The post Data Sufficiency Questions: How to Know When Both Statements Together Are Not Sufficient appeared first on Veritas Prep Blog.
]]>Let’s try to answer these questions in today’s post using using one of our own Data Sufficiency questions.
A certain car rental agency rented 25 vehicles yesterday, each of which was either a compact car or a luxury car. How many compact cars did the agency rent yesterday?
(1) The daily rental rate for a luxury car was $15 higher than the rate for a compact car.
(2) The total rental rates for luxury cars was $105 higher than the total rental rates for compact cars yesterday
We know from the question stem that the total number of cars rented is 25. Now we must find how many compact cars were rented.
There are four variables to consider here:
Let’s examine the information given to us by the statements:
Statement 1: The daily rental rate for a luxury car was $15 higher than the rate for a compact car.
This statement gives us the difference in the daily rental rates of a luxury car vs. a compact car. Other than that, we still only know that a total of 25 cars were rented. We have no data points to calculate the number of compact cars rented, thus, this statement alone is not sufficient. Let’s look at Statement 2:
Statement 2: The total rental rates for luxury cars was $105 higher than the total rental rates for compact cars yesterday.
This statement gives us the difference in the total rental rates of luxury cars vs. compact cars (we do not know the daily rental rates). Again, we have no data points to calculate the number of compact cars rented, thus, this statement alone is also not sufficient.
Now, let’s try to tackle both statements together:
The daily rate for luxury cars is $15 higher than it is for compