had less impact on their level of happiness than did their focus (or lack of focus) on the current activity. Lack of focus seems to lead to lack of contentment. (Source Harvard Gazette)
So you can actually be very content studying the GMAT, if you can just cultivate your ability to focus on it!
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.
]]>Why would this be? (Rhetorical question) The passage may discuss many different facets, but each question is typically about one specific thing. As such, you don’t need to know everything; you only need to know about the information being asked in the problem. Better than that, the questions on Reading Comprehension passages can be categorized into four broad categories. This means that you can prepare for any question that could be posed, even if you haven’t read a word of the passage yet (like book reports in high school).
Today I’d like to delve deeper into one of the question types: Function questions. Function questions, like an inquisitive toddler, seek only to ask “why”. Why would the author say this? Why would this issue be mentioned? Why would the author use that specific word? The question is more interested in asking you “why” than in asking you “what”. In these instances, we must determine why something was mentioned, be it a word or a sentence, and what function it served in the passage.
The first strategy on these questions is always to read the surrounding sentences. The context often provides the framework for the passage or word in question, and helps explain it in a larger sense. The most important words will be contained in the sentence before or after what you’re being asked to evaluate, but the entire paragraph may be relevant to the issue. We expand our search in concentric circles from the epicenter and evaluate the entire context in order to ensure we capture the essence of what’s being asked.
Let’s look at an example of a function question and how to approach this type of Reading Comprehension question. As on the exam, we will begin with a passage and then the 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 wellkept dormitories and boardinghouses. 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.
So after a lot of text (340 words), we can finally look at a function question. However, a rudimentary understanding of the passage would be helpful, so let’s can sum up some of the main elements of this text before proceeding. The passage is concerned with worker rights in 1820s at the Lowell Textile Mills, and at one point, these workers went on strike for better conditions. In the end the women who worked there couldn’t do much for themselves but their efforts led to many other workers acquiring better rights, and their legacy is unquestionable (also they may have founded LMFAO). Now that we understand the broad strokes of the passage, let’s look at the question:
The author uses the word “ironically” in the 1st paragraph to indicate that
(A) None of the people who ran the Lowell Mills expected that the workers would organize to express dissatisfaction with working conditions.
(B) The women who worked at the Lowell Mills did not realize how fortunate they were to work at such a place.
(C) It could be considered surprising that an early effort to demand better working conditions began in an environment that was especially designed to promote worker satisfaction.
(D) The people who created the working environment for the women at the Lowell Mills did not really understand what it was they needed.
(E) It was unusual for women workers of the time to organize, regardless of their work environment.
This question is asking about a specific word in the first paragraph, so we can already get a sense that correctly answering this question will hinge entirely on what we retain from the first paragraph. This would be an ideal opportunity to go back and reread the first paragraph (go ahead, I can wait). Apart from discussing how young the women were, the paragraph spends a lot of time going over the conditions of the workers. Specifically, the conditions seemed designed to assuage any fears about the workers’ condition. After several lines about how great the conditions were, and then states that “ironically, it was here that dissatisfaction with the conditions brought about a strike”
There’s a definite disconnect between extolling the features of the slave labor textile mills, and the fact that people actually revolted. The connection is that it’s ironic that a strike would begin here, of all places, as everything was designed to promote worker satisfaction. That’s our prediction, and one of the answer choices should more or less match that prediction. Looking at them one by one we can determine which answer is correct:
(A) None of the people who ran the Lowell Mills expected that the workers would organize to express dissatisfaction with working conditions.
This is close but it’s not about the organizer’s expectations, it’s about the fact that these conditions were likely better than everywhere else. Also the use of the word “none” is strong language and should raise eyebrows. What if one person expected it but nine didn’t? Would it still be valid? It wouldn’t be, which means this choice is incorrect.
(B) The women who worked at the Lowell Mills did not realize how fortunate they were to work at such a place.
How fortunate they were to be working long hours for low wages? Granted other jobs may not have been any better, but the author’s tone here is not this aggressive or patronizing. We cannot defend this choice.
(C) It could be considered surprising that an early effort to demand better working conditions began in an environment that was especially designed to promote worker satisfaction.
Bingo, this perfectly matches our prediction and will be our correct answer. We will evaluate the two others for completeness’ sake, though.
(D) The people who created the working environment for the women at the Lowell Mills did not really understand what it was they needed.
This may or may not be true, but it wouldn’t be ironic. (We could solve this issue with some sensitivity training!) This choice is incorrect.
(E) It was unusual for women workers of the time to organize, regardless of their work environment.
This is true, but again, it is not ironic. The irony is that the conditions were comparatively good, not that it was women organizing together. This choice is incorrect.
It’s important to remember that for many Reading Comprehension questions, having a full 360° understanding of the passage is not required to get the correct response. In this instance, it only took the information contained in the first paragraph to determine that the correct answer was C. Often, simply understanding a single paragraph or sentence can unlock the answer and allow you to move to the next question.
For function questions, the immediate context needs to be evaluated and then the function of the word (or paragraph) becomes apparent. I will delve into the other question types in subsequent blog posts, but for now hopefully you can practice putting the “fun” in function questions.
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.
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