The GMAT will give you 100% credit for selecting the correct answer, even if you got there by flipping a coin, taking a wild guess or only selecting an answer choice based on the letters of your last name (I tend to pick either A or D if I’m making a complete guess). In class, I’ve asked many students how they get to the answer choice they provided me, and often their reasoning is wrong but they still land on the correct square. The GMAT has no way of differentiating sound logic from blind luck (or false positives, as they’re often called), so sometimes you get answers right purely by chance.
Of course, you can often determine which answer choice is correct without necessarily knowing exactly why. Especially on a multiple choice exam, you can often backsolve using the answer choices and find that answer choice A is correct even if the reasoning is hazy. On test day, there is no incentive to spending undue time to determine why the answer must be correct, no trophy for your approach. While preparing for the exam, you can certainly take time to investigate patterns and paradigms that seem to repeat regularly.
As a simple example, you probably know that a number is divisible by 3 if the sum of its digits is divisible by 3 (hence 93 or 1335 would be divisible by 3 because the sum of the digits is 12 in each case). You don’t necessarily need to know why; simply recognizing that it always works is enough on the GMAT.
However, sometimes it’s interesting to delve deeper into number properties as mathematics has so many interesting (well, interesting to me) properties that help you understand math better. Let’s look at an example:
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?
This type of question shouldn’t take you too long to figure out. Even if the question seems somewhat arbitrary, it is simply asking you to take a prime number, square it, and divide the product by 12 to find the remainder. Picking any prime number (greater than 3) should solve this problem, but we’ll want to look at a few just to make sure the pattern holds.
Since the prime numbers 2 and 3 are excluded from consideration, we can begin at the next prime number, which is 5. 5^2 is 25, and 25 divided by 12 gives us 2 with remainder 1 (remember that the remainder is what’s left over after you find the quotient). Since we picked one prime number and got the result of 1, we could already select that answer choice and move on. However, it’s probably cautious to at least consider a couple of other options before hastily selecting answer choice B.
The next prime number would be 7, and 7^2 is 49. If you divide 49 by 12, you get 4, remainder 1. The pattern seems to hold. The next one is 11? 11^2 is 121, which divided by 12 gives 10, remainder 1. The pattern seems pretty solid here. Let’s pick a random bigger prime number just to be sure: say 31. 31^2 is 961, which divided by 12 gives 80, with remainder 1 again. At this point we’re pretty sure that the remainder will always be 1, and can pick answer choice B with confidence. (Feel free to do a dozen more if you’d like, it always holds).
Again, though, on test day, you might make this selection after checking only one or two numbers. But since we’re still preparing for the exam (if you’re reading this during your GMAT they will undoubtedly cancel your score), let’s dive into why this pattern holds. It certainly seems odd that for any prime number, this property will hold, especially considering that prime numbers can be hundreds of digits long.
To see why this holds, let’s consider what this pattern means. The square of the number n, less 1, is divisible by 12. This can be expressed as (n^2 – 1) is divisible by 12. This might remind you of the difference of squares, because it’s of the form n^2 – x^2, where x happens to be 1. We can thus transform this equation to: (n-1) * (n+1) is divisible by 12. This form will be more helpful in detecting the underlying pattern.
For a number to be divisible by 12, it must be divisible by 2, 2 and 3. If I were to take three consecutive numbers n-1, n and n+1, one of these three must necessarily be divisible by 3. Remember that multiples of 3 occur every third number, so it is impossible to go three consecutive numbers without one of them being a multiple of 3. And since n has been defined to be a prime number greater than 3, it cannot be n. Thus either n+1 or n-1 must be divisible by 3.
Similarly, if n is a prime greater than 3, then it must be odd. Clearly, then, n-1 must be even, and n+1 must be even. Since both of these numbers are divisible by 2, their product must be divisible by 4. This means that for any two numbers (n-1) * (n+1) where n is a prime greater than 3, the product will be divisible by 2, by 2 and by 3, and therefore by 12.
On test day, figuring out the correct answer to the question is your main priority (not taking too long and not soiling yourself are two other big ones). Recognizing a pattern and making a decision based on the pattern is sufficient to get the question right, but it’s an interesting exercise to look into why certain patterns hold, why certain truths are inescapable. There’s no trophy for understanding math properties (not even a Nobel Prize), but identifying things that must be true goes a long way towards getting the right answer.
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.
]]>In other cases, the question seems to have been specifically designed to thwart an algebraic approach. While there’s no official litmus test, there are some predictable structural clues that will often indicate that algebra is going to be nothing short of hemorrhage-inducing.
Here’s my personal heuristic; if an algebraic scenario involves hideously complex quadratic equations, I avoid the algebra. If, on the other hand, algebra leaves me with one or two linear equations to solve, it will almost certainly be a viable option. You might not recognize which category the question falls under until you’ve done a bit of leg-work. That’s fine. The key is not to get too invested in one approach and to have the patience and flexibility to alter your strategy midstream, if necessary.
Let’s look at some scenarios with unusually complex algebra. Here’s a GMATPrep® question:
A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?
