How did it go last time with the rate problem? I’ve got another story problem for you, but this time we’re going to cover a different math area.

Just a reminder: here’s a link to the first (and long ago) article in this series: making story problems real. When the test gives you a story problem, do what you would do in the real world if your boss asked you a similar question: a back-of-the-envelope calculation to get a “close enough” answer.

If you haven’t yet read the earlier articles, go do that first. Learn how to use this method, then come back here and test your new skills on the problem below.

This is a GMATPrep® problem from the free exams. Give yourself about 2 minutes. Go!

* “Jack and Mark both received hourly wage increases of 6 percent. After the wage increases, Jack’s hourly wage was how many dollars per hour more than Mark’s?

“(1) Before the wage increases, Jack’s hourly wage was $5.00 per hour more than Mark’s.

“(2) Before the wage increases, the ratio of Jack’s hourly wage to Mark’s hourly wage was 4 to 3.”

Data sufficiency! On the one hand, awesome: we don’t have to do all the math. On the other hand, be careful: DS can get quite tricky.

Okay, you and your (colleague, friend, sister…pick a real person!) work together and you both just got hourly wage increases of 6%. (You’re Jack and your friend is Mark.) Now, the two of you are trying to figure out how much more you make.

Hmm. If you both made the same amount before, then a 6% increase would keep you both at the same level, so you’d make $0 more. If you made $100 an hour before, then you’d make $106 now, and if your colleague (I’m going to use my co-worker Whit) made $90 an hour before, then she’d be making…er, that calculation is annoying.

Actually, 6% is pretty annoying to calculate in general. Is there any way around that?

There are two broad ways; see whether you can figure either one out before you keep reading.

First, you could make sure to choose “easy” numbers. For example, if you choose $100 for your wage and half of that, $50 an hour, for Whit’s wage, the calculations become fairly easy. After you calculate the increase for you based on the easier number of $100, you know that her increase is half of yours.

Oh, wait…read statement (1). That approach isn’t going to work, since this choice limits what you can choose, and that’s going to make calculating 6% annoying.

Second, you may be able to substitute in a different percentage. Depending on the details of the problem, the specific percentage may not matter, as long as both hourly wages are increased by the same percentage.

Does that apply in this case? First, the problem asks for a relative amount: the difference in the two wages. It’s not always necessary to know the exact numbers in order to figure out a difference.

Second, the two statements continue down this path: they give relative values but not absolute values. (Yes, $5 is a real value, but it represents the difference in wages, not the actual level of wages.) As a result, you can use any percentage you want. How about 50%? That’s much easier to calculate.

Okay, back to the problem. The wages increase by 50%. They want to know the difference between your rate and Whit’s rate: Y – W = ?

“(1) Before the wage increases, Jack’s hourly wage was $5.00 per hour more than Mark’s.”

Okay, test some real numbers.

Case #1: If your wage was $10, then your new wage would be $10 + $5 = $15. In this case, Whit’s original wage had to have been $10 – $5 = $5 and so her new wage would be $5 + $2.50 = $7.50. The difference between the two new wages is $7.50.

Case #2: If your wage was $25, then your new wage would be $25 + $12.50 = $37.50. Whit’s original wage had to have been $25 – $5 = $20, so her new wage would be $20 + $10 = $30. The difference between the two new wages is…$7.50!

Wait, seriously? I was expecting the answer to be different. How can they be the same?

At this point, you have two choices: you can try one more set of numbers to see what you get or you can try to figure out whether there really is some rule that would make the difference always $7.50 no matter what.

If you try a third case, you will discover that the difference is once again $7.50. It turns out that this statement is sufficient to answer the question. Can you articulate why it must always work?

The question asks for the difference between their new hourly wages. The statement gives you the difference between their old hourly wages. If you increase the two wages by the same percentage, then you are also increasing the difference between the two wages by that exact same percentage. Since the original difference was $5, the new difference is going to be 50% greater: $5 + $2.50 = $7.50.

(Note: this would work exactly the same way if you used the original 6% given in the problem. It would just be a little more annoying to do the math, that’s all.)

Okay, statement (1) is sufficient. Cross off answers BCE and check out statement (2):

“(2) Before the wage increases, the ratio of Jack’s hourly wage to Mark’s hourly wage was 4 to 3.”

Hmm. A ratio. Maybe this one will work, too, since it also gives us something about the difference? Test a couple of cases to see. (You can still use 50% here instead of 6% in order to make the math easier.)

Case #1: If your initial wage was $4, then your new wage would be $4 + $2 = $6. Whit’s initial wage would have been $3, so her new wage would be $3 + $1.5 = $4.50. The difference between the new wages is $1.5.

Case #2: If your initial wage was $8, then your new wage would be $8 + $4 = $12. Whit’s initial wage would have been $6, so her new wage would be $6 + $3 = $9. The difference is now $3!

Statement (2) is not sufficient. The correct answer is (A).

Now, look back over the work for both statements. Are there any takeaways that could get you there faster, without having to test so many cases?

In general, if you have this set-up:

– The starting numbers both increase or decrease by the same percentage, AND

– you know the numerical difference between those two starting numbers

? Then you know that the difference will change by that same percentage. If the numbers go up by 5% each, then the difference also goes up by 5%. If you’re only asked for the difference, that number can be calculated.

If, on the other hand, the starting difference can change, then the new difference will also change. Notice that in the cases for the second statement, the difference between the old wages went from $1 in the first case to $2 in the second. If that difference is not one consistent number, then the new difference also won’t be one consistent number.

Key Takeaways: Make Stories Real

(1) Put yourself in the problem. Plug in some real numbers and test it out. Data Sufficiency problems that don’t offer real numbers for some key part of the problem are great candidates for this technique.

(2) In the problem above, the key to knowing you could test cases was the fact that they kept talking about the hourly wages but they never provided real numbers for those hourly wages. The only real number they provided represented a relative difference between the two numbers; that relative difference, however, didn’t establish what the actual wages were.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

In the past, we’ve talked about making story problems real. In other words, when the test gives you a story problem, don’t start making tables and writing equations and figuring out the algebraic solution. Rather, do what you would do in the real world if someone asked you this question: a back-of-the-envelope calculation (involving some math, sure, but not multiple equations with variables).

If you haven’t yet read the article linked in the last paragraph, go do that first. Learn how to use this method, then come back here and test your new skills on the problem below.

This is a GMATPrep® problem from the free exams. Give yourself about 2 minutes. Go!

* “Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

“(1) Machines X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does.

“(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does.”

You work in a factory. Your boss just came up to you and asked you this question. What do you do?

In the real world, you’d never whip out a piece of paper and start writing equations. Instead, you’d do something like this:

I need to figure out the difference between how long it takes X alone and how long it takes Y alone.

Okay, statement (1) gives me some info. Hmm, so if machine X takes 1 hour to do the job by itself, then the two machines together would take two-thirds…let’s see, that’s 40 minutes…

Wait, that number is annoying. Let’s say machine X takes 3 hours to do the job alone, so the two machines take 2 hours to do it together.

What next? Oh, right, how long does Y take? If they can do it together in 2 hours, and X takes 3 hours to do the job by itself, then X is doing 2/3 of the job in just 2 hours. So Y has to do the other 1/3 of the job in 2 hours. Read more

Welcome to the third part of our series focusing on the First Glance in Sentence Correction. If you haven’t read the previous installments yet, you can start with how to find a starting point on a Sentence Correction problem when the starting point doesn’t leap out at you.

Try out the First Glance on the below problem and see what happens! This is a GMATPrep® problem from the free exams.

* “Most of the purported health benefits of tea comes from antioxidants—compounds also found in beta carotene, vitamin E, and vitamin C that inhibit the formation of plaque along the body’s blood vessels.

“(A) comes from antioxidants—compounds also found in beta carotene, vitamin E, and vitamin C that

“(B) comes from antioxidants—compounds that are also found in beta carotene, vitamin E, and vitamin C, and they

“(C) come from antioxidants—compounds also found in beta carotene, vitamin E, and vitamin C, and

“(D) come from antioxidants—compounds that are also found in beta carotene, vitamin E, and vitamin C and that

“(E) come from antioxidants—compounds also found in beta carotene, vitamin E, and vitamin C, and they”

The First Glance definitely helps on this one: comes vs. come is a singular vs. plural verb split, indicating a subject-verb agreement issue. Now, when you read the original sentence, you know to find the subject.

So what is the subject of the sentence? It’s not the singular tea, though it’s tempting to think so. The subject is actually the word most, which is a SANAM pronoun.

The SANAM pronouns: Some, Any, None, All, More / Most

These pronouns can be singular or plural, depending on the context of the sentence. Consider these examples:

Read more

Last time, we talked about how to find a starting point on a Sentence Correction problem when the starting point doesn’t leap out at you. If you haven’t read that article yet, go ahead and do so.

The first step of the SC process is a First Glance, something that didn’t help out a whole lot on last week’s problem. Let’s try out the First Glance again and see what happens!

This GMATPrep® problem is from the free exams.

* “Often incorrectly referred to as a tidal wave, a tsunami, a seismic sea wave that can reach up to 150 miles per hour in speed and 200 feet high, is caused by underwater earthquakes or volcanic eruptions.

“(A) up to 150 miles per hour in speed and 200 feet high, is

“(B) up to 150 miles per hour in speed and heights of up to 200 feet, is

“(C) speeds of up to 150 miles per hour and 200 feet high, are

“(D) speeds of up to 150 miles per hour and heights of up to 200 feet, is

“(E) speeds of up to 150 miles per hour and as high as 200 feet, are”

What did you do for the First Glance? The glance is designed to give you an upfront hint about one issue that the sentence might be testing before you actually start reading the full sentence. Take a look at the beginning of the underline, including the beginning of all five answer choices.

The split is between up to and speeds of up to. There isn’t an obvious grammar rule here, so the issue is likely to revolve around meaning: do we need to say speeds of or is it enough to say just up to?

Think about this while reading the original sentence. What do you think?

The phrase reach up to could go in several different directions—is it going to say up to 150 miles in length? up to 150 feet high?—so it’s preferable to clarify right up front that the wave is reaching speeds of up to 150 miles per hour.

In addition, the sentence contains parallelism:

can reach up to X [150 miles per hour in speed] and Y [200 feet high]

The portion before the parallelism starts must apply to both the X and Y portions, so the original sentence says:

can reach up to 200 feet high

That might sound kind of clunky and it is: up to and high are redundant.

Okay, answer (A) is incorrect and answer (B) repeats both issues (it neglects to specify speeds of up to 150 and it contains faulty parallelism.).

Check the parallelism in the other choices:

“(C) speeds of up to [150 miles per hour] and [200 feet high]

“(D) [speeds of up to 150 miles per hour] and [heights of up to 200 feet]

“(E) speeds of [up to 150 miles per hour] and [as high as 200 feet]”

In answer (C), the Y portion is the measurement (200 feet), so the X portion should also be the measurement…but it’s nonsensical to say speeds of up to 200 feet high. Likewise, in (E), the Y portion is a prepositional phrase, so it matches the prepositional phrase in the X portion. Now, the sentence says speeds of as high as 200 feet—equally nonsensical.

The only one that makes sense is answer (D): speeds of up to 150 and heights of up to 200.

The correct answer is (D).

You might also have noticed, in the original sentence, that the last underlined word is the verb is. Sentence Correction problems always have at least one difference at the beginning of the underline and at the end, so glance down the end of the choices.

Interesting! Is vs. are. What subject goes with this verb? Here’s the original sentence again:

“Often incorrectly referred to as a tidal wave, a tsunami, a seismic sea wave that can reach up to 150 miles per hour in speed and 200 feet high, is caused by underwater earthquakes or volcanic eruptions.”

The modifiers have been crossed out. The subject is tsunami, a singular noun, so the verb should be the singular is. Answers (C) and (E) are incorrect for this reason.

Key Takeaways: The First Glance in Sentence Correction

(1) Before reading the original sentence, make it a habit to glance at the word or couple of words at the start of the underline and each answer choice. Sometimes, the split will be obvious: an is vs. are split, for example, clearly indicates subject-verb agreement.

(2) Sometimes the split will be less obvious, as with up to vs. speeds of up to. In this case, if the split is fairly easy to remember, just keep the variations in mind as you read the original sentence, so that you can analyze the difference right away. You may see immediately that speeds of up to is more clear, and your knowledge that the sentence is testing this meaning might also alert you to some of the meaning issues introduced by the faulty parallelism.

(3) Making a subject-verb match in the midst of a bunch of modifiers can be tricky. Learn how to strip the modifiers out and take the sentence down to its basic core structure.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

Want to learn more? Read on to part 3.

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Have you ever worked with someone who inevitably managed to come up with things to do that were a complete waste of time? Maybe it was an insecure boss who was never confident about what he was doing, so he went for the “everything and the kitchen sink” approach to generating deliverables in the last few days before the deadline. Or maybe it was a fellow student on a group project, someone so diligent (cough, cough) that she wanted to turn in a 20-page report when the teacher suggested 10 pages (and actually specified a 12-page limit).

You know who I’m talking about, right? We’ve all run across these situations in our academic or working lives. You want to be polite…but you also want to get your work done and not waste time on activities that don’t really help you reach the overall goal.

The GMAT is trying to waste your time

Okay, the test writers are not literally sitting there cackling and saying, “How can we get them to waste their lives?!?” But the overall sentiment still holds because of the way that the GMAT is constructed. You already know the classic “If you get something right, they give you something harder” pattern, right?

Well, at some point, that “something harder” is going to be something that isn’t worth your time. You’re probably not going to get it right no matter what you do. Even if you do, you’re going to use up valuable time that you could be using on other problems.

Most important of all, you’re going to be using up your finite brain energy on something that probably isn’t going to pay off. How many times in your life have you crashed towards the end of a test or a long day at work because your brain just couldn’t keep going any longer? The GMAT is a “where you end is what you get” test: if you crash before the end of the section, your score will suffer greatly.

This is basically no different than that co-worker who’s trying to get you to build a marketing presentation when the client has specifically requested that you analyze the pros and cons of acquiring a competitor. Tomorrow at the client meeting, it won’t matter how good your intentions were. Your client is going to be mad that you wasted time on something that doesn’t actually help them.

Read more

//youtu.be/fi1Do93UizU

Learn about the rewarding teaching opportunities with Manhattan Prep at our upcoming online open houses on July 28, August 21, or September 28th. Here’s the scoop:

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All Manhattan Prep instructors earn $100/hour for teaching and tutoring – up to four times the industry standard. These are part-time positions with flexible hours, allowing you to pursue other career interest. Many of our instructors maintain full-time positions, engage in entrepreneurial endeavors, or pursue advanced degrees concurrently while teaching for Manhattan Prep. (To learn more about our exceptional instructors, read their bios or view this short video).

Learn about how to transform your passion for teaching into a lucrative and fulfilling part-time career by joining us for one of the following Online Open House events!

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GMAC just released new 2015 editions of its three The Official Guide for GMAT® Review books. Here’s what you need to know as you decide whether to buy these books and how to use them.

What changed?

The three books in question are The Official Guide for GMAT Review 2015 (formerly known as the 13^th edition of the Official Guide, or OG), The Official Guide for GMAT Quantitative Review 2015 (formerly known as the 2^nd edition of the Quant Review), and The Official Guide for GMAT Verbal Review 2015 (formerly known as the 2^nd edition of the Verbal Review). I’ll refer to these throughout this article as OG2015, QR2015, and VR2015, respectively.

The questions (and explanations) contained in all three 2015 versions are the same as the questions (and explanations) in the previous versions. There are no new questions.

The new editions do come with special codes to access an online software program that contains the problems from the books. Now, when you want to do a set of random OG problems, you don’t have to create the sets for yourself—you can have the online software do it for you. (OG2015 also still provides online access to the 50 Integrated Reasoning questions that come with the 13^th edition of the book.)

The online software also has some short videos (one for each book) starring the incomparable Dr. Lawrence Rudner, Chief Psychometrician for GMAC, answering frequently asked questions from students.

How does the software work?

The software for all three books gives you the ability to choose Practice mode or Exam mode. In addition, OG2015 offers a Diagnostic test mode that contains the questions from chapter 3 of the printed book.

Certain features are offered in all three modes:

– Question Type, Number, and Difficulty. You can choose from among the different question types (PS, DS, SC, CR, RC), as well as by difficulty bucket (easy, medium, hard, or all). You can also decide how many questions you want to be in the set.

– Timing. The software will keep track of how much time you spend per question, as well as your overall time for that set of questions. (It does not, though, give you a time limit, so you will have to set one for yourself.)

– Bookmarks. You can bookmark problems that you want to remember for some reason—maybe your guesses or the ones that you want to try again before checking the answer or explanation.

– Calculator. Yes, the software offers a calculator, even though you’re not allowed to use a calculator on the quant section of the real test. My recommendation: pretend this button doesn’t exist.

– Pause. You can pause the question set. This is useful if someone suddenly rings your doorbell, but do not pause the software while continuing to work on the problem. Otherwise, your data will be skewed and you won’t really be able to tell what your strengths and weaknesses are.

In the Diagnostic and Exam modes, you can only move forward in the question set (as on the real exam), but in Practice mode, you can move back and forth. If you come back to a problem for the second time, the software will actually remember how much time you spent before and will start counting your time where you left off! I was really impressed with this feature.

I do have to warn you about three other somewhat-faulty features (maybe these will be changed in future). First, when you click to go to the next question, the software does not ask you to confirm. That’s fine in Practice mode, where you’re allowed to go backwards, but in Diagnostic and Exam modes, if you accidentally click “next question,” you will be moved to the next problem even if you have not yet entered an answer—and there is no way to go back.

Second, in any of the three modes, you’ll be able to go to a results screen when done with a question set. For both Exam and Practice modes, these question sets will be saved and you’ll be able to review them at any time in the future. In Diagnostic mode, however, you can only see the results screen right after you have finished the problem set. Once you close out of that area (or out of the software entirely), that data will disappear, so make sure you take screen shots of the results screen before you leave that area of the program. (In fact, I recommend taking the screen shots immediately after finishing a Diagnostic set. I accidentally clicked something that took me out of that part of the program and lost all of my data before I could review it.)

Third, in both Practice and Exam modes, the RC questions are offered one at a time, not in sets of 3 or 4 (as on the real test). For this reason, I recommend doing RC questions out of the physical book. Reading an entire passage only to answer a single question is not a good use of study time.

I was also excited to see that the Practice mode offered a “notes” feature, where you can actually type notes to yourself while working on the problem. I was disappointed that those notes seemed to disappear afterwards. When I was reviewing the results screen and the problem explanations, I couldn’t find any way to access my notes again.

How do I get the most out of these new books?

If you already have the previous incarnations of these books (OG13, VR2, and QR2), then I don’t actually recommend buying the new editions unless money is not a concern for you. The most important thing is to have access to the questions themselves. While the new software does make it much easier to set up problem sets, many people probably aren’t going to pay $46 just for that.

If you don’t yet have these books, though, then of course you’ll want to get the 2015 editions. In that case, here’s how I would use the new features:

1. In the first week or two of your study, take the Diagnostic mode tests. I would do these in 5 separate sittings, one for each question type. You don’t need to set yourself a hard overall time limit, but do pay attention to that clock and be honest with yourself when a problem just isn’t happening. Guess and move on. (Note: if you’re taking our class, then you can dispense with this step and save the problems for review later in your studies.)

2. As you work through whatever material you’re using to learn all about the math, grammar, and question types tested on the GMAT, you will initially try just a couple of OG problems that directly test whatever you recently studied. In this case, you won’t be using the OG software because the software doesn’t let you select by topic.

After you get at least halfway through your study material though (e.g., about 3 of our 5 quant books, or halfway through the chapters in the SC book), you can start to set up random sets of questions for yourself using the software’s Practice mode. When you’re offered a question on a topic you haven’t studied yet, just do your best; this will help you to have an idea of your strengths and weaknesses so that you know how much time to spend when you do get to that topic.

Whether you want to do random sets of problems or choose specific topics, here are some guidelines for creating your own OG problem sets.

3. Save Exam mode for a bit later in your studies, after you’ve been through all of your main study material once. Both Practice and Exam modes are pulling from the same pool of questions, but Exam mode imposes some additional restrictions that make your practice closer to the real test (for example, you can’t go back to questions that you’ve already completed).

In sum

Everyone should be studying with the Official Guide materials—nothing is better than the real thing! If you already have the 13^th edition or 2^nd edition books, don’t feel that you must buy the 2015 editions, but if you don’t, then certainly get the latest versions and take advantage of the new online problem set program.

Happy studying!

So you’re smart, clever, and creative? … Then you’re going to love this photo caption contest! Once a week for the next four weeks we’re going to post a photo of a scene from GMAT Interact on our Facebook Photo Caption Contest page for you to caption for your chance to win GMAT Interact™ (a $899 value)!

GMAT Interact is a comprehensive, self-paced program that features 35+ lessons that are interactive, fun, and completely driven by you. Designed around the student-teacher connection, expert Manhattan Prep instructors guide students through every topic tested on the GMAT, one section at a time, asking them questions and prompting them to think about the content presented. What’s more: every response a student gives helps personalize the lesson. It’s what many are calling “the best self-study method out there right now.”

Here’s how the contest works:
Every Monday for the next four weeks, we will be posting a photo of a scene from GMAT Interact on our Facebook Photo Caption Contest App for you to caption. Our weekly winner will be announced each Monday when we post the new pic to quote! Judging is based on creativity and votes accumulated on captions — so be sure to share your caption with your friends, and encourage them to vote for you.

So what are you waiting for? Head on over to our Facebook Photo Caption Contest now to see this week’s photo and be sure to check back next week for the winner!

We’ve invited mbaMission to share their Business School Essays Analyses as they’re released for the 2014-2015 application season. Here is their analysis for Massachusetts Institute of Technology (Sloan).

The MIT Sloan School of Management bucks conventionality this admissions season and has added to the word count for its application essays—moving from a maximum of 1,000 words to 1,250. The school’s first essay question remains the same as last year’s, but its second essay prompt presents an interesting challenge in that the admissions committee asks you to do exactly what it does not want you to do in reality: write your own recommendation letter. At least in this case, the school is allowing you to do so in the light of day. Thankfully, perhaps, Sloan has dropped its befuddling optional essay, which had invited applicants to share any additional information in any format. Candidates will be content to see clearer directives in the program’s essay questions. As always, our analysis follows…

Essay 1:  The mission of the MIT Sloan School of Management is to develop principled, innovative leaders who improve the world and to generate ideas that advance management practice. Discuss how you will contribute toward advancing the mission based on examples from your past work and activities. (500 words or fewer)
Read more