Memorize what? I’m not going to tell you yet. Try this problem from the GMATPrep® free practice tests first and see whether you can spot the most efficient solution.
All right, have you got an answer? How satisfied are you with your solution? If you did get an answer but you don’t feel as though you found an elegant solution, take some time to review the problem yourself before you keep reading.
Step 1: Glance Read Jot
Take a quick glance; what have you got? PS. A given equation, xy = 1. A seriously ugly-looking equation. Some fairly “nice” numbers in the answers. Hmm, maybe you should work backwards from the answers?
Jot the given info on the scrap paper.
Step 2: Reflect Organize
Oh, wait. Working backwards isn’t going to work—the answers don’t stand for just a simple variable.
Okay, what’s plan B? Does anything else jump out from the question stem?
Hey, those ugly exponents…there is one way in which they’re kind of nice. They’re both one of the three common special products. In general, when you see a special product, try rewriting the problem usually the other form of the special product.
Step 3: Work
Here’s the original expression again:
Interesting. I like that for two reasons. First of all, a couple of those terms incorporate xy and the question stem told me that xy = 1, so maybe I’m heading in the right direction. Here’s what I’ve got now:
And that takes me to the second reason I like this: the two sets of exponents look awfully similar now, and they gave me a fraction to start. In general, we’re supposed to try to simplify fractions, and we do that by dividing stuff out.
How else can I write this to try to divide the similar stuff out? Wait, I’ve got it:
They’re almost identical! Both of the terms cancel out, as do the terms, leaving me with:
I like that a lot better than the crazy thing they started me with. Okay, how do I deal with this last step?
First, be really careful. Fractions + negative exponents = messy. In order to get rid of the negative exponent, take the reciprocal of the base:
Next, dividing by 1/2 is the same as multiplying by 2:
That multiplies to 16, so the correct answer is (D).
Key Takeaways: Special Products
(1) Your math skills have to be solid. If you don’t know how to manipulate exponents or how to simplify fractions, you’re going to get this problem wrong. If you struggle to remember any of the rules, start building and drilling flash cards. If you know the rules but make careless mistakes as you work, start writing down every step and pausing to think about where you’re going before you go there. Don’t just run through everything without thinking!
(2) You need to memorize the special products and you also need to know when and how to use them. The test writers LOVE to use special products to create a seemingly impossible question with a very elegant solution. Whenever you spot any form of a special product, write the problem down using both the original form and the other form. If you’re not sure which one will lead to the answer, try the other form first, the one they didn’t give you; this is more likely to lead to the correct answer (though not always).
(3) You may not see your way to the end after just the first step. That’s okay. Look for clues that indicate that you may be on the right track, such as xy being part of the other form. If you take a few steps and come up with something totally crazy or ridiculously hard, go back to the beginning and try the other path. Often, though, you’ll find the problem simplifying itself as you get several steps in.
* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.
Welcome to the final installment in a series of three articles about meaning and sentence structure in sentence correction. Our first one tested meaning and also covered issues related to having to break the sentence into chunks. In the second, we talked about how to use that chunk idea to strip the sentence down to the core structure vs. the modifiers.
Today, I’ve got a third GMATPrep® problem for you following some of these same themes (I’m not going to tell you which ones till after you’ve tried the problem!).
* “Today’s technology allows manufacturers to make small cars more fuel-efficient now than at any time in their production history.
“(A) small cars more fuel-efficient now than at any time in their
“(B) small cars that are more fuel-efficient than they were at any time in their
“(C) small cars that are more fuel-efficient than those at any other time in
“(D) more fuel-efficient small cars than those at any other time in their
“(E) more fuel-efficient small cars now than at any time in”
The first glance doesn’t indicate a lot this time. The answers change from small cars to more (fuel-efficient small cars), which isn’t much of a clue. Go ahead and read the original sentence.
What did you think? When I first read it, I shrugged and thought, “That sounds okay.” If you can’t come up with something to tackle from the first glance or the first read-through, then compare answers (A) and (B), looking for differences.
Hmm. I see—do we need to say that are more fuel-efficient? Maybe. Answer (C) uses that same structure. Oh, hey, answer (C) tosses in the word other! I know what they’re doing!
If you’ve seen the word other tested within a comparison before, you may know, too. If not, get ready to make a note. Take a look at these two sentences:
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Last time, we tried a problem that tested meaning; we also discussed how to compare entire chunks of the answer choices. Today, we’re going to combine those two things into a new skill.
Try this GMATPrep® problem from the free exams and then we’ll talk about it.
* “The striking differences between the semantic organization of Native American languages and that of European languages, in both grammar and vocabulary, have led scholars to think about the degree to which differences in language may be correlated with nonlinguistic differences.
