What motivates you to be a GMAT instructor?
“I have been teaching the GMAT for 10 years because I absolutely love what the test is designed to assess and how it makes you learn and think. This is not a content regurgitation test, but rather it is one that assesses who is good at taking basic content and using that to solve very difficult problems and reasoning puzzles. I believe that the skills and thinking processes the GMAT assesses are invaluable not only in business but in all walks of life. I really enjoy unlocking this way of thinking for students and teaching them to love a test that they may have at first despised!”
If you could give three pieces of advice to future GMAT test takers, what would they be?
“1) Do not waste 3 months preparing on your own, receive a low score, and THEN sign up for a high quality GMAT prep course. Take our full GMAT course before you even open a book or read about the GMAT. It will save you so much time, energy, and frustration.
2) Bring your underlying skills up to par before you start our course or do any type of GMAT preparation. Sign up several weeks before the start date and thoroughly complete all of the necessary Skillbuilders form our curriculum. Everyone has some skills that need refreshing and you will be better equipped to get the important takeaways from the class and from the individual homework questions when you have done this first.
3) Learn how to get the proper takeaways from each question and, most importantly, become a critical thinker. To succeed on the GMAT you must be all of the following: a pattern thinker, critical thinker who is able to play devil’s advocate, conceptual thinker, and a precise reader. During your preparation, learn from your mistakes and realize that you must do a fairly large number of questions and tests before these abilities can be properly developed.
Is there a common misconception of the GMAT or of what is a realistic GMAT score?
“I think there are many important misconceptions about the test as a whole and the scoring system in particular. As I have intimated earlier, the biggest misconception about the GMAT is that it is a content test in which memorizing all the rules and the underlying content will allow you to do well. This is certainly not the case and it is why so many students get frustrated when they prepare on their own. The GMAT is so different from the tests that you were able to ace in college with memorization ‘allnighters.’ Also, I think people underestimate how competitive and difficult the GMAT really is. Remember that you are competing against a highly selective group of college graduates from around the world who are very hungry to attend a top US business school. This test is no joke and requires an intensive preparation geared toward success in higher order thinking and problem solving.”
How do you personally ensure that students who are struggling end up with the knowledge and skills they need to be successful on the GMAT?
“As a company, we have done this by creating a curriculum that works for everyone and that addresses all of the underlying knowledge and skills required for success. By creating a separate set of ‘Skillbuilders’ for each lesson and accompanying videos done by our most veteran instructor, we allow each person to bring their underlying skills up to par before each lesson. In the lesson, we focus on the important problem solving skills and critical thinking skills that are harder for each person to develop on their own. Personally, I take a lot of pride in my ability to spot individual weaknesses quickly (both with content and with problem solving skills) and help my students address those effectively so they are better prepared for the test.”
Read the rest of the interview here!
Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!
]]>Now, at a restaurant, you may be particularly hungry and decide to order both the soup and the salad (and the frog legs while we’re at it). Similarly, on forms, someone who selects both options is being confusing. Perhaps you’ve smoked once and didn’t like it. Perhaps you smoke only on long weekends when the Philadelphia Eagles have a winning record. Sometimes people decide they don’t want to pick between the two choices given. However, if the question were changed to “have you ever smoked a cigarette?” and then given yes or no options, the decision becomes much easier. You have to be in one camp or the other, there is no sitting on the fence (like Humpty Dumpty).
For questions that set up this kind of duality, the entire spectrum of possibilities is essentially covered in these two options. There is no third option; there is no “It’s Complicated” selection. There isn’t even a section for you to explain yourself in the comments below. On these questions, you have to either be on one side or the other, you cannot be in both. Equally, you cannot be in the “neither” camp either. Necessarily, to this point in your life, you have either smoked a cigarette or you have not. Since one of them must be true, this certainty offers some insight on inference questions in critical reasoning.
As you probably recall, inference questions require that an answer choice must be true at all times. This isn’t always easy to see as many answer choices seem likely, but simply are not guaranteed. Sometimes, on inference questions, you get two answer choices that are compliments of one another. You get two choices that say something to the effect of “Ron is always awesome” and “Ron is not always awesome”. Even I would go for the latter here, but clearly one of these must be correct. They cannot both be correct, but they also cannot both be false. Having two answer choices like this guarantees that one of them must be the correct answer, and makes your task considerably easier.
Let’s look at an example:
A few people who are bad writers simply cannot improve their writing, whether or not they receive instruction. Still, most bad writers can at least be taught to improve their writing enough so that they are no longer bad writers. However, no one can become a great writer simply by being taught how to be a better writer, since great writers must have not only skill but also talent.
Which one of the following can be properly inferred from the passage above?
(A) All bad writers can become better writers
(B) All great writers had to be taught to become better writers.
(C) Some bad writers can never become great writers.
(D) Some bad writers can become great writers.
(E) Some great writers can be taught to be even better writers.
Since this is an inference question, we must read through the answer choices because there are many possible answers that could be inferred from this passage. When reading through the passage, you probably note that answers C and D are somewhat complimentary. Either the bad writers can become great writers, or they can’t. However, some people might be miffed by the fact that “some writers” is vague and could mean different people in different contexts. However, while the term “some writers” is undoubtedly abstract, it can refer to any subset of writers one or greater (and up to the entire group). Any group of bad writers is thus conceivable in this passage, but the answer choice must be true at all times, so the groups comprised of “some writers” can mean anyone, and these two groups can be considered equivalent.
If you recognize that either answer choice C or answer choice D must be the answer, then you can easily skip over the other three choices. For completeness’ sake, let’s run through them quickly here. Answer choice A directly contradicts the first sentence of this passage: Some bad writers simply cannot improve their writing. Answer choice B contradicts the major point of this passage, which is that great writers have a combination of skill and talent, and you cannot teach talent. Answer choice E makes sense as an option, but it doesn’t necessarily have to be true. This is a classic example of something that’s likely true in the real world, but not necessarily guaranteed by this particular passage.
This leaves us with two options to consider. Can bad writers become great writers, or can they never become great writers? As mentioned above, great writers are born with some level of talent that cannot be mimicked by practice alone. The passage explicitly states “no one can one can become a great writer simply by being taught how to be a better writer”. Even though some bad writers can improve their writing with some help (perhaps even writing a Twilight Saga), some cannot improve their writing at all. If these bad writers cannot improve their writing, they necessarily will never become great writers. Answer choice C must be true based on the passage.
Looking at answer choice D in contrast, it states: “some bad writers can become great writers”. Perhaps some can, but this cannot be guaranteed in any way from the passage. It’s possible that all the writers are terrible even after year of practice. In fact, since we know that some will never improve (the opposite), this conclusion is certainly is not guaranteed. Answer choice C is supported by the passage, answer choice D seems conceivable in the real world, but it is certainly not assured.
On the GMAT, as in life, when confronted with two complimentary choices, you have to end up making a choice. In this instance, because you typically have five choices to consider, whittling the competition down to two choices already saves you time and gives you confidence. Recognizing which option must always be true is all that’s left to do, and that often comes down to playing Devil’s Advocate. When you’re tackling a decision such as this, consider what has to be true, and you’ll make the right choice.
Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!
Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.
]]>Today, we bring another tip for you to help get that dream score of 51 – if you must write down the data given, write down all of it! Let us explain.
If you think that you will need to jot down the data given in the question and then solve it on your scratch pad (instead of in your mind), you must jot down every single detail. It is easy to overlook small things which are difficult to express algebraically such as ‘x is an integer’. These details are often critical and could make all the difference between an ‘unsolvable’ question and a ‘solvable within 2 minutes’ one. Once you start solving the question on your scratch pad, you will not refer back to the original question again and again and hence might forget these details. Have them along with the rest of the data. Read every word of the question carefully, and ensure that it is consolidated on your scratch pad. For example, look at this question:
A set of five positive integers has an arithmetic mean of 150. A particular number among the five exceeds another by 100. The rest of the three numbers lie between these two numbers and are equal. How many different values can the largest number among the five take?
It is a difficult question because it incorporates statistics as well as maxmin – both tricky topics. On top of it, people often overlook the ‘are equal’ part of the question here. The reason for that is that they are actively looking for implications of the sentences and the moment they read “The rest three numbers lie between these two numbers”, they go back to the previous sentence which tells us “A particular number among the five exceeds another by 100”. They then make a note of the fact that 100 is the range of the five positive integers. In all this excitement, they miss the three critical words “and are equal”. Ensure that when you go to the sentence above, you pick the next sentence from the point where you left it. Another thing to note here is that all numbers are positive integers. This information will be critical to us.
Let’s demonstrate how you will solve this question after incorporating all the information given.
Question: A set of five positive integers has an arithmetic mean of 150. A particular number among the five exceeds another by 100. The rest of the three numbers lie between these two numbers and are equal. How many different values can the largest number among the five take?
(A) 18
(B) 19
(C) 21
(D) 42
(E) 59
Solution:
Let’s assume that the 5 natural numbers in increasing order are: a, b, b, b, a+100
We are given that a < b < a+100.
Also, we are given that a and b are positive integers. This information is critical – we will see later why.
The average of the 5 numbers is (a+b+b+b+a+100)/5 = 150
(a+b+b+b+a+100) = 5*150
2a+3b = 650
We need to find the number of distinct values that a can take because a+100 will also take the same number of distinct values.
Now there are two methods to proceed. Let’s discuss both of them.
Method 1: Pure Algebra – Write b in terms of a and plug it in the inequality
b = (650 – 2a)/3
a < (650 – 2a)/3 < a+100
3a < 650 – 2a < 3a + 300
Now split it into two inequalities: 3a < 650 – 2a and 650 – 2a < 3a + 300
Inequality 1: 3a < 650 – 2a
5a < 650
a < 130
Inequality 2: 650 – 2a < 3a + 300
5a > 350
a > 70
So we get that 70 < a < 130. Since a is an integer, can we say that a can take all values from 71 to 129? No. What we are forgetting is that b is also an integer. We know that
b = (650 – 2a)/3
For which values will be get b as an integer? Note that 650 is not divisible by 3. You need to add 1 to it or subtract 2 out of it to make it divisible by 3. So a should be of the form 3x+1.
b = (650 – 2*(3x+1))/3 = (648 – 6x)/3 = 216 – 2x
Here, for any positive integer x, b will be an integer.
From 71 to 129, we have the following numbers which are of the form 3x+1:
73, 76, 79, 82, 85, … 127
This is an Arithmetic Progression. How many terms are there here?
Last term = First term + (n – 1)*Common Difference
127 = 73 + (n – 1)*3
n = 19
a will take 19 distinct values so the last term i.e. (a+100) will also take 19 distinct values.
Method 2: Using Transition Points
Note that a < b < a+100
Since a < b, let’s find the point where a = b, i.e. the transition point
2a + 3a = 650
a = 130 = b
But b must be greater than a. If we increase b by 1, we need to decrease a by 3 to keep the average same. But decreasing a by 3 decreases the largest number i.e. a+100 by 3 too; so we need to increase b by another 1.
We get a = 127 and b = 132. This give us the numbers as 127, 132, 132, 132, 227. Here the average is 150
Since b < a+100, let’s find the point where b = a+100
2a + 3(a+100) = 650
a = 70, b = 170
But b must be less than a+100. If we decrease b by 1, we need to increase a by 3 to keep the average same. But increasing a by 3 increases the largest number, i.e. a+100 by 3 too, so we need to decrease b by another 1.
We get a = 73 and b = 168. This gives us the numbers as 73, 168, 168, 168, 173. Here the average is 150
Values of a will be: 73, 76, 79, ….127 (Difference of 3 to make b an integer)
This is an Arithmetic Progression.
Last term = First term + (n – 1)*Common difference
127 = 73 + (n – 1)*3
n = 19
a will take 19 distinct values so the last term i.e. (a+100) will also take 19 distinct values.
Answer (B)
Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!
]]>Watch this video to learn how you can find hidden hints within statements and how that can help you avoid any GMAT traps. You don’t want to leave any points on the table.
Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!
By Brian Galvin
]]>A common strategy in puzzles is to build the outsides or the corners first, as these pieces are more easily identifiable than a typical piece, and then try and connect them wherever possible. Indeed, you are unlikely to have ever solved a puzzle without needing to jump around (except for puzzles with 4 pieces or so).
Similarly, you are often faced with GMAT questions that seem like intricate puzzles, and this same strategy of jumping around can be applied. If you start at the beginning of a question and make some strides, you may find your progress has been jammed somewhere along the way and you must devise a new strategy to overcome this roadblock. Jumping around to another part of the problem is a good strategy to get your creative juices flowing.
Let’s say a math question is asking you about the sum of a certain series. A simplistic approach (possibly one used by a Turing machine) would sequentially count each item and keep a running tally. However, a more strategic approach might involve jumping to the end of the series, investigating how the series is constructed, and finding the average. This average can then be multiplied by the number of terms to correctly find the sum of a series in a couple of steps, whereas the brute force approach would take much longer. Since the GMAT is an exam of how you think, the questions asked will often reward your use of logical thinking and your understanding of the underlying math concepts.
Let’s look at a sequence and see how thinking out of order can actually get our thinking straight:
In the sequence a1, a2, a3, an, an is determined for all values n > 2 by taking the average of all terms a1 through an1. If a1 = 1 and a3 = 5, then what is the value of a20?
(A) 1
(B) 4.5
(C) 5
(D) 6
(E) 9
This question is designed to make you waste time trying to decipher it. A certain pattern is established for this sequence, and then the twentieth term is being asked of us. If the sequence has a pattern for all numbers greater than two, and it gave you the first two numbers, then you could deduce the subsequent terms to infinity (and beyond!). However, only the first and third terms are given, so there is at least an extra element of determining the value of the second term. After that, we may need to calculate 16 intermittent items before getting to the 20th value, so it seems like it might be a time consuming affair. As is often the case on the GMAT, once we get going this may be easier than it initially appears.
If a1 is 1 and a3 is 5, we actually have enough information to solve a2. The third term of the sequence is defined as the average of the first two terms, thus a3 = (a1 + a2) / 2. This one equation has three variables, but two of them are given in the premise of the question, leading to 5 = (1 + a2) /2. Multiplying both sides by 2, we get 10 = 1 + a2, and thus a2 has to be 9. The first three terms of this sequence are therefore {1, 9, 5}. Now that we have the first three terms and the general case, we should be able to solve a4, a5 and beyond until the requisite a20.
The fourth term, a4 is defined as the average of the first three terms. Since the first three terms are {1, 9, 5}, the fourth term will be a4 = (1 + 9 + 5) / 3. This gives us 15/3, which simplifies to 5. A4 is thus equal to 5. Let’s now solve for a5. The same equation must hold for all an, so a5 = (1 + 9 + 5 + 5) /4, which is 20/4, or again, 5. The third, fourth and fifth terms of this sequence are all 5. Perhaps we can decode a pattern without having to calculate the next fourteen numbers (hint: yes you can!).
A3 is 5 because that is the average of 1 and 9. Once we found a3, we set off to find subsequent elements, but all of these elements will follow the same pattern. We take the elements 1 and 9, and then find the average of these two numbers, and then average out all three terms. Since a3 was already the average of a1 and a2, adding it to the equation and finding the average will change nothing. A4 will similarly be 5, and adding it into the equation and taking the average will again change nothing. Indeed all of the terms from A3 to A∞ will be equal to exactly 5, and they will have no effect on the average of the sequence.
You may have noticed this pattern earlier than element a5, but it can nonetheless be beneficial to find a few concrete terms in order to cement your hypothesis. You can stop whenever you feel comfortable that you’ve cracked the code (there are no style points for calculating all twenty elements). Indeed, it doesn’t matter how many terms you actually calculate before you discover the pattern. The important part is that you look through the answer choices and understand that term a20, like any other term bigger than a3, must necessarily be 5, answer choice C.
While understanding the exact relationship between each term on test day is not necessary, it’s important to try and see a few pattern questions during your test prep and understand the concepts being applied. You may not be able to recognize all the common GMAT traps, but if you recognize a few you can save yourself valuable time on questions. If you find yourself faced with a confusing or convoluted question, remember that you don’t have to tackle the problem in a linear fashion. If you’re stuck, try to establish what the key items are, or determine the end and go backwards. When in doubt, don’t be afraid to skip around (figuratively, literal skipping is frowned upon at the test center).
Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!
Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.
]]>In this post, we discussed how to use graphing techniques to easily solve very high level questions on nested absolute values. We don’t think you will see such high level questions on actual GMAT. The aim of putting up the post was to illustrate the use of graphing technique and how it can be used to solve simple as well as complicated questions with equal ease. It was aimed at encouraging you to equip yourself with more visual approaches.
We gave you two questions at the end of that post to try on your own. We have seen quite a bit of interest in them and hence will discuss their solutions today.
The solutions involve a number of graphs and hence we have made pdf files for them.
Question 1: Given that y = x – 5 – 10 5, for how many values of x is y = 2?
Question 2: Given that y = x – 3 – x, for what range of x is y = 3?
Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!
]]>The advantage of the matrix box is that it highlights the innate relationships that must be true, but that are not always easy to keep track of. For instance, if a box contains 100 paperclips, some of which are metallic and some of which are plastic, then if we find 40 paperclips made of metal, there must necessarily be 60 that are made of plastic. The binary nature of the information guarantees that all the elements will fall into one of the predetermined categories, so knowing about one gives you information about the other.
The matrix box allows you to catalogue information before it becomes overwhelming. Anyone who’s studied the GMAT for any length of time (five minutes is usually enough) knows that the exam is designed to be tricky. As such, questions always give you enough information to solve the problem, but rarely give you the information in a convenient manner. Setting up a proper matrix box essentially sets you up to solve the problem automatically, as long as you know what to do with the data provided.
Let’s look at an example and what clues us into the fact that we should use a matrix box.
Of 200 students taking the GMAT, all of them have college degrees, 120 have been out of college for at least 3 years, 70 have business degrees, and 60 have been out of college for less than 3 years and do not have business degrees. How many of them have been out of college for at least 3 years and have business degrees.
A) 40
B) 50
C) 60
D) 70
E) 80
The principle determinant on whether we should use Venn diagrams or matrix boxes is whether the data has any overlap. In this example, it’s very hard to believe that a student could both have a business degree and not have a business degree, so it looks like the information can’t overlap and a matrix box approach should be used. Before we set up the matrix box, it’s important to know that the axes are arbitrary and you could put the data on either axis and end up with essentially the same box. We can thus proceed with whichever method we prefer. The box may look like what we have below:
Business Degree 
No Business Degree 
Total 

At least 3 years 

Less than 3 years 

Total 
Without filling out any information, it’s important to note that the “Total” column and row will be the most important parts. They allow us to determine missing information using simple subtraction. If we have the total figures, as little as one piece of information in the inside squares would be enough to solve every missing square (like the world’s simplest Sudoku). Let’s populate the total numbers provided in the question:
Business Degree 
No Business Degree 
Total 

At least 3 years 
120 

Less than 3 years 

Total 
70 
200 
With these three pieces of information, we can fill out the remaining “Total” squares by simply subtracting the given totals.
Business Degree 
No Business Degree 
Total 

At least 3 years 
120 

Less than 3 years 
80 

Total 
70 
130 
200 
Now all we would need to reach the correct answer is one piece of information: any of the remaining four squares. Luckily the question stem will always provide at least one of these, as the problem is unsolvable otherwise. Problems may be tricky and convoluted on the GMAT, but they will never be impossible. Looking back at the question, there are 60 students who have been out of college for less than 3 years and do not have business degrees. Plugging in this value we get:
Business Degree 
No Business Degree 
Total 

At least 3 years 
120 

Less than 3 years 
60 
80 

Total 
70 
130 
200 
Using a little bit of basic math we can turn this into:
Business Degree 
No Business Degree 
Total 

At least 3 years 
70 
120 

Less than 3 years 
20 
60 
80 
Total 
70 
130 
200 
And finally the completed:
Business Degree 
No Business Degree 
Total 

At least 3 years 
50 
70 
120 
Less than 3 years 
20 
60 
80 
Total 
70 
130 
200 
The question was asking for how many students have been out of college for at least 3 years and have business degrees, but using this method we could solve any potential question (Other than “What is the meaning of life”?). Since the number of students with business degrees who have been out of college three years or more is 50, the correct answer will be answer choice B.
In matrix box problems, setting up the question is more than half the battle. Correctly setting up the parameters will ensure that the rest of the problem gets solved almost automatically, and all you have to do is avoid silly arithmetic mistakes or getting ahead of yourself too quickly. Remember that if the information doesn’t overlap, it will likely make for a good matrix box problem. On these types of questions, don’t be afraid to think inside the box.
Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!
Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.
]]>Before you begin, you might want to review the post that discusses standard deviation: Dealing With Standard Deviation
So here goes the question.
Question: Given that set S has four odd integers and their range is 4, how many distinct values can the standard deviation of S take?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Solution: Recall what standard deviation is. It measures the dispersion of all the elements from the mean. It doesn’t matter what the actual elements are and what the arithmetic mean is – the standard deviation of set {1, 3, 5} will be the same as the standard deviation of set {6, 8, 10} since in each set there are 3 elements such that one is at mean, one is 2 below the mean and one is 2 above the mean. So when we calculate the standard deviation, it will give us exactly the same value for both sets. Similarly, standard deviation of set {1, 3, 3, 5, 6} will be the same as standard deviation of {10, 12, 12, 14, 15} and so on. But note that the standard deviation of set {25, 27, 29, 29, 30} will be different because it represents a different arrangement on the number line.
Let’s look at the given question now.
Set S has four odd integers such that their range is 4. So it could look something like this {1, x, y, 5} when the elements are arranged in ascending order. Note that we have taken just one example of what set S could look like. There are innumerable other ways of representing it such as {3, x, y, 7} or {11, x, y, 15} etc.
Now in our example, x and y can take 3 different values: 1, 3 or 5
x and y could be same or different but x would always be smaller than or equal to y.
 If x and y were same, we could select the values of x and y in 3 different ways: both could be 1; both could be 3; both could be 5
 If x and y were different, we could select the values of x and y in 3C2 ways: x could be 1 and y could be 3; x could be 1 and y could be 5; x could be 3 and y could be 5.
For clarification, let’s enumerate the different ways in which we can write set S:
{1, 1, 1, 5}, {1, 3, 3, 5}, {1, 5, 5, 5}, {1, 1, 3, 5}, {1, 1, 5, 5}, {1, 3, 5, 5}
These are the 6 ways in which we can choose the numbers in our example.
Will all of them have unique standard deviations? Do all of them represent different distributions on the number line? Actually, no!
Standard deviations of {1, 1, 1, 5} and {1, 5, 5, 5} are the same. Why?
Standard deviation measures distance from mean. It has nothing to do with the actual value of mean and actual value of numbers. Note that the distribution of numbers on the number line is the same in both cases. The two sets are just mirror images of each other.
For the set {1, 1, 1, 5}, mean is 2. Three of the numbers are distance 1 away from mean and one number is distance 3 away from mean.
For the set {1, 5, 5, 5}, mean is 4. Three of the numbers are distance 1 away from mean and one number is distance 3 away from mean.
The deviations in both cases are the same > 1, 1, 1 and 3. So when we square the deviations, add them up, divide by 4 and then find the square root, the figure we will get will be the same.
Similarly, {1, 1, 3, 5} and {1, 3, 5, 5} will have the same SD. Again, they are mirror images of each other on the number line.
The rest of the two sets: {1, 3, 3, 5} and {1, 1, 5, 5} will have distinct standard deviations since their distributions on the number line are unique.
In all, there are 4 different values that standard deviation can take in such a case.
Answer (B)
Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!
]]>Arguably the single most common trap the authors set for you is evident in this question, which we invite you to answer before you read the rest of this post:
Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 15 ounces of chocolate. How much chocolate is left over if he uses all the dough but only wants the cookies to consist of 20% chocolate?
(A) 3
(B) 6
(C) 7.2
(D) 7.8
(E) 9
Now, we don’t want to gloss over the math here but there’s plenty of opportunity to practice with word problems and ratios in other posts and resources, so let’s cut to the true takeaway here. Most students will correctly arrive at the amount of chocolate used by employing a method similar to:
If the 36 ounces of dough are to be 80% of the total weight, then 36 = 4/5 * total.
That means that the total weight is 45 ounces, and so when we subtract out the 36 ounces of dough, there’s 9 ounces of chocolate in the cookies.
So…the answer is E. Right?
Wrong. Go back and doublecheck the question – the question asks for how much chocolate is LEFT OVER, not how much is USED. To be correct, you’d need to go back to the 15 original ounces of chocolate, subtract the 9 used, and correctly answer that 6 were left.
What’s the trap? GMAT questions are frequently set up so that you can answer the wrong question. If a question asks you to solve for y, it typically makes it easier to first solve for x…and then x is a trap answer. If a question asks you to strengthen a conclusion, the best way to weaken it is likely to be an answer choice. If a question asks for the maximum value, the minimum is going to be a trap.
The most common wrong answer to any problem on the GMAT is the right answer to the wrong question.
So take precaution – to avoid this trap, make sure that you:
Few outcomes are more disappointing than doing all the work correctly but still getting the question wrong. The GMAT doesn’t do partial credit, so on a question like this falling for the trap is just as bad as not knowing how to get started. Get credit for what you know how to do – make sure you pause before you submit your answer to make sure that it answers the proper question!
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By Brian Galvin
]]>Needless to say, many people opted to cancel their scores out of fear that a disappointing result would reflect badly on them and hinder their chances of being accepted into the school of their choice. The overall takeaway of my article was that most people felt that they did badly on the GMAT, and therefore tended to cancel their scores more often than they should have.
Lo and behold, in the summer of 2014 the GMAC (the FIFA of the GMAT) decided to change this policy and allow students to see their scores before deciding whether or not to cancel them. This decision was met with jubilation and applause (by me) from most prospective students, as this situation was entirely preferable to the previous circumstances. However, some students still are unclear when they should cancel their scores and when they shouldn’t. As such, I figured this would be a golden opportunity to revisit this topic and discuss cancelling your scores under the new world order.
First, let’s begin with the bad news. If you cancel your score, you are not refunded your 250$ fee for taking the exam. Nor can you retake the exam the next day; the same 31 day waiting period applies. Perhaps most jarringly, your record will still indicate that a score was cancelled, meaning that there will still be some record of the GMAT having been taken, just no accompanying score. Finally, if you do decide to cancel your score, you can subsequently change your mind and ask for the score to be reinstated, although this will incur an additional cost of 100$, and must be done within 60 days of the test date.
Let’s begin with some valid reasons why someone would consider cancelling their scores. Firstly, if you sleep very badly the night before or something goes very wrong in your personal life (worse than Menudo breaking up), you may be incapable of concentrating properly and your score will consequently suffer. In these situations, when you know you can do significantly better, it may be a good idea to cancel your score. Another instance would be if you took the exam and got some score, perhaps a 600, and then retook it and scored 450, a considerably worse result. Since the goal is to try and show improvement from one GMAT to the next, a marked decline could send the wrong message to the schools of your choice. This is another instance where cancelling your score may be a legitimate option.
If we explore some of the situations where it may be less advisable to cancel your score, we can start with a good rule of thumb: If it’s your first GMAT, you should (practically) never cancel your score. Why? Because if you cancel your score, you remove your baseline GMAT score. The best case scenario may be to take the exam once, ace it, and never look back (or possibly go back to teach it years later), but the reality is most people end up taking this exam more than once. The current average number of times someone takes the GMAT is about 2.7, meaning that many people take the exam two or three times before getting the score they want. If you’re aiming for a 650, and only get a 550 on the first try, then subsequent scores will demonstrate perseverance and determination, two skills sought after in business professionals. Cancelling your first score will only raise questions as to how badly it went (210?) and why you elected to remove the only thing on an otherwise blank canvas.
Sometimes, you score a 600 the first time, decide you want a 650, and retake the exam and only get a 610 or 620. This shows some improvement, but many people become depressed that it doesn’t show enough improvement, especially if they studied for several months to achieve this moderate increase. Again, cancelling this updated score will only raise questions as to how badly the test went, and a small improvement is still an improvement. Most GMAT schools take the best GMAT score as their reference, so even a 10 point progress from 600 to 610 could be enough to make a difference in your application. The same principle applies if your score went down slightly, say to 580. While a slight decline isn’t cause for a celebration, it’s a minor hiccup that demonstrates that you can consistently stay within the same range. Also, cancelling a slight drop opens the possibility that you did very badly on this second attempt and opted to cancel the score, artificially exaggerating how poorly the test actually went.
Sometimes, the idea of cancelling your score will come up before you’re even done with the test. Halfway through the verbal section, when you’re wallowing in the fact that you guessed the last three questions, your brain may take solace in the idea of cancelling the exam score. Sometimes you’ll contemplate it during a difficult stretch in the quantitative section (sometimes even on question 1!). The fact that you can now see your score before deciding whether to cancel it is a huge benefit in your choice as it removes the guesswork from the equation. No matter how badly you think you’re doing, at least you can see the score, make a decision, and even potentially reverse that decision within a couple of months.
When it comes to cancelling scores on the GMAT, the rule of thumb is that you shouldn’t cancel your score unless some “force majeure” or act of God came into the equation. The rule change allows us more flexibility in our decision making process, but the same factors must still be considered. If this is the first time you take the exam, your score is higher than any of your previous scores or if you just feel like you’re stinking up the exam (figuratively, not literally), you probably shouldn’t cancel your score. If your score truly is abysmal, then you can take a page from Pacific Rim and say “We are cancelling the apocalypse!” and be confident in your decision. The GMAT is designed to be tricky, but at least all the guesswork about cancelling your score has been removed for 2014 and beyond.
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Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.
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