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GMAT 101: Sections, Question Types & Study Strategies
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Conquering Two 800-Level GMAT Problems
Wednesday, September 10 (8:00 – 10:00 PM EDT)
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Hitting 730: How to Get a Harvard-Level GMAT Score
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Survival Guide: 14 Days to Study for the GMAT
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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.

You’ve heard a million times that you’re supposed to create Official Guide (OG) problem sets in order to practice for the test. But how do you actually do so in a way that will help you get the most out of your study?

Fear not! This article is coming to your rescue.

Initially, when you’re studying a new topic or problem type, you won’t do sets of problems; instead, you’ll just try one problem at a time. As you gain experience, though, you’re going to want to do 3 problems in a row, or 5, or 10.

Why?

Because the real test will never give you just one problem!

The GMAT will give you many questions in a row and they’ll be all jumbled up—an SC, then a couple of CRs, then back to another SC (that tests different grammar rules than the first one), and so on.

You want to practice two things:

(1) Jumping around among question types and topics

(2) Managing your timing and mental energy among a group of questions

When do I start doing problem sets?

You’re going to use problem sets to test your skills, so you’ve got to develop some of those skills first. If you’re using our Strategy Guides to study, then at the end of one chapter, you’ll do only two or three OG problems to make sure that you understood the material in the chapter.

Later, though, when you finish the Guide, do a set of problems that mix topics (and question types) from that entire book. Make sure you can distinguish between the similar-but-not-quite-the-same topics in that book, and also practice your skills on both problem solving and data sufficiency. As you finish subsequent Guides, your sets can include problems from everything you’ve done so far. Keep mixing it up!

How do I make the sets?

You’ll need to balance three things when you create a problem set:

(1) Number of problems. Initially, start out with about 3 to 5 problems. As you gain experience and add topics, you’ll increase the size of the sets—we’ll talk more about this a little later.

(2) Type of problem and content.
(a) For quant, always do a mix of Problem Solving (PS) and Data Sufficiency (DS). For verbal, mix at least two of the three types; you can include all three types in larger sets.
(b) Do not do a set of 3 or more questions all from the same chapter or content area—for example, don’t do 3 exponents questions in a row. You know exactly what you’re about to get and the real test will never be this nice to you.

(3) Difficulty level.
(a) Include a mix of easier, medium, and harder questions in your set. For all types except Reading Comprehension, the OG places problems in roughly increasing order of difficulty. On average, aroblem 3 is easier than a problem 50, which is easier than a problem 102. (This does not mean that problem 5 is necessarily harder than problem 3. In general, higher question numbers represent harder questions, but the increase is not linear from problem to problem.)
(b) Note: your personal strengths and weaknesses will affect how you perceive the problems—you might think a lower-numbered problem is hard or a higher-numbered problem is easy. They are… for you! Expect that kind of outcome sometimes.

Timing!

Next, calculate how much time to give yourself to do the problem set.
Read more

We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:

A coin purse contains 13 coins, each worth 1, 5, 10, or 25 cents; the total value of the coins is 150 cents. How many 10-cent coins are in the purse?

(1) The 13 coins can be divided among five separate envelopes so that each envelope contains the same total monetary value.

(2) The 13 coins can be divided among six separate envelopes so that each envelope contains the same total monetary value.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Read more