“(A) that of European languages, in both grammar and vocabulary, have
“(B) that of European languages, including grammar and vocabulary, has
“(C) those of European languages, which include grammar and vocabulary, have
“(D) those of European languages, in grammar as well as vocabulary, has
“(E) those of European languages, both in grammar and vocabulary, has”
At first glance, the underline isn’t super long on this one, Glance down the first word of each answer. What does a split between that and those signify?
Both are pronouns, so they’re referring to something else in the sentence. In addition, one is singular and one is plural, so it will be important to find the antecedent (the word to which the pronoun refers).
Next, read the original sentence. What do you think? It isn’t super long but it still manages to pack in some complexity. Learn how to strip it down and you’ll be prepared for even more complex sentence structures.
My first thought was: okay, now I see why they offered that vs. those. Should the pronoun refer to the plural differences or to the singular organization?
It could be easy to get turned around here, so strip down the sentence structure:
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As dedicated readers of this blog may have guessed, this is a follow up to my earlier post When is it Time to Guess on Quant? Timing troubles are not, however, exclusive to the Quant section, so in this piece I’ll talk about some common scenarios that bedevil students on the Verbal section.
As with Quant, not all guesses are created equal. The earlier you decide to guess, the more likely that you will make a random guess. If, on the other hand, you’re far enough into the question that you’ve eliminated 2-3 answer choices, then you’ll be making an educated guess.
One immediate difference between guessing on Quant and Verbal is that guessing strategy is essentially identical for both Problem Solving and Data Sufficiency questions. Each of the Verbal question types, on the other hand, has less in common. That being said, there are a lot of parallels in guessing strategy among the three types.
No matter the question, there are really three distinct stages at which it becomes a better idea to guess than to keep going. I’ll briefly describe each stage, then show how it connects to each of the Verbal question types.
Stage 1: No Clear Starting Point
As a general rule, if you haven’t really made progress on a question after 30 seconds or so, it’s usually a good idea to just make a random guess and save your energy for a question you’re more comfortable with.
Reading Comprehension Stage 1: I don’t know where in the passage to look.
The great thing about Reading Comprehension (or at least its saving grace) is that the correct answer has to have support in the passage. With the vast majority of RC questions, as long as you can find and reread the relevant portion of the passage, you can find an answer choice that will match what you read. In fact, you should be able to answer to come up with your own answer to most RC questions before you even look at the answer choices.
Many questions provide good clues as to where in the passage to look for the answer (seriously – a surprising amount of questions are very helpful in that regard). Things get much tougher when they don’t. So here’s your first big clue that it may be time to guess. If you’ve read the question, and you’ve skimmed through the passage looking for an answer, and you still don’t feel like you found what the question was asking about, it’s time to guess.
At this point, you could guess randomly, but I would recommend taking one quick pass through the answer choices. If any choice contradicts your understanding of the passage, eliminate it. After you’ve each answer once, pick from the remaining.
Sentence Correction Stage 1: I don’t understand the sentence and the underline is long.
On the Verbal section, you have to answer 41 questions in 75 minutes, which is less than 2 minutes per question. Critical Reasoning and Reading Comprehension are naturally time-consuming, so that time is going to have be saved largely on Sentence Correction. Remember that you only have an average of 1 minute and 20 seconds to answer these things.
If you’re struggling to even understand what the sentence is saying, then it will almost certainly take too long to properly analyze the answer choices, especially if the underline is long. No need to fight through the pain. Just take a quick scan through the answer choices and pick one that doesn’t sound immediately wrong.
Critical Reasoning Stage 1: I don’t understand what the argument is saying.
To my mind, good process on Critical Reasoning questions means being in control the whole way through the process. The worst situation to be in is one in which you’re hoping that the answer choices will help you make sense of the argument. Four out of the five answer choices are actively trying to trick you, and the GMAT has gotten pretty good at tricking people over the years. By the time you get to the answer choices, you need to understand the argument well enough to effectively evaluate each choice.
Consequently, if you’ve read the argument two or three times, and still can’t articulate to yourself the link between the premises and the conclusion, you shouldn’t waste time with the answer choices.
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The GMAT quant section has many faces – there are a number of content areas, and it is best to try to master as many of them as you can before test day. It is important, however, that you not compartmentalize too much. In many of the harder questions in fact, two or more topics often show up together. You can easily find quadratics in a consecutive integer question, coordinate geometry in a probability question, number properties in a function question, for example. One common intersection of two topics that I find surprises many students is that of geometry and algebra. Many people expect a geometry question to be about marking up diagrams with values or tick marks to show equality and/or applying properties and formulas to calculate or solve. While these are no doubt important skill sets in geometry, don’t forget to pull out one of the most important skills from your GMAT tool bag – the almighty variable! x’s and y’s have a welcomed home in many a geometry question, though you might find that you are the one who has to take the initiative to put them there!
Take a look at this data sufficiency question from GMATPrep®
In the figure shown, the measure of PRS is how many degrees greater than the measure of PQR?
(1) The measure of QPR is 30 degrees.
(2) The sum of the measures of PQR and PRQ is 150 degrees.
How did you do? Don’t feel bad if you’re a little lost on this one. This is a difficult question, though you’ll see that with the right moves it is quite doable. At the end of this discussion, you’ll even see how you could put up a good guess on this one.
As is so often the case in a data sufficiency question, the right moves here start with the stem – in rephrasing the question. Unfortunately the stem doesn’t appear to provide us with a lot of given information. As indicated in the picture, you have a 90 degree angle at PQR and that seems like all that you are given, but it’s not! There are some other inherent RELATIONSHIPS, ones that are implied by the picture. For example PRS and PRQ sum to 180 degrees. The problem, however, is how do you CAPTURE THOSE RELATIONSHIPS? The answer is simple – you capture those relationships the way you always capture relationships in math when the relationship is between two unknown quantities – you use variables!
But where should you put the variables and how many variables should you use? This last question is one that you’ll likely find yourself pondering a number of times on the GMAT. Some believe the answer to be a matter of taste. My thoughts are always use as few variables as possible. If you can capture all of the relationships that you want to capture with one variable, great. If you need two variables, so be it. The use of three or more variables would be rather uncommon in a geometry question, though you could easily see that in a word problem. Keep one thing in mind when assigning variables: the more variables you use, usually the more equations you will need to write in order to solve.
As for the first question above about where to place the variables, you can take a closer look in this question at what they are asking and use that as a guide. They ask for the (degree) difference between PRS and PQR. Since PRS is in the question, start by labeling PRS as x. Since PRS and PRQ sum to 180 degrees, you can also label PRQ as (180 – x) and RPS as (180 – x – 90) or (90 – x).
Can you continue to label the other angles in triangle PRQ in terms of x or is it now time to place a second variable, y? Since you still have two other unknown quantities in that triangle, it’s in fact time for that y. The logical place of where to put it is on PQR since that is also part of the actual question. The temptation is to stop there – DON’T! Continue to label the final angle of the triangle, QPR, using your newfound companions, x and y. QPR can be labeled as [180 – y – (180 – x)] or (x – y). Now all of the angles in the triangle are labeled and you are poised and ready to craft an algebraic equation/expression to capture any other relationships that might come your way.
Before you rush off to the statements, however, there is one last step. Formulate what the question is really asking in terms of x and y. The question rephrases to “What is the value of x – y?”
Now you can finally head to the statements. Oh the joy of a fully dissected data sufficiency stem – 90% of the work has already been done!
Statement (1) tells you that the measure of QPR is 30 degrees. Using your x – y expression from the newly labeled diagram as the value of QPR, you can jot down the equation x – y = 30. Mission accomplished! The statement is sufficient to answer the question “what is the value of x – y?”
Statement (2) indirectly provides the same information as statement (1). If the two other angles of triangle PQR sum to 150 degrees, then QPR is 30 degrees, so the statement is sufficient as well. If you somehow missed this inference and instead directly pulled from the diagram y + (180 – x) and set that equal to 150, you’d come to the same conclusion. Either way the algebra saves the day!
The answer to the question is D, EACH statement ALONE is sufficient to answer the question asked.
NOTE here that from a strategic guessing point of view, noticing that statements (1) and (2) essentially provide the same information allows you to eliminate answer choices A, B and C: A and B because how could it be one and not the other if they are the same, and C because there is nothing gained by combining them if they provide exactly the same information.
The takeaways from this question are as follows:
(1) When a geometry question has you staring at the diagram, uncertain of how to proceed in marking things up or capturing relationships that you know exist – use variables! Those variables will help you move through the relationships just as actual values would.
(2) In data sufficiency geometry questions, when possible represent the question in algebraic form so the target becomes clear and so that the rules of algebra are there to help you assess sufficiency.
(3) Once you have assigned a variable, continue to label as much of the diagram in terms of that variable. If you need a second variable to fully label the diagram, use it. If you can get away with just one variable and still accomplish the mission, do so.
Most GMAT test-takers know that they need to develop clear strategies when it comes to different types of word problems, and most of those involve either muscling your way through the problem with some kind of practical approach (picking numbers, visualizing, back-solving, logical reasoning) or writing out algebraic equations and solving. There are of course pluses and minuses to all of the approaches and those need to be weighed by each person on an individual basis. What few realize, however, is that geometry questions can also demonstrate that level of complexity and thus can often also be solved with the tools of algebra. When actual values are few and far between, don’t hesitate to pull out an “x” (and possibly also a “y”) and see what kind of equations/expressions you can cook up.
For more practice in “algebrating” a geometry question, please see OG 13th DS 79 and Quant Supplement 2nd editions PS 157, 162 and DS 60, 114 and 123.
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