If you have a strong business school application, you likely won’t need a near-perfect GMAT score for admission into a top MBA program. But how do you know if your GMAT score is up to par? Below is an infographic that details the GMAT scores for the best business schools:

Scroll down to learn if your GMAT score is competitive enough for the top business schools:

*Important to note: officially, the GMAT scale for verbal and quantitative goes up to 60, but in practice, the scale tops out at 51. Nowadays, a verbal subscore of 46 would get you in the 99th GMAT score percentile, while a 51 quant subscore would be in the 97th.*

To accurately assess your GMAT score, you must understand the big picture of GMAT admissions, and remember that your GMAT score is just one part of your application.

First, familiarize yourself with GMAT scoring. Then, compare your score to the average GMAT scores of admitted students at your target programs. Keep in mind that an average score for a top business school is not the bare minimum you need to get in–approximately half of applicants get into that school with less than that average score. That means you can think about it as just that–an average score.

If your GMAT is good enough for the programs you like, then focus your energy on strengthening other aspects of your application. And if your score doesn’t quite make the cut, then consider retaking the GMAT only so you can distinguish yourself from other applicants with a similar application profile to yours.

Ultimately, you have to decide what is a good GMAT score for you. GMAT scores may be paramount to the application process, but even a 720 combined score won’t get you into the best business schools without a strong application to back it up. Your entire profile must honestly and effectively represent your successes, abilities, and potential.

Still … a 720 can’t hurt.

If you need help getting there, then reach out about our Magoosh GMAT Prep! And while you’re at it, leave us a comment below with your thoughts about this infographic.

Along the way, there are many ups and downs, and major doses of discouragement mixed in with the fleeting highs and successes. So it can be tough to stay motivated and remember what all the hard work is for.

But as someone wise once said, “If you fix your eyes on the goal, the journey there will seem less daunting.” (Ok, I admit it. I just came up with that myself…but you get the point!) Keeping your eyes on the prize, on the future career that lies at the end of the MBA journey, can help make the difficulties of the now much less overwhelming.

So as you make your way through the trenches of the MBA application process, check out our new Slideshare of inspiring quotes to help you stay motivated:

Hope that at least cheered you up! And, if you have a favorite quote from the Slideshare or if you think of another one that should be in there, please let us know with a comment in the comment box below.

**Hello and Welcome to GMAT Tuesday!**

Today, we are going to talk about how to study for the Verbal Section of the GMAT.

Some high-level highlights:

1) Structure

- Know the format of the GMAT Verbal Section before test day. For example, you need to know:
- The number of questions (41)
- How long the section lasts (75 minutes)
- Whether it’s computer adaptive like the Quantitative Section (It is.)
- That you can’t go back after answering a question
- The question types you’ll see (critical reasoning, reading comprehension, sentence correction)
- Strategies for solving each question type

2) Read, Read, Read, Read … !

- Immerse yourself in words by reading as much as you can.
- Really. You really can’t read enough.
- Try to read 40-50 pages per day, or approximately 1-2 hours
- What should you read?
- Try a mixture of books, articles, magazines, newspapers, fiction, and non-fiction.
- We recommend The Economist, The NY Times, The New Yorker, Arts and Letters Daily, and The Atlantic.
- Be comfortable reading different things (even math!) and interpreting an author’s meaning.

3) Think in your own words

- When you read, practice digesting the information and putting it into your own words.
- Synthesize and summarize.

4) Focus on ONE area at a time

- Choose a question type (critical reasoning, for example) and focus only on it for a designated amount of time (maybe a week or so).
- Understand sub-question types and common wrong answer types.
- Complete practice questions and review your wrong answers.
- Become an expert in that area, then move on to another question type.
- Don’t forget to go back and review, even after you’ve moved on to another aspect of the GMAT Verbal Section.

5) Review

- Review concepts and question types – don’t just move from one concept to the next and never return.
- Answer the same questions again, even if you got them right the first time.

]]>

Check us out for interviews with the Magoosh team, including this one with Magoosh CEO, Bhavin Parikh! You’ll learn more about Magoosh’s mission and the people behind your prep.

We hope you enjoy! Don’t forget to subscribe and share with your friends.

Video suggestions? Leave them in the comments, below.

