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These competitive scholarships are offered to individuals who (1) currently work full-time in an organization that promotes positive social change, (2) plan to use their MBA to work in a public, not-for-profit, or other venture with a social-change oriented mission, and (3) demonstrate clear financial need. The Social Venture Scholars will all enroll in a special online preparation course taught by two of Manhattan Prep’s expert instructors within one year of winning the scholarship.
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Yesterday, the whole wide internet was shocked by the Jeopardy dominance of “This dude Michael”, but here at Manhattan Prep we weren’t surprised at all. We already knew that dude was smart and we knew that dude had the mathematical wherewithal to bet $7,000 without batting an eyelash.
Here at MPrep we know that dude as Michael Bilow (one of those people who command such respect that he must always be talked about using his last name lest anyone in earshot mistakenly attribute an anecdote or joke to some less deserving Michael). On Jeopardy, he lived up to his legend taking home the fourth highest single-day winnings in Jeopardy history: $57,198.
Michael Bilow joined the Manhattan Prep family in 2011 using his perfect GRE score and spectacular teaching chops to secure a role as an LA-based GRE instructor. A few years later we realized we needed more Bilow in our business so we asked him to join the Marketing Department. He took a position as our Business Data Analyst, while continuing to teach GRE classes and pursue his PhD. After seeing him flawlessly juggle those responsibilities, we never had any doubt that he would take the Jeopardy world by fire.
By now the whole country knows of Bilow’s intellectual prowess, but we know so much more. Michael is a dedicated practitioner of improv, a delightful presence in Google Hangout meetings, and a stylish dresser. We can’t wait for his next trip to the New York City headquarters so he can buy us a drink with his winnings after he takes a quick a nap in a tutoring pod.
Congrats, Michael Bilow! Keep it up!
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If you have two equations, you can solve for two variables.
This rule is a cornerstone of algebra. It’s how we solve for values when we’re given a relationship between two unknowns:
If I can buy 2 kumquats and 3 rutabagas for $16, and 3 kumquats and 1 rutabaga for $9, how much does 1 kumquat cost?
We set up two equations:
2k + 4r = 16
3k + r = 9
Then we can use either substitution or elimination to solve. (Try it out yourself; answer* below).
On the GMAT, you’ll be using the “2 equations à 2 variables” rule to solve for a lot of word problems like the one above, especially in Problem Solving. Be careful, though! On the GMAT this rule doesn’t always apply, especially in Data Sufficiency. Here are some sneaky exceptions to the rule…
2 Equations aren’t always 2 equations
Welcome to our third and final installment dedicated to those pesky maximize / minimize quant problems. If you haven’t yet reviewed the earlier installments, start with part 1 and work your way back up to this post.
I’d originally intended to do just a two-part series, but I found another GMATPrep® problem (from the free tests) covering this topic, so here you go:
“A set of 15 different integers has a median of 25 and a range of 25. What is the greatest possible integer that could be in this set?
Here’s the general process for answering quant questions—a process designed to make sure that you understand what’s going on and come up with the best plan before you dive in and solve:
Fifteen integers…that’s a little annoying because I don’t literally want to draw 15 blanks for 15 numbers. How can I shortcut this while still making sure that I’m not missing anything or causing myself to make a careless mistake?
Hmm. I could just work backwards: start from the answers and see what works. In this case, I’d want to start with answer (E), 50, since the problem asks for the greatest possible integer.
We’re going to kill two birds with one stone in this week’s article.
Inference questions pop up on both Critical Reasoning (CR) and Reading Comprehension (RC), so you definitely want to master these. Good news: the kind of thinking the test-writers want is the same for both question types. Learn how to do Inference questions on one type and you’ll know what you need to do for the other!
That’s actually only one bird. Here’s the second: both CR and RC can give you science-based text, and that science-y text can get pretty confusing. How can you avoid getting sucked into the technical detail, yet still be able to answer the question asked? Read on.
Try this GMATPrep® CR problem out (it’s from the free practice tests) and then we’ll talk about it. Give yourself about 2 minutes (though it’s okay to stretch to 2.5 minutes on a CR as long as you are making progress.)
“Increases in the level of high-density lipoprotein (HDL) in the human bloodstream lower bloodstream cholesterol levels by increasing the body’s capacity to rid itself of excess cholesterol. Levels of HDL in the bloodstream of some individuals are significantly increased by a program of regular exercise and weight reduction.
“Which of the following can be correctly inferred from the statements above?
“(A) Individuals who are underweight do not run any risk of developing high levels of cholesterol in the bloodstream.
“(B) Individuals who do not exercise regularly have a high risk of developing high levels of cholesterol in the bloodstream late in life.
“(C) Exercise and weight reduction are the most effective methods of lowering bloodstream cholesterol levels in humans.
“(D) A program of regular exercise and weight reduction lowers cholesterol levels in the bloodstream of some individuals.
“(E) Only regular exercise is necessary to decrease cholesterol levels in the bloodstream of individuals of average weight.”
Got an answer? (If not, pick one anyway. Pretend it’s the real test and just make a guess.) Before we dive into the solution, let’s talk a little bit about what Inference questions are asking us to do.
Inference questions are sometimes also called Draw a Conclusion questions. I don’t like that title, though, because it can be misleading. Think about a typical CR argument: they usually include a conclusion that is…well…not a solid conclusion. There are holes in the argument, and then they ask you to Strengthen it or Weaken it or something like that.
Last time, we discussed two GMATPrep® problems that simultaneously tested statistics and the concept of maximizing or minimizing a value. The GMAT could ask you to maximize or minimize just about anything, so the latter skill crosses many topics. Learn how to handle the nuances on these statistics problems and you’ll learn how to handle any max/min problem they might throw at you.
Feel comfortable with the two problems from the first part of this article? Then let’s kick it up a notch! The problem below was written by us (Manhattan Prep) and it’s complicated—possibly harder than anything you’ll see on the real GMAT. This problem, then, is for those who are looking for a really high quant score—or who subscribe to the philosophy that mastery includes trying stuff that’s harder than what you might see on the real test, so that you’re ready for anything.
Ready? Here you go:
“Both the average (arithmetic mean) and the median of a set of 7 numbers equal 20. If the smallest number in the set is 5 less than half the largest number, what is the largest possible number in the set?
Out of the letters A through E, which one is your favorite?
You may be thinking, “Huh? What a weird question. I don’t have a favorite.”
I don’t have one in the real world either, but I do for the GMAT, and you should, too. When you get stuck, you’re going to need to be able to let go, guess, and move on. If you haven’t been able to narrow down the answers at all, then you’ll have to make a random guess—in which case, you want to have your favorite letter ready to go.
If you have to think about what your favorite letter is, then you don’t have one yet. Pick it right now.
I’m serious. I’m not going to continue until you pick your favorite letter. Got it?
From now on, when you realize that you’re lost and you need to let go, pick your favorite letter immediately and move on. Don’t even think about it.
Manhattan Prep is holding a two one-day auditions for new GMAT, GRE, and LSAT instructors in Dallas and Fort Worth! Come join us February 7th in Dallas or February 8th in Fort Worth at 10:00 AM and transform your passion for teaching into a lucrative and fulfilling part-time or full-time career.
Manhattan Prep offers instructors flexible hours and great pay ($100/hour for all teaching and $116/hour on all tutoring). In addition to teaching classes, instructors can work on other projects such as curriculum development.
Our regular instructor audition process, which includes a series of video, online, and in-person mock lessons, usually takes weeks, even months, to complete. However, we are offering one-day events on February 7th and on 8th for teachers interested in working with us. All candidates who attend will receive a decision that day.
The events will take place in Dallas and Fort Worth at the locations listed below. It is open to candidates who live in the area, who have teaching experience, and who are GMAT, LSAT, or GRE experts.
The audition will include several rounds of lessons, as well as other activities. Each round will be pass/ fail. The day will begin at 10 AM and may last as late as 5:30 PM for those who make it to the final round. Candidates will need to prepare lessons for some rounds; we will send a more detailed instruction packet to those who sign up for the event.
Dallas, TX (Saturday, February 7, 2015)
Meridian Business Center
3010 LBJ Freeway, Suite 1200
Dallas, TX 75234
Fort Worth, TX (Sunday, February 8, 2015)
Courtyard Fort Worth at University
3150 Riverfront Drive
Fort Worth, TX 76107
To register, please email Rina at email@example.com. Make sure to include in your full name, an attachment of your resume detailing your teaching experience, and an official GRE, GMAT, or LSAT score report. We look forward to meeting you in February!
Recently, I was discussing sentence structure with one of my classes and we practiced a crucial but difficult GMAT skill: how to strip an SC sentence to its core components. Multiple OG problems can be solved just by eliminating faulty sentence cores—and the real GMAT is testing this skill today more than we see in the published materials.
So I’m going to write a series of articles on just this topic; welcome to part 1 (and props to my Wednesday evening GMAT Fall AA class for inspiring this series!).
Try out this GMATPrep® problem from the free exams. (Note: in the solution, I’m going to discuss aspects of our SC Process; if you haven’t learned it already, go read about it right now, then come back and try this problem.)
* “With surface temperatures estimated at minus 230 degrees Fahrenheit, Jupiter’s moon Europa has long been considered far too cold to support life, and with 60 square miles of water thought to be frozen from top to bottom.
“(A) Europa has long been considered far too cold to support life, and with
“(B) Europa has long been considered far too cold to support life, its
“(C) Europa has long been considered as far too cold to support life and has
“(D) Europa, long considered as far too cold to support life, and its
“(E) Europa, long considered to be far too cold to support life, and to have”
The First Glance does help on this one, but only if you have studied sentence structure explicitly. Before I did so, I used to think: “Oh, they started with Europa because they added a comma in some answers, but that doesn’t really tell me anything.”
But I’ve learned better! What is that comma replacing? Check it out: the first three answers all have a verb following Europa. The final two don’t; that is, the verb disappears. That immediately makes me suspect sentence structure, because a sentence does have to have a verb. If you remove the main verb from one location, you have to put one in someplace else. I’ll be watching out for that when I read the sentence.
And now it’s time to do just that. As I read the sentence, I strip it down to what we call the “sentence core” in my mind. It took me a long time to develop this skill. I’ll show you the result, first, and then I’ll tell you how I learned to do it.
The “sentence core” refers to the stuff that has to be there in order to have a complete sentence. Everything else is “extra”: it may be important later, but right now, I’m ignoring it.
I greyed out the portions that are not part of the core. How does the sentence look to you?
Notice something weird: I didn’t just strip it down to a completely correct sentence. There’s something wrong with the core. In other words, the goal is not to create a correct sentence; rather, you’re using certain rules to strip to the core even when that core is incorrect.
Using this skill requires you to develop two abilities: the ability to tell what is core vs. extra and the ability to keep things that are wrong, despite the fact that they’ll make your core sound funny. The core of the sentence above is:
Europa has long been considered too cold to support life, and.
Clearly, that’s not a good sentence! So why did I strip out what I stripped out, and yet leave that “comma and” in there? Here was my thought process:
|Text of sentence||My thoughts:|
|“With…”||Preposition. Introduces a modifier. Can’t be the core.|
|“With surface temperatures estimated at minus 230 degrees Fahrenheit,”||Each word I’ve italicized introduces a new noun modifier. Nothing here is a subject or main verb. *|
|“Jupiter’s moon Europa”||The main noun is Europa; ignore the earlier words.|
|“Europa has long been considered far too cold to support life,”||That’s a complete sentence. Yay.|
|“, and”||A complete sentence followed by “comma and”? I’m expecting another complete sentence to follow. **|
|“with 60 square miles of water thought to be frozen from top to bottom.”||Same deal as the beginning of the sentence! Each word I’ve italicized introduces a new modifier. Nothing here that can function as a subject or main verb.|
* Why isn’t estimated a verb?
Estimated is a past participle and can be part of a verb form, but you can’t say “Temperatures estimated at minus 230 degrees Fahrenheit.” You’d have to say “Temperatures are estimated at…” (Note: you could say “She estimated her commute to be 45 minutes from door to door.” In other words, estimated by itself can be the main verb of a sentence. In my example, though, the subject is actually doing the estimating. In the GMATPrep problem above, the temperatures can’t estimate anything!)
** Why is it that I expected another complete sentence to follow the “comma and”?
The word and is a parallelism marker; it signals that two parts of the sentence need to be made parallel. When you have one complete sentence, and you follow that with “comma and,” you need to set up another complete sentence to be parallel to that first complete sentence.
She studied all day, and she went to dinner with friends that night.
The portion before the and is a complete sentence, as is the portion after the and.
(Note: the word and can connect other things besides two complete sentences. It can connect other segments of a sentence as well, such as: She likes to eat pizza, pasta, and steak. In this case, although there is a “comma and” in the sentence, the part before the comma is not a complete sentence by itself. Rather, it is the start of a list.)
Okay, so my core is:
Europa has long been considered too cold to support life, and.
And that’s incorrect. Eliminate answer (A). Either that and needs to go away or, if it stays, I need to have a second complete sentence. Since you know the sentence core is at issue here, check the cores using the other answer choices:
Here are the cores written out:
“(B) Europa has long been considered too cold to support life.
“(C) Europa has long been considered as too cold to support life and has 60 square miles of water.
“(D) Europa and its 60 square miles of water.
(On the real test, you wouldn’t have time to write that out, but you may want to in practice in order to build expertise with this technique.)
Answers (D) and (E) don’t even have main verbs! Eliminate both. Answers (B) and (C) both contain complete sentences, but there’s something else wrong with one of them. Did you spot it?
The correct idiom is consider X Y: I consider her intelligent. There are some rare circumstances in which you can use consider as, but on the GMAT, go with consider X Y. Answers (C), (D), and (E) all use incorrect forms of the idiom.
Answer (C) also loses some meaning. The second piece of information, about the water, is meant to emphasize the fact that the moon is very cold. When you separate the two pieces of information with an and, however, they appear to be unrelated (except that they’re both facts about Europa): the moon is too cold to support life and, by the way, it also has a lot of frozen water. Still, that’s something of a judgment call; the idiom is definitive.
The correct answer is (B).
Go get some practice with this and join me next time, when we’ll try another GMATPrep problem and talk about some additional aspects of this technique.
Key Takeaways: Strip the sentence to the Core
(1) Generally, this is a process of elimination: you’re removing the things that cannot be part of the core sentence. With rare exceptions, prepositional phrases typically aren’t part of the core. I left the prepositional phrase of water in answers (C) and (D) because 60 square miles by itself doesn’t make any sense. In any case, prepositional phrases never contain the subject of the sentence.
(2) Other non-core-sentence clues: phrases or clauses set off by two commas, relative pronouns such as which and who, comma + -ed or comma + ing modifiers, -ed or –ing words that cannot function as the main verb (try them in a simple sentence with the same subject from the SC problem, as I did with temperatures estimated…)
(3) A complete sentence on the GMAT must have a subject and a working verb, at a minimum. You may have multiple subjects or working verbs. You could also have two complete sentences connected by a comma and conjunction (such as comma and) or a semi-colon. We’ll talk about some additional complete sentence structures next time.
* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.