A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800
Simple enough. Let’s say the sides of this rectangular park are a and b. We know that the perimeter is 2a + 2b, so 2a + 2b = 560. Let’s simplify that to a + b = 280.
The diagonal of the park will split the rectangle into two right triangles with sides a and b and a hypotenuse of 200. We can use the Pythagorean theorem here to get: a^2 +b^2 = 200^2.
So now I’ve got two equations. All I have to do is solve the first and substitute into the second. If we solve the first for a, we get a = 280- b. Substitute that into the second to get: (280 – b)^2 + b^2 = 200^2. And then… we enter a world of algebraic pain. We’re probably a minute in at this point, and rather than flail away at that awful quadratic for several minutes, it’s better to take a breath, cleanse the mental palate, and try another approach that can get us to an answer in a minute or so.
Anytime we see a right triangle question on the GMAT, it’s worthwhile to consider the possibility that we’re dealing with one of our classic Pythagorean triples. If I see root 2? Probably dealing with a 45:45:90. If we see a root 3? Probably dealing with a 30:60:90. Here, I see that the hypotenuse is a multiple of 5, so let’s test to see if this is, in fact, a 3x:4x:5x triangle. If it is, then a + b should be 280.
Because 200 is the hypotenuse it corresponds to the 5x. 5x = 200 à x = 40. If x = 40, then 3x = 3*40 = 120 and 4x = 4*40 = 160. If the other two sides of the triangle are 120 and 160, they’ll sum to 280, which is consistent with the equation we assembled earlier.
And we’re basically done. If the sides are 120 and 160, we can just multiply to get 120*160 = 19,200. (And note that as soon as we see that ‘2’ is the first non-zero digit, we know what the answer has to be.)
Here’s one more from the Official Guide:
A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?
First the algebraic setup. If we want T towels that we buy for D dollars each, and we’re spending $120, then we’ll have T*D = 120.
If the price were increased by $1, the new price would be D+1, and if we could buy 10 fewer towels, we could then afford T -10 towels, giving us (T-10)(D+1) = 120.
We could solve the first equation to get T = 120/D. Substituting into the second would give us (120/D – 10)(D + 1) = 120. Another painful quadratic. Cue hemorrhage.
So let’s work with the answers instead. Start with D. If the current price were $4, we could buy 30 towels for $120. If the price were increased by $1, the new price would be $5, and we could buy 120/5 = 24 towels. But we want there to be 10 fewer towels, not 6 fewer towels so D is out.
So let’s try B. If the initial price had been $2, we could have bought 60 towels. If the price had been $1 more, the price would have been $3, and we would have been able to buy 40 towels. Again, no good, we want it to be the case that we can buy 10 fewer towels, not 20 fewer towels.
Well, if $4 yields a gap that’s too narrow (difference of 6 towels), and $2 yields a gap that’s too large (difference of 20 towels), the answer will have to fall between them. Without even testing, I know it’s C, $3.
This is all to say that it’s a good idea to go into the test knowing that your first approach won’t always work. Be flexible. Sometimes the algebra will be clean and elegant. Sometimes a strategy is better. If the algebra yields a complex quadratic, there’s an easier way to solve. You just have to stay composed enough to find it.
* GMATPrep® questions courtesy of the Graduate Management Admissions Council.
Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!
By David Goldstein, a Veritas Prep GMAT instructor based in Boston.
]]>However, sometimes you encounter Sentence Correction passages that are as long as paragraphs. Your job is the same no matter the length of the text, but Sentence Correction problems require you to evaluate every decision point among the answer choices. The longer the sentence, the more decision points you may have to consider. The number of false decision points also tends to increase as the sentence length increases. False decision points are differences between answer choices in which both options are acceptable, so making a choice based on such a decision point could erroneously eliminate a valid answer choice. Indeed, picking between an alternative and a substitute is an exercise in futility.
Another issue that comes up is mental fatigue. Conventional grammatical wisdom postulates that sentences longer than 20-25 words begin to lose their effectiveness, as the human brain struggles to process all the information. Run-on sentences can cause readers to disengage as they find themselves apathetic to the point that the author is trying to make. Often students report a lack of interest on longer passages, and an increased urge to simply select an answer choice (sometimes at random) to move on to a different question.
Let’s look at an example, which clocks in at an impressive 51 words.
The first trenches that were cut into a 500-acre site at Tell Hamoukar, Syria, have yielded strong evidence for centrally administered complex societies in northern regions of the Middle East that are arising simultaneously with but independently of the more celebrated city-states of southern Mesopotamia, in what is now southern Iraq.
(A) that were cut into a 500-acre site at Tell Hamoukar, Syria, have yielded strong evidence for centrally administered complex societies in northern regions of the Middle East that are arising simultaneously with but
(B) that were cut into a 500-acre site at Tell Hamoukar, Syria, yields strong evidence that centrally administered complex societies in northern regions of the Middle East were arising simultaneously with but also
(C) having been cut into a 500-acre site at Tell Hamoukar, Syria, have yielded strong evidence that centrally administered complex societies in northern regions of the Middle East were arising simultaneously but
(D) cut into a 500-acre site at Tell Hamoukar, Syria, yields strong evidence of centrally administered complex societies in northern regions of the Middle East arising simultaneously but also
(E) cut into a 500-acre site at Tell Hamoukar, Syria, have yielded strong evidence that centrally administered complex societies in northern regions of the Middle East arose simultaneously with but
The first thing you might notice is that, not only is this sentence way too long, most of it is underlined. That means it will take a fair amount of time just to peruse the answer choices. Our best strategy will probably not be to read through the five similar answer choices without any specific goal.