]]>

Applying the rule incorrectly causes quite a few errors on the quant section, particularly with Data Sufficiency questions. This is the fifth in a series of posts on avoiding those errors:

In my first three posts on this topic we saw that sometimes two equations aren’t enough to allow us to solve for two variables, or even for one. That is, we saw that sometimes, information that seems sufficient isn’t in fact sufficient.

The trick was that the rule above isn’t correct as written. The correct rule is that a system of *n* distinct linear equation is sufficient to solve for *n* variables, but that sometimes the GMAT gives you systems of equivalent (not distinct) equations, or exponential or quadratic (not linear) equations, and that the rule doesn’t apply to such systems.

In my last post we saw that sometimes information that *doesn’t* seem sufficient turns out to be, even when the equations in question are distinct and linear, because the *story problem* imposes implicit constraints that the equations might miss.

In this post we’ll see another sort of system of equations for which information that *doesn’t* seem sufficient turns out to be.

Take a couple of minutes to tackle this problem:

If 4x – z = 6y + z, what is the value of *z*?

(1) 2x – 5 = 3y

(2) 3x – 11 = 2z

**(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.

In this case, if we too quickly apply the rule described above, we’ll probably choose (C). After all, we have three variables—*x*, *y*, and *z*—and so presumably we need three equations, the one in the question stem and the two in the statements.

And, though the correct answer isn’t in fact (C), there’s something to that logic. We would in fact need all three equations to determine the values of all three variables, but our question asks just for the value of *z*.

Whenever the question stem presents you with an equation with multiple variables and asks you to solve for one of them, you should immediately rewrite the equation to find a more useful question.

Specifically, you should *isolate the variable you’re asked to solve for* and then *focus on the expression equal to that variable*. Here’s what that would look like for this problem:

*4x – z = 6y + z*

Add *z* to each side of the equation and subtract *6y* from each side.

*2z = 4x – 6y*

Divide each side by 2.

*z = 2x – 3y*

So our real question is, “What is the value of *2x – 3y*?”

Does the equation *2x – 5 = 3y *allow us to solve for *2x – 3y*?

Manipulate the left-hand side of the equation to isolate *2x – 3y *and let the right-hand side of the equation take care of itself.

*2x – 5 = 3y*

Subtract 3*y* to each side of the equation and add 5 to each side.

*2x -3y = 5*

So Statement (1) is sufficient. Eliminate answers (B), (C), and (E).

Does the equation *3x – 11 = 2z allow us to solve for 2x – 3y?*

Perhaps you can see right away that it does not, since that equation incudes the variable *z* (which we don’t want) but doesn’t include the variable *y* (which we need). If that isn’t obvious, proceed as above: manipulate the left-hand side of the equation to isolate *2x – 3y and let the right-hand side of the equation take care of itself. *

*3x – 11 = 2z*

Add 11 to each side.

*3x = 2z + 11*

Multiply each side by 2/3.

Subtract 3*y* from each side.

Since the right-hand side of the equation is *not* a constant, it doesn’t appear as though Statement (2) is sufficient by itself. Eliminate (D). The correct answer is (A).

]]>

A) The Duke MBA application requires the following materials:

- A completed online application form
- One-page resume
- 2 professional letters of recommendation
- 3 short answer essay questions (250 characters each) and 2 long essays (2 pages each)
- Scanned copies of official transcripts (hard copies are required after admission)
- Valid GMAT or GRE score
- For students for whom English is not their native language, a valid TOEFL, PTE or IELTS score
- An interview – interviews are open to all applicants, regardless of round applying, in the Open Interview period (open approximately mid-September through mid-October), and after that interviews are by invitation. U.S. applicants in the Early Action round are required to interview during the Open Interview period.
- The application fee. We do offer a number of opportunities for a reduced application fee.

**Q) What type of individual do you think would thrive at the Duke-Fuqua school, and why?**

A) Fuqua attracts a tremendously diverse class of students who come from a myriad of different professional and personal backgrounds. Our students also go into a wide array of different industries and career paths after graduation. The kinds of students who do well at Fuqua are those who want to be involved and engaged in the communities of which they are a part. They are individuals who want to make a difference – they want to participate in classroom discussions, lead student clubs, and take advantage of new opportunities. They want to leave a legacy – this is what we mean when we say we are looking for “Leaders of Consequence.” Because our community is one that promotes innovation, and one in which we expect our students to provide ideas, challenges, and drive change, those who seek out those challenges and opportunities are those who do best at Fuqua.

**Q) International students often face additional sets of challenges when applying to programs in the U.S. Are there any resources you would recommend or advice you would share with international students applying to your school?**

A) Be sure you know what the application requirements are for each school, and start collecting transcripts/mark sheets and any other required documentation early, in time for your application or admission. Language tests can also take a while to schedule and have scores reported, so be sure you allow plenty of time (a month or more, if possible) to take the exam in advance of the application deadline. Also, student visa paperwork can take a while, so plan to apply earlier in the admissions cycle to ensure you have enough time to complete your visa. It can be difficult, if not impossible, to visit schools you are considering, so be sure you connect with alumni in your area. Talking to current students via email or Skype are also great ways to learn about programs first hand. But find an opportunity if you can to meet with an alumnus in person – you will learn a lot about a program from an alum’s firsthand experience and career path since graduation. And those insights can be great information to use in your essays.

**Q) What is the biggest misconception you have encountered when it comes to getting admitted into the Duke MBA program?**

A) That there are minimums, of any kind, that would automatically qualify/disqualify someone from admission. Applicants may say, “I know I won’t get in because I don’t have a 700 GMAT/100 TOEFL/3 years of work experience,” and that just isn’t right. Each applicant is considered as an individual, a multi-faceted person who brings more to the class than just his/her statistics. There is no magic number or formula for any part of the application. Everyone has a unique and compelling story, you just have to tell it.

**Q) What type of financial aid do you offer to students in your program?**

A) First of all, we do offer merit-based financial aid in the form of scholarships. Everyone who applies is considered for merit-based scholarships, and there is no additional requirement or essay in order to be considered. Scholarship decisions will be based on the same criteria we consider for admission, for those individuals who are outstanding in one or more areas of the application. We do also offer financial aid packages, including the International Student Loan program, which allows non-U.S. students to borrow 90% of the cost of attendance with no U.S. co-signer required.

**Q) How do you think a Duke MBA differs from an MBA at any other institution?**

A) If you ever read anything about Fuqua or talked to any of our students or alumni, you have heard the term “Team Fuqua.” Team Fuqua is a real thing – it’s tangible on campus and it affects your entire Fuqua experience, from application to student life to alumni involvement. This means that if you come to campus as a visitor, our students will come up to you and offer to show you around or answer your questions. They may invite you to lunch or even, if the time is right, to come with them to a Duke basketball game. It means that as a student, you will prep together with your classmates for an important job interview, even if you are all interviewing for the same position. Our students genuinely want success not only for themselves, but for their teammates. And as an alum, that legacy and support continues. If you ever need to consult an old professor on a project, or reach out to a fellow alum you’ve never met at a company you want to work for, you will find a welcoming supporter. Team Fuqua is really what defines us and makes this experience truly transformational.

**Q) Any last words you would like to share with prospective MBA students?**

A) It may sound cliché, but be yourself in this process, that’s the best advice I can give anyone. No matter how polished and well-written your application may be, if it isn’t reflective of who you really are, that inauthenticity is what comes through. Spend time getting to know yourself and your motivations for pursuing an MBA, and spend time getting to know the schools to which you are applying. Make your applications specific and reflective of your individual story. The best applications are the ones in which the voice and story of the applicant is consistent through all parts of the application.

**Author bio:**

*Allison Jamison is the Director of Recruitment and Marketing for The Duke MBA – Daytime and MMS programs at The Fuqua School of Business. Allison joined the Admissions team at Fuqua in 2006, and has spent most of her career at Fuqua focused on recruitment outreach and communications. As a proud Army spouse, Allison also serves as Fuqua’s military liaison for applicants and students. She holds a Bachelor of Science in Commerce from the University of Virginia and an MBA from the University of Texas. *

]]>

**Hello! Happy Tuesday!**

Today we are talking about the big picture stuff that you’ll need to know in order to improve your GMAT Quant game. Things like:

1. Structure

- Know the format of the GMAT Quantitative section before test day. For example, you should know:
- The number of questions in the section (37)
- How long the section lasts (75 minutes)
- Whether it’s computer adapted like the Verbal section (It is.)
- The types of questions you’ll see on the section (problem solving, data sufficiency)
- Strategies for solving each question type

2. NO CALCULATORS

- You can’t use a calculator on this section of the test. Get good at mental math!