With run-on sentences, you want to be methodical and review each decision point as it comes up. As noted before, some may be false decision points and you cannot eliminate any choice. However, some words are low hanging fruit, such as verbs or pronouns, which have to be in specific forms (i.e. singular vs. plural). Connectors to and from the underlined portion are often significant as well, since they serve as springboards from one section to the next.
Looking at the original sentence (answer choice A) and going through the words, we’re looking for verbs and pronouns that can help guide our decisions. The first verb encountered is “were cut”, but the verb cut is tricky because it has the same form in the past, the present and the future. Answer choice C’s “having been cut” seems unnecessarily wordy, but that is not necessarily enough to eliminate it outright, so we’ll keep it with an asterisk and continue looking for other verbs.
The next verb encountered is “have yielded”, and a cursory comparison of the other answer choices reveals a 3-2 split between “have yielded” and “yields”. The subject of the verb is “The first trenches”, which is plural. The verb formulation of “yields” only works if the subject is singular, and thus we can eliminate these answer choices with 100% certainty as they contain agreement errors. Answer choices B and D can both be eliminated.
Continuing on, the second verb we encounter is “are arising”. Everything else about specific locations, sizes of land and other minutiae can be ignored using the slash-and-burn technique. We’re on a mission to compare specific terms that can help illuminate errors in various answer choices. Answer choice C has “were arising” and answer choice E has “arose”. The subject of the verb is “societies”, and therefore any of the three could be correct from an agreement standpoint. However, the timelines vary from present to past continuous to simple past, and the rest of the sentence began with the past-tense verb “have yielded”, meaning that the present tense would be erroneous. Answer choice A can be eliminated because of a timeline error.
At this point, only answer choices C and E remain. The verbs are not identical in the two options, but either one could conceivably make sense, so we must look for other differences in order to differentiate between the two. Looking through the answer choices, there are no pronouns to compare, but the first and last words are not the same. These connectors often cause answer choices to be eliminated because they make sense with the underlined portion but they do not fit nicely into the rest of the sentence (like merging onto the highway on a horse and buggy).
Answer choice C is already on our radar because of the wordy verb choice, but let’s examine how it fits back into the sentence at the end. The societies “were arising simultaneously…” is missing the word “with” in order to make grammatical sense. You arise simultaneously with something else. The original sentence had this word, but answer choice C omits the key words, and it’s difficult to see because the text is so verbose. This incorrect construction dooms answer choice C. Only answer E remains as the correct choice.
As with any Sentence Correction question, process of elimination is the name of the game. However, when the sentences get very long, very technical, or otherwise disengaging, you have to go through the text in a methodical manner. The best words to compare are the verbs, the pronouns and the connectors to and from the underlined portion. If you have a sound strategy, you’ll be able to execute the run on sentence correction.
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.
]]>This may seem somewhat paradoxical, but the quant section on the GMAT isn’t testing your math ability. The skills that allowed the quantitatively-inclined to ace their tests in high school and college not only have limited value on the GMAT, but actually undermine test-takers, prompting them to grind through calculations when the question is really about how to avoid those very calculations.
Take this * GMATPrep® question, for example.
Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?
I. At least one of the homes was sold for more than $165,000.
II. At least one of the homes was sold for more than $130,0000 and less than $150,000
III. At least one of the homes was sold for less than $130,000.
A. I only
B. II only
C. III only
D. I and II
E. I and III
Perhaps you were tempted to do it algebraically. Maybe you thought you had to evaluate every scenario independently. If that was the case, you’re in good company. Most of the students I’ve taught over the years have had the same instinctive response. But we need to keep reminding ourselves about the aforementioned axiom: the GMAT isn’t testing math ability. It’s testing fluid thinking ability under pressure. So let’s take a deep breath and think about this for a moment.
How can I make this easier? What if I could construct a very simple scenario that violates two of the three statements?
The simplest possible scenario I can think of involves a set where the first 14 terms are equal to 130,000 exactly. (Clearly, in this case, the middle term, or median will be 130,000.) Then the last member will have to be enormous in order to increase the average to 150,000. (If you were so inclined, you could do 14*130,000 + x = 15*150,000 and solve for x. x would be 430,000. But there’s no need to actually do this. It’s enough to see that x will be way more than 165,000.)
Well, this set {130, 130, 130, …430} proves that we don’t HAVE to have anything below 130,000. Kill Statement III. And it also proves that we don’t HAVE to have anything between 130,000 and 150,000. Kill II. We’re done. Only I has to be true, and there’s no need to test another scenario, because we’ve already logically disproved the other statements. The answer must be A, I only. All we needed was one simple scenario.
Now let’s look at a second GMATPrep® problem that, on the surface, appears to have absolutely nothing to do with the previous one.
Which of the following lists the number of points at which a circle can intersect a triangle?
1) 2 and 6 only
2) 2,4 and 6 only
3) 1,2,3 and 6 only
4) 1,2,3,4 and 6 only
5) 1,2,3,4,5 and 6
Again, the default response is to just start grinding through scenarios with the hope that, eventually, you’ll hit all of them. But that’s not a very efficient approach. Let’s slow down and think strategically. How can we save time? Well, look at the statements. Notice that there’s plenty of overlap, but only choice E has ‘5’ as a possibility. So if we can draw a triangle that intersects a circle at 5 points, I’ll know that’s the answer.
So, I’ll draw a circle:
Now I’ll draw 5 points on the circle, and try to draw a triangle through those points.
Looks like I can do it. I’m done. E is the answer.
(Interesting Parenthetical Note: if you were the question writer and were trying to concoct a question/answer that would that would be most difficult and time consuming for a test-taker, wouldn’t you have the correct answer contain the greatest number of possibilities? That’s another clue that E is where we want to start.)
The big takeaway here is that it’s good if we can keep reminding ourselves that the GMAT isn’t interested in our raw computational ability. What the GMAT is interested in is our ability to make good decisions under pressure. So when you see a tough question, slow down. Look at the answers. Then think of the simplest possible scenarios that will allow you to test those answers in the fewest number of steps.
* GMATPrep® questions courtesy of the Graduate Management Admissions Council.
Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!
By David Goldstein, a Veritas Prep GMAT instructor based in Boston.
]]>On questions where the entire goal of the question remains a mystery even as you try and come to a conclusion, the best strategy is to leverage all the information provided to you. As an example, if the question asks you about a specific property of an odd number, then try plugging in a few odd numbers to see what’s going on. You can then plug in a few even numbers to contrast the two; this often sheds some light on why only odd figures were selected in the premise. Exploiting seemingly inconsequential hints like these might be the difference between getting the right answer and wasting copious amounts of time on a single question, so look for hints in the set up.
Another important thing to remember is that you are just looking for a single answer choice. On the GMAT, there are no part marks for development, and a single incorrect calculation can sink an otherwise flawless algorithm. So you’re going for the correct answer more than a perfect understanding of what the question is testing. Understanding the question generally leads to a correct answer, but stumbling on the correct choice is worth exactly the same number of points on the GMAT (The Maxwell Smart approach). This also means that eliminating incorrect answer choices is valuable, as worst case you can take an educated guess that’s 50/50 instead of one out of five.
Let’s look at one of these WTF (Want To Finish) questions and see if we can figure out a solution:
If x and y are both prime, is x*y = 323?
(1) x is the first prime number after 18
(2) y is the last prime number before 180
(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 but neither statement is sufficient alone.
(D) Each statement alone is sufficient to answer the question.
(E) Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.
So the first thing that came to my mind is “Wow, that’s random”. The premise seems so arbitrary that it makes many approaches seem irrelevant. Even knowing that the two numbers are prime, we cannot quickly determine whether they must multiply to 323 without some more analysis and manipulation. Luckily, this is a Data Sufficiency question, so we have two additional statements that can help guide our analysis.
It’s important to note that in Data Sufficiency, we are trying to determine whether we can say with certainty that the two numbers multiply together to 323. This also means that if we can determine with certainty that the two numbers cannot multiply to 323, we have sufficient data. The uncertainty arises when we don’t know either way (i.e. maybe), so that provides a good framework for our analysis.
The first statement gives us a big hint, telling us that x is the first prime number after 18. This very quickly implies that x must be 19. We now have a hint as to why the number 323 was chosen (perhaps the author drove a Mazda in the ‘90s). If 323 is not a multiple of 19, then statement 1 will provide definitive evidence that x*y cannot possibly equal 323. Short of using a calculator, we can find multiples of 19 that are nearby and iterate manually until we find the correct answer. 19 x 20 would be easy to calculate as we can consider it as 19 x 2 x 10, or 38 x 10, or 380. From there, we can drop 19s until we get in the correct range.
380 – 19 is 361
361 – 19 is 342
342 – 19 is 323
You might be able to get there faster than by using this strategy, but after a few seconds of calculations, you can determine that 19 * 17 yields exactly 323. The question indicated that x and y would both be prime numbers, and 17 is indeed a prime number, so the possibility exists. However, it’s important to note that we know nothing (John Snow) about the value of y, other than it is a prime number. It could just as easily be 2, or 7, or 30203 (yes that’s a prime; I like palindromes). Since y could have any prime value, there’s insufficient evidence to determine that the product of x and y must be 323. Statement 1 is insufficient, and we can eliminate answer choices A and D.