3. Content

- Know the concepts tested in the section (algebra, arithmetic, geometry, word problems, etc.)

4. High Frequency Concepts

- Know which concepts are tested most frequently, so you can focus your time efficiently. Some common concepts include percentages, linear equations, and rates & proportions.

5. Math prep is not for spectators

- You have to do math to learn math! Be sure to go practice your math and critical thinking skills (after you watch this video, of course.)

6. Strategies

- It’s important to have a strong math foundation and to know your GMAT math strategies, so that you can focus your time on the critical aspects of the questions and not on the calculations.

]]>

1) On a ferry, there are 50 cars and 10 trucks. The cars have an average mass of 1200 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 60 vehicles on the ferry?

- 1200 kg
- 1500 kg
- 1800 kg
- 2100 kg
- 2400 kg

2) In Plutarch Enterprises, 70% of the employees are marketers, 20% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000?

- $80,000
- $130,000
- $240,000
- $290,000
- $320,000

3) At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $56,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?

- $24,000
- $28,000
- $32,000
- $36,000
- $40,000

4) In a company of only 20 employees, 10 employees make $80,000/yr, 6 employees make $150,000/yr, and the 4 highest-paid employees all make the same amount. If the average annual salary for the 20 employees is $175,000/yr, then what is the annual salary of each highest-paid employee?

- $250,000
- $300,000
- $350,000
- $400,000
- $450,000

5) In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let R be the average rental price for all apartments in the building. If R is $5,600 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $10,400 higher that R, then what percentage of apartments in the building are two-bedroom apartments?

- 26%
- 35%
- 39%
- 42%
- 52%

6) At a certain upscale restaurant, there just two kinds of food items: entrees and appetizers. Each entrée item costs $30, and each appetizer item costs $12. Last year, it had a total of 15 food items on the menu, and the average price of a food item on its menu was $18. This year, it added more appetizer items, and the average price of a food item on its menu dropped to $15. How many appetizer items did it add this year?

- 3
- 6
- 9
- 12
- 15

Solutions will appear at the end of the article.

For the purposes of the GMAT, the weighted average situations occurs when we combine groups of different sizes and different group averages. For example, suppose in some parameter, suppose the male employees in a company have one average score, and the females have another average score. If there were an equal number of males and females, we could just average the two separate gender averages: that would be ridiculously easy, which is precisely why the GMAT will never present you with two groups of equal size in such a question. Instead, the number of male employees and number of female employees will be profoundly different, one significantly outnumbering the other, and then we will have to combine the individual gender averages to produce a total average for all employees. That’s a weighted average.

That example, included just two groups, which is common, but sometimes there are three, and conceivably, on a very hard problem, there could be four groups. Each group is a different size, each has its own average, and the job is to find the average of everyone all together. Or, perhaps the question will give us most of the info for the individual groups, and give us the total average for everyone, and then ask us to find the size or average of a particular group.

We have three basic approaches we can take to these question.

Remember that, even with ordinary average questions, thinking in terms of the sum can often be helpful. We *can’t* add or subtract averages, but we *can* add or subtract sums! Right there is the key to one approach to the weighted average situation. If we calculate the sums for each separate group, we can simply add these sums to get the sum of the whole group. Alternately, if we know the size of the total group and the total average for everyone, we can figure out the total sum for everyone, and simply subtract the sums of the individual groups in order to find what we need.

Some weighted average problems give percents, not actual counts, of individual groups. In that case, we could simply pick a convenient number for the size of the population, and use the sums method from there. For example, if group A has 20% of the population, group B has 40% of the population, and group C also has 40% of the population, then we could just pretend that group A has one person, groups B & C each have two people, and total population has five people. From this, we could calculate all our sums.

This method always works, although is not always the most convenient in more advanced problems. This will be demonstrated in a few of the answers below.

Sometimes the information about the sizes of individual groups is given, not in absolute counts of members, but simply in percents or proportions. In the problems above, question #2 simply gives percents, and question #5 asks for a percent. Yes, we could use Approach I, but there’s a faster way.

In Approach II, we simply multiply each group average by the percent of the population, expressed as a decimal, which that group occupies. When we add these products up, the sum is magically the total average for everyone. Suppose we have three groups, groups J and K and L which together constitute the entire population. Suppose this summarizes their separate information:

The percent have to be expressed in decimal form, so that:

Then, the total average is simply given by

This approach will be demonstrated in #2 below.

This final method can be hard to understand at first, but if you appreciate it, it is an incredibly fast time-saver. This approach only works if there are exactly two groups, no more.

Suppose there are two groups in a population, group 1 and group 2, and suppose that group 1 is bigger than group 2. Let’s also suppose that group 1 has a lower group average, and group 2 has the higher group average. Of course, the total combined average of the two groups together will be between the two individual group averages. In fact, because group 1 is bigger, the combined average will have to be closer to group 1’s average, and further away from group 2’s average.

Now, think about a number line, with the two individual group averages and the total averages indicated on the number line.

On that number line, I have labeled d1, the distance from the average of group #1 to the combined average, and d2, the distance from the combined average to the average of group 2. The ratio of these two distances is equal to a ratio of the size of the two individual groups. Let’s think about this. The bigger group, here group 1, will have more of an effect on the combined average and therefore will be closer to the combined average—a smaller distance. Therefore, the ratio of the distances must equal the reciprocal of the same ratio of the sizes of the groups:

Let’s say group 1 is 3 times larger than group 2. This means d2, the distance from group 2’s average to the combined average, would have to be 3 times bigger than d1, the distance from group 1’s average to the combined average. If the latter is x, then the former is 3x, and the total distance is 4x. If we know the averages of the two groups individually, we would simply have to divide the difference between those group averages by 4: the combined average would be one part away from group 1’s average, or three parts away from group 2’s average.

This approach is hard to explain clearly in words. You really have to see it demonstrated in the solutions below to understand it fully. Once you understand it, though, this is an extremely fast method to solve many problems.

If the above article gave you any insights, you may want to give the practice problems another look. Remember, in your practice problems on weighted averages, practice all three of these methods. The more ways you have to understand any problems, the more options you will have on test day!

1) **Method I: using sums**

We will divide the two masses by 1000, 1.2 and 3 respectively, to simplify calculations. Note the use of the Doubling and Halving trick in the first multiplication.

sum for cars = 50*1.2 = 100*0.6 = 60

sum for trucks = 10*3 = 30

total sum = 60 + 30 = 90

To find the total average, we need to divide this total sum by the total number of vehicles, 60.

Since we divided masses by 1000 earlier, we need to multiply by 1000 to get the answer. Total average = 1500 kg. Answer =** (B)**

**Method II: proportional placement of the total average**

Cars to trucks is 5:1, so if the distance between the car’s average and truck’s average were divided into 6 parts, the car’s average is 1 part away from the total average, and the truck’s average is 5 parts away.

Well, the difference in the two group averages is 3000 – 1200 = 1800 kg. Divide that by six: each “part” is 300 kg. Well, the total average must be 300 kg bigger than 1200 kg, or 5*300 kg smaller than 3000 kg. Either way, that’s 1500 kg. Answer =** (B)**

2) We will approach this use the proportion & percents approach. Divide all dollar amounts by 1000 for smaller numbers. Multiply each group average by the percent expressed as a decimal:

marketers = 0.70*50 = 35

engineers = 0.20*80 = 16

managers = 0.10*x = 0.1x

where x is the average salary for the managers. These three should add up to the average for all employees:

35 + 16 + 0.1x = 80

0.1x = 80 – 35 – 16

0.1x = 29

x = 290

Now, multiply the 1000 again, to get back to real dollar amounts. The average salary for managers is $290,000. Answer = **(D) **

3) **Method I: using sums**

We can use this if we pick a value for the average salary for the silver employees. It actually doesn’t matter what value we pick, because averages will fall in the same relative places regardless of whether all the individual values are slid up and down the number line. The easiest value by far to pick is zero. Let’s pretend that the silver folks make $0, and the gold folks make $56. (I divided dollars by 1000 for simplicity).

Now, we also have to simplify the numbers of employees. We could reduce the number of employees as long as we preserve the relative ratio.

silver : gold = 120:160 = 12:16 = 3:4

So everything would be the same if we just had 3 silver employees and 4 gold employees. OK, now find the sums.

silver = 3*0 = 0

gold = 4*56

I am not even going to bother to multiply that out, because we know that the next step is to divide by 7, the total number of employees.

total average = 4*56/7 = 4*8 = 32

The average salary is $32,000, which is $32,000 higher than the average for the silver employees. Answer = **(C)**

**Method II: proportional placement of the total average**

The ratio of silver employees to gold employees is

silver : gold = 120:160 = 12:16 = 3:4

If we divide the distance between the two averages by 7, then silver will be “four parts” away from the total average, and gold will be “three parts” away.

Well, the difference is $56,000, so that divided by 7 is $8000. That’s one part. Four parts would be $32,000, which has to be the distance from the silver average to the total average.

Answer = **(C) **

4) We will approach this using sums. The individual employee numbers are small. We will divide all dollar amounts by 1000, for easier calculations. Call the highest-paid employee salary x. Then the sums are

lowest = 10*80 = 800

middle = 6*150 = 3*300 = 900

highest = 4x

Individual sums must add up to the total sum.

800 + 900 + 4x = 3500

4x = 1800

2x = 900

x = 450

The salary of each of those four highest paid employees is $450,000.

Answer = **(E)**

5) This question is designed for an analysis involving proportional placement of the mean. First, observe that R is much closer to the average for one-bedroom apartments, so there must be more one-bedroom apartments and fewer two-bedroom apartments.

The ratio of the distances to R is

5600:10400 = 56:104

Cancel a factor of 8 from both 56 and 104

56:104 = 7:13

One-bedroom apartments are “13 parts” of the building, and two-bedroom apartments are “7 parts.” That’s a total of 7 + 13 = 20 parts in the building. Two-bedroom apartments constitute 7/20 of the apartments in the building. Since 1/20 = 5%, 7/20 = 35%.

Answer = **(B)**

6) **Method I: using sums**

First, last year. Let x be the number of entrees. Then (15 – x) is the number of appetizers. The sums are:

entrees = 30x

appetizers = (15 – x)*12 = 12*15 – 12x = 6*30 – 12x = 180 – 12x

total = 15*18 = 30*9 = 270

Notice the use of the Doubling and Halving trick in the second and third lines. The two individual sums should add up to the total sum.

30x + 180 – 12x = 270

18x = 90

x = 5

They start out with 5 entrees and 10 appetizers.

Let N be the number of appetizers added, so now there are 5 entrees and (10 + N) appetizers. We need to solve for N. Again, the sums:

entrees = 5*30 = 150

appetizers = (10 + N)*12 = 120 + 12N

total = (15 + N)*15 = 225 + 15N

Again, the two individual sums should add up to the total sum.

150 + 120 + 12N = 225 + 15N

270 = 225 + 3N

45 = 3N

15 = N

They added 15 more appetizers. Answer = **(E)**

Method I was do-able, but we had to solve for many values.

**Method II: proportional placement of the total average**

Originally, the entrée price was 30 – 18 = 12 from the total average, and the appetizer price was 18 – 12 = 6. This means there must have been twice as many appetizers as entrees. Therefore , with 15 items, there must have been 10 appetizers and 5 entrees.

The number of entrees doesn’t change. The average drops to $15, so the distance from the entrée price is now 30 – 15 = 15, and the distance from the appetizer price is now 15 – 12 = 3. That’s a 5-to-1 ratio, which means there must be 5x as many appetizers as entrees. Since there still are 5 entrees, there must now be 25 appetizers, so 15 have been added.

Answer = **(E)**

If you know how to employ this method, it is much more elegant.

]]>

Applying the rule incorrectly causes quite a few errors on the quant section, particularly with Data Sufficiency questions. This is the fourth in a series of posts on avoiding those errors:

In my last three posts we saw that sometimes two equations aren’t enough to allow us to solve for two variables, or even for one. That is, we saw that sometimes, information that seems sufficient isn’t in fact sufficient.

The trick was that the rule above isn’t correct as written. The correct rule is that a system of n distinct linear equation is sufficient to solve for n variables, but that sometimes the GMAT gives you systems of equivalent (not distinct) equations, or exponential or quadratic (not linear) equations, and that the rule doesn’t apply to such systems.

Today, we’ll see that sometimes information that doesn’t seem sufficient turns out to be, even when the equations in question are distinct and linear. How does that happen?

Take a minute or two to answer this problem:

Andres bought exactly two sorts of donuts, old-fashioned donuts and jelly donuts. If each old-fashioned donut costs $0.75 and each jelly donut costs $1.20, how many jelly donuts did Andres buy?

(1) Andres bought a total of eight donuts.

(2) Andres spent exactly $7.35 on donuts.

**(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.

In this case, if we too quickly apply the rule described above, we’ll probably choose (C) after a bit of algebra. It turns out, though, that (C) is not the correct answer.

Let j=the number of jelly donuts Andres purchased and 1.2j=the amount that Andres spent on jelly donuts.

Note that we want to solve for j.

Let f=the number of old-fashioned donuts Andres purchased and 0.75f=the amount that Andres spent on old-fashioned donuts.

The question stem doesn’t give us an equation. (Well, it could give us 1.2j+0.75f=t, where t=the total dollars spent on donuts, but that equation isn’t useful.)

We can rewrite statement (1) as an equation:

(1) j+f=8

Obviously that doesn’t allow us to solve for j. Eliminate answers (A) and (D).

We can rewrite statement (2) as an equation:

1.2j+0.75f=7.35

This doesn’t seem to be sufficient either. After all, solving for j yields a weird variable expression, j=6.125-0.833…f. So we’ll probably eliminate (B) as well.

You could solve for j using both statements together but you don’t really need to do the math, since they’re obviously distinct linear equations. It’s enough to note that they are sufficient together without actually figuring out that j=3.

The trouble with that approach is that (2) is in fact sufficient. Yes, if we look at Statement (2) merely as an algebraic equation and we ignore the story that gave rise to the equation, then we have an infinite number of solutions for the pair j and f. Let’s make a little function table, assigning simple integer values to f and letting those determine corresponding values for j:

f | j |
---|---|

1 | 5.5 |

2 | 4.875 |

3 | 4.25 |

4 | 3.625 |

5 | 3 |

6 | 2.275 |

. | . |

. | . |

Do you see the trap? For every value of f except f=5, j turns out to be a mixed number. The story imposed an implicit constraint, that the values for f and j be positive integers. It turns out that this constraint means that there is exactly one acceptable solution to the equation in Statement (2), and so that the answer is (B) rather than (C).

When a DS story problem yields a system of distinct linear equations but implicitly requires that solutions be integers, the smart thing to do is to test values. Generally the numbers involved won’t be very large, so the arithmetic won’t be too daunting.

Above I stipulated a value for f and then determined a value for j. It might look as though I did this solely because I’d already rewritten Statement (2) as a function from f to j. I had another reason to start with f though: I can more easily see if a number is a multiple of 1.2 than of 0.75.

Sound mysterious? Let’s see how we’d actually check for possible integer solutions to Statement (2). First, stipulate an integer value for f, then calculate 0.75f, then subtract that product from 7.35 to see how much money is left for jelly donuts. If the money left isn’t a multiple of 1.2, don’t consider it further:

f | .75f | 7.35-0.75f | multiple of 1.2? |
---|---|---|---|

1 | 0.75 | 6.60 | no |

2 | 1.50 | 5.85 | no |

3 | 2.25 | 5.10 | no |

4 | 3.00 | 4.35 | no |

5 | 3.75 | 3.60 | yes |

6 | 4.50 | 2.85 | no |

7 | 5.25 | 2.10 | no |

8 | 6.00 | 1.35 | no |

9 | 6.75 | 0.60 | no |

Yes, but it would be a bad idea on the GMAT, so we’re not going to go into it.

]]>

**Hello, and welcome back to GMAT Tuesdays with Kevin!**

In today’s video, I’ll help you determine how long you need to study for the GMAT, in order to achieve your goal score. Here’s a quick breakdown of the criteria I’ll discuss:

1. How do you handle standardized testing?

- If you’re not blessed with natural test-taking abilities (most of us aren’t), you’ll likely have to study for a longer period of time.

2. How much time do you have to study?

- It’s generally better to schedule short blocks of study time each day, over a long period of time.

3. How does your base GMAT score compare to your target GMAT score?

- If you need to increase your score 50-100 points, you’ll probably need to schedule about 3 months of studying (1-2 hrs/day + ~4 hrs on the weekend).
- If you need to increase your score 100+ points, you’ll probably need to study for about 6 months (1-2 hrs/day + ~4 hrs on the weekend).

4. What are your strengths and weaknesses?

- Focus on your weaknesses!

That’s all for today. See you next week!

]]>