Statement 2 indicates that y is the last prime number before 180, but it is important to remember that we must evaluate this statement alone. We now have no information about the value of x, other than it is a prime number. Statement 2 gives us a specific value of y, even if we’re not exactly sure what it is. We could do a little math and check to see if 179 (the number right before 180) is a prime, and in this case it is. The verification process is somewhat tedious, you have to check to see if it’s divisible by any prime number smaller than the square root of the number, so once you check 2, 3, 5, 7, 11 and 13, you’re confident than 179 is a prime number.
Knowing only that x is a prime number, we must now try and determine whether 179 and any prime could yield a product of 323, and the answer is very quickly no. The smallest prime number is 2, and 179 * 2 is already 358. You can also visually determine that 179 is more than half of 323, so there’s no need to even formally calculate the result. This statement on its own guarantees that x * y can never be 323, and thus is sufficient information to answer the question. The correct selection is answer choice B, as this statement alone is sufficient.
It is important to point out that these statements, taken together, give very clear numbers for both x and y. When this happens, you know that you can combine the statements and get only one value. That value may or may not be 323 (in this case it’s really, really not), but either way it provides sufficient information to definitively answer the question. However, it is almost always going to be the wrong answer, as it simply provides too much information. There’s no mystery or intrigue left, everything is laid out on the sheet in front of you. In business, as in life, if something seems too good to be true, it usually is.
Indeed, this question is essentially testing to see whether you’ll overpay for information on Data Sufficiency. However, at first blush, it just seems like an arbitrary collection of numbers with a question attached. When faced with similar head-scratchers, keep in mind that the statements (and/or answer choices) will provide hints. Trying to factor out 323 without any hints is a challenging endeavour, so look for hints and exploit them as much as possible. Hopefully, on test day, the only head scratching you’ll do is wondering which school you’ll go to with your outstanding score.
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 GMAT Enhanced Score Report is here.
This new add-on report, which costs $24.95 USD, will provide you with diagnostic feedback from your official GMAT exam, including such information as:
-Performance (percentile ranking) by question type, with question types including Data Sufficiency vs. Problem Solving; Arithmetic vs. Algebra/Geometry; Critical Reasoning vs. Sentence Correction vs. Reading Comprehension
-Time management by question type, broken down by the same categories above
-Time management by correct vs. incorrect answers for Integrated Reasoning
-Percent of Integrated Reasoning questions answered correctly
So those are the features, but the question remains…is this worth $25? And the answer is a little less concrete than you might like: it depends. Why?
*The report won’t give you question-by-question feedback, so you’ll never know if you got that crazy coordinate geometry problem at #17 right or wrong, and you won’t know which individual problems you spent way too much time on. You’ll get much more aggregate data, which may or may not help.
*If your performance was pretty similar to that of your practice tests – which ought to be the case for most examinees who have taken several practice tests – the report should likely match your expectations. If you’ve prepared well for the test, there shouldn’t be many surprises in that report.
*However, some users will see some VERY enlightening information. Say, for example, you were quite strong on Critical Reasoning and Reading Comprehension (~80th percentile each) but significantly less adept on Sentence Correction (
So who will benefit from the report? Those who have some outliers or anomalies in their performance. If you were 60th percentile on quant, and a combination of 55th, 62nd, 63rd, and 59th on DS, PS, Arith, Alg/Geo, you’re not going to learn very much from that report. But if one area is significantly higher or significantly lower than the others, you’ll learn something.
And so what’s the advice?
-If you’re going to retake the exam, the Enhanced Score Report is essentially a 10% increase on your next registration fee, and has the potential to be pretty enlightening. Especially if you’re likely to spend $25 over the next month on Starbucks or Amazon impulse purchases or anything else extraneous, it’s a good idea to put that $25 toward the score report. You might not learn anything, but the chance that you’ll learn something is substantial enough that you should leave no stone unturned.
-But if you have $25 left in your GMAT budget and the choice is between the Enhanced Score Report or a tool like the GMAT Question Pack or one of the Official Guide supplements, choose the extra practice. If you’ve prepared thoroughly there shouldn’t be too many surprises on that report, and whatever you’d learn you’d have to improve by practicing anyway.
So in sum, GMAT retakers should probably pony up the $25 because the more you know about your performance, the higher the likelihood that you can improve it. Almost all Veritas Prep instructors agree – we want to see those reports from our students! But don’t be surprised if the report only confirms what you suspected. The Enhanced Score Report is a tool to guide your hard work, not a substitute for the effort required to improve.
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
]]>As an example, think about a passage that deals with the Super Bowl. It’s very possible that the passage will discuss how good the Seahawks’ defense is, or how good Tom Brady is as a quarterback. The conclusion could then be something like how the Patriots will likely win (disclaimer: this was written before the Super Bowl). If a question was asked about what assumption is needed to reach the conclusion, the correct answer choice must be about Tom Brady or the Seahawks’ defense, given that’s what was discussed as evidence. If an answer choice discusses the catching ability of Rob Gronkowski or the Patriots’ (alleged) (systemic) pattern of cheating, then it is going outside the scope of the question and cannot be the correct selection.
It is important to note that strengthen and weaken questions may sometimes provide new information, so you should be on the lookout for things that weren’t written verbatim in the text. Nonetheless, for assumption questions, it’s easy to select an answer choice that provides new information but goes outside the scope of what was discussed. A choice that has no basis in the passage is usually a clear indicator of a trap answer.
Let’s look at an example to demonstrate scope in assumption questions:
It is a mistake to give post office employees individual discretion as to when to inspect or open suspicious packages. If individual employees are allowed to open “suspicious” packages without first following a strict protocol, it is only a matter of time before all packages will arrive having already been opened due to some postal employee’s idle curiosity.
The conclusion above is based on which of the following assumptions?
(A) Postal service managers are the only people with the authority to open suspicious packages.
(B) Suspicious packages are indistinguishable from all other kinds of packages.
(C) The efficiency of the postal service will be greatly reduced if more packages are inspected.
(D) There is currently no protocol in place for the inspection of suspicious packages.
(E) Postal employees desire to open packages out of curiosity.
This question is asking about which assumption is required for the conclusion, which warns that all parcels will eventually be opened by overzealous mail carriers. While it’s somewhat understandable to be concerned about the privacy of your mail, the author’s fears may be unfounded (I’m more concerned about the NSA). The evidence provided in the passage is about when packages are allowed to be opened and verified. The passage mentions that only suspicious packages are allowed to be opened, but there are protocols in place that dictate when this verification can occur.
For assumption questions, the best strategy is to employ the Assumption Negation Technique and negate each answer choice to see if the conclusion falls down without the negated assumption. This approach is similar to the strategy of knocking down beams in a home to see which one was load-bearing. (Not something I’d recommend). If the conclusion falls down without this assumption, then it was absolutely required. If it changes nothing, then it was purely decorative and can be ignored.
Beginning with answer choice A, let’s negate them and see if the author’s paranoia is still defensible. The negation will be underlined to differentiate the negated form from the original assumption:
(A) Postal service managers are not the only people with the authority to open suspicious packages.
If this were true, then there might be even more people who could open errant parcels. This makes the author’s argument more likely to be true, as seemingly random people could have authority to open packages. If nothing else, it certainly doesn’t lessen the chances of the author’s prediction coming to be, so this assumption is not required.
(B) Suspicious packages are not indistinguishable from all other kinds of packages.
This double negation is saying that suspicious packages are easy to distinguish from other kinds of packages. If this were true, the employees would be able to tell which packages were suspicious, but they would nonetheless have the authority to open any package. Therefore, the fact that they can ascertain in most instances what constitutes a “suspicious” package would not necessarily stop them opening other packages. The passage is arguing that postal workers would open everything if given unilateral power, whether the package was deemed suspicious or not. This answer choice is probably the closest incorrect choice, but the scope alerts us to the superfluous nature of this assumption.
(C) The efficiency of the postal service will not be greatly reduced if more packages are inspected.
This answer choice is discussing how the efficiency of the postal office (which many people think is an oxymoron) would not be affected by increasing the number of inspected packages. While this may quell the fears of some people who assume that more inspections would slow down the service, the author’s argument is primarily concerned with the privacy aspect of the inspections. This answer choice is thus out of scope, as the efficiency of the post office was (somehow) never in question.
(D) There is currently no a protocol in place for the inspection of suspicious packages.
This answer choice, negated, indicates that there is already a protocol in place for suspicious packages. If this were true, it would actually strengthen the argument, as there would be no reason to give postal workers additional power to open packages. The system would indeed be working fine the way it is, and this argument only demonstrates the author’s point, it does not weaken it.
(E) Postal employees do not desire to open packages out of curiosity.
This answer choice, by process of elimination, must be the correct choice. However, let’s confirm that it makes sense. If postal employees did not want to open packages out of (idle) curiosity, then the author’s entire argument would fall apart. Indeed, the entire argument relies on the fact that the postal employees will open every package they possibly can. If we could ensure that this was not the case (say with a hypnotic suggestion or some Borg nanoprobes), then the whole argument would become moot. Answer choice E is an assumption required by the conclusion, because without it, the argument falls apart.
On questions such as these, it’s entirely possible to get reeled in by an enticing answer choice. Remember to use the Assumption Negation Technique to verify whether an assumption is actually necessary or whether it just sounds important. The incorrect answer choices provided are designed to tempt you, so keep an eye on the evidence provided in the passage as well. If the answer sounds good, but isn’t based on the evidence provided, then much like the guy at my gym with halitosis, it is out of scope.
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.
]]>How is it that you can confidentially answer question after question while obviously missing quite a few questions that felt “easy?”
One culprit is the subtlety of the official GMAT questions overall. No other questions do as good a job of luring you into confidently choosing the wrong answer. This can happen on problem solving, but today I would like to focus on Data Sufficiency.
I sometimes refer to Data Sufficiency as “the Silent Killer” because the very structure of the Data Sufficiency question invites you to choose the wrong answer. This is because you do not know that you have forgotten to consider something. There are no values in the answer choices to help you see what you might have overlooked. That is why the person choosing the incorrect answer is often more confident than is the one who got the question right.
As you can see it is often difficult to gauge how you are doing on Data Sufficiency. And because the Quantitative section adapts as a whole, missing these data sufficiency questions results in the computer selecting lower-level questions in problem solving. So the problem solving questions may have seemed easier because they actually were at a lower level.
This is a pattern that I have seen repeated many times on practice exams. Students miss mid-level data sufficiency questions in the first part of the exam. This results in lower level questions being offered, and the student keeps missing just enough problems (of both Data Sufficiency and Problem Solving) to keep the difficulty level from increasing.
The result? A quant section that felt comfortable because most of the questions were below the level that would really challenge the student. This may be what happened to you.
How to avoid this fate:
With Data Sufficiency questions there are no answer choices to provide a check on your assumptions or calculations. You must be your own editor and look for mistakes before you confirm your answer. Fortunately, there are several things you can do:
Think with your pen. Do not presume that you will remember what the question is asking, the facts you are given, or the hidden facts that are implied by the question stem. Note these things on your scratch paper so that you do not forget them. It may seem unnecessary to write “x is integer” or “must be positive” but just think of how dangerous it would be to forget this information!
Do your work early. Rewording the question is a great way to make data sufficiency more fool-proof. For example, it is much easier to comprehend the question “Is x a multiple of 4” than it is to wrestle with the questions “Is x/2 a multiple of 2?” Think about what the question is really asking and re-word it when you can.
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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.
As an example, remember open-book tests. These tests always seemed easier when they were discussed in theory than when they were attempted in practice. An open book test must necessarily test you on more obscure and convoluted material, otherwise the test becomes too easy and everyone gets 100. Closed-book tests, by contrast, can concentrate on the core material and gauge how much preparation each student has put in. Adding more tools only serves to make the test more difficult in order to overcome these enhancements.
With a calculator, asking you to calculate the square root of an 8 digit number or the 9^{th} power of an integer is trivial if you only have to plug in some numbers. However, if you need to actually reason out a strategic approach in your head, you have accomplished more than a thousand brute force calculations would. On the GMAT, the mathematics behind a question will always be doable without a calculator, but the strategy chosen and the way you set up the equations will generally be the difference between the correct answer in two minutes and a guess in four.
Let’s look at a question where the math isn’t too difficult, but can get tedious:
Alice, Benjamin and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8 and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
(A) 3 / 140
(B) 1 / 28
(C) 3 / 56
(D) 3 / 35
(E) 7 / 40
This is a probability question, and therefore we must calculate the chances of any one event occurring. However, the question is asking about several possibilities, specifically any occurrence where two players win and the third loses (think of any romantic comedy). This means that we have to calculate several outcomes and manually add these probabilities. This is entirely feasible, but it can be somewhat tedious. Let’s look at the best way to avoid getting bogged down in the math:
Firstly, the three players’ are suitably abbreviated as A, B and C (convenient, GMAT, convenient). We therefore want to find the probability that A and B occur, but that C does not occur (denoted as A, B, ⌐C). This represents one of our desired outcomes. However, this is not the only possibility, as any situation where two occur and the other doesn’t is acceptable as well. Thus we can have A and C but not B (A, ⌐B, C), or B and C but not A (⌐A, B, C). The sum of these three outcomes is the desired fraction, so only some math remains.
Let’s do them in order. For (A, B, ⌐C), we take the probability of A, multiplied by the probability of B, and then multiplied by the probability of 1-C. If the chances of C are 2 / 7, then the probability of them not occurring must be the compliment of this, which is 5 / 7. The calculation is thus:
1 / 5 * 3 / 8 * 5 / 7.
In a multiplication, we only care about multiplying the numerators together, and then multiplying the denominators together. There is no need to put these elements on common denominators. The math gives us:
(1* 3 * 5) / (5 * 8 * 7). This is 15 / 280.
There is a strong temptation to cancel out the 5 on the numerator and on the denominator to make the calculation easier, but you should avoid such temptation on questions such as these. Why? (I’m glad you asked). If you simplified this equation, you would get the equivalent fraction of 3 / 56, which is easier to calculate, but since we still have to execute two more multiplications, we will end up adding fractions that have different denominators. This is not a pleasant experience without a calculator, and likely will cause us to revert to our common denominator for all three fractions, which is 5 * 8 * 7 or 280. Additionally, now that we’ve calculated it once, we don’t need to worry about the denominator for the following fractions, it will always be the same. Let’s continue and hopefully this strategy will become apparent.
The next fraction is (A, ⌐B, C), which is equivalent to
1 / 5 * 5 / 8 * 2 / 7. Note that ⌐B is (1 – 3/8)
Executing this calculation yields a result of 10 / 280.
Finally, we need (⌐A, B, C), which is equivalent to
4 / 5 * 3 / 8 * 2 / 7. Note that ⌐A is (1 – 1/5)
Executing this last fraction gives us 24 / 280.
Once we have these three fractions, we must add them together in order to get the probability of any one of them occurring (“or” probability, as opposed to “and” probability”). This is simple because they’re all on the same denominator, so we get 15 / 280 + 10 / 280 + 24 / 280 which is 49 / 280.
Now that we have this number, we can try to simplify it. 49 is a perfect square that is only divisible by 1, 7 and 49, whereas 280 has many factors, but one of them fairly clearly is 7. We can thus divide both terms by 7, and get 7 / 40. Since the numerator is a prime number, there is no additional simplification possible. 7 / 40 is answer choice E, and it is the correct pick on this question.
Had we simplified each probability as much as possible, we would have ended up with 3 / 56, 2 / 56 and 3 / 35. While the addition would not be impossible, it would become much more difficult. In fact, to correctly add these numbers together, you’d have to put them on their least common multiple, which would be 280 again. There is usually no point in simplifying fractions in questions like this because they must usually be recombined at the end. Save time and don’t convert once only to convert back.
The math on this question is not difficult, but having to add together multiple fractions and simplifying expressions can be quite time-consuming. With a calculator, you could simply add the decimals together, regardless of their fractional equivalents. However, the GMAT doesn’t allow you that shortcut on test day (unless you approximate in your head), so you must find a better tactic. The difference between solving all the questions and running out of time on the math section is often the approach you take on each question. Keep up a consistent strategy and you’ll solve a large fraction of the questions you face on test day.
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.
]]>Firstly, if you’ve never heard the song, please feel free to listen to it now. The chorus is discussing how Ariana would have “one less problem” without the person she’s currently serenading (surprisingly this isn’t a Taylor Swift song). The issue with the lyric is that problems are countable, and as such she should actually be singing “one fewer problem without you”. Perhaps the extra syllable messed up the harmony, or perhaps the songwriter hadn’t brushed up on their grammar prior to writing the song, but this is the type of issue students often struggle with because they don’t understand the underlying rule.
When it comes to counting things, there are two broad categories: items that are countable, and items that are not countable. The former comprises most tangible things we can imagine: computers, cars, cats, cookies, cans of Coke and countless conceivable commodities (This sentence brought to you by the letter C). The latter comprises things that are uncountable, such as water, sand or hair. You can count grains of sand or strands of hair, but you cannot count actual sand or hair, so these words get treated a little differently.
The rule is that for any noun that is countable, you must use “fewer” if you are going to decrease it. For any noun that is not countable, you must use “less” to decrease it. As an example, I want less water in my cup; I do not want fewer water in my cup. That example makes sense to most people. However, the converse is just as true: I want fewer bottles of water, not less bottles of water. If the item in question is scarce, similar words will be used. You can say that there is little water, but you wouldn’t say that there is few water left. Note how these words have the same etymology as “less” and “fewer”, respectively.
If the sentence calls for an increase, more is acceptable for both countable and uncountable elements. As an example, you can say that you want more water in your cup, or you can say that you want more bottles of water. Other synonyms exist as well, of course, but the delineation is much cleaner for decreases than for increases, so that structure appears more often on the GMAT. If the item in question is in abundance, similar words will also be used. You can say that there is much water, but you can’t say that there is many water. Much and many follow these same countable/uncountable rules.
The difference between items that are countable or uncountable is not unique to the GMAT, these rules apply to everyday language, they are simply enforced more rigorously on this test. Failure to choose the proper word in a Sentence Correction problem will result in an incorrect answer choice. As such, it behooves us to be aware of the grammatical difference between countable and uncountable elements, as it regularly comes up on the GMAT.
Let’s look at an example to illustrate the point:
The controversial restructuring plan for the county school district, if approved by the governor, would result in 20% fewer teachers and 10% less classroom contact-time throughout schools in the county.
A) in 20% fewer teachers and 10% less
B) in 20% fewer teachers and 10% fewer
C) in 20% less teachers and 10% less
D) with 20% fewer teachers and 10% fewer
E) with 20% less teachers and 10% less
Looking at the answer choices, it becomes fairly clear that the correct answer will hinge primarily on the difference between “fewer” and “less”. If we recall the rules for countable vs. uncountable, anything that we can count must use the adjective “fewer”, while anything that is not countable must use the adjective “less”.
For this example, the first reduction is in the number of teachers. Teachers are human beings (often handsome ones!), and are therefore countable. You can want to spend less time with a specific teacher, but you cannot (correctly) say that you want the school to have less teachers. The request must be for fewer teachers. This already eliminates answer choices C and E because they use the incorrect term.
The second reduction is about classroom time. Time is a wondrous and magical thing (or so young people tell me), but it is not countable. Yes, you can break up time into countable units, such as seconds or minutes, just as you can break up sand into grams or ounces, but holistically time is intangible and therefore uncountable. The plan calls for less time in the classroom, not fewer time. This eliminates answer choices B and D because they use the incorrect term. Only answer A remains and it is indeed the correct answer.
As mentioned earlier, the rules around countable and uncountable nouns are fairly precise, but you are unlikely to be corrected in everyday conversation if you misuse a term. Since the GMAT is testing logic, precision and general attention to detail, it is a perfect type of question to try and trap hurried students who don’t always notice the difference. In daily conversation (and on the radio), you can often get away with imprecision in language. However, if you understand the nuances between countable and uncountable nouns, to paraphrase Ariana Grande, you’ll have one fewer problem on the GMAT.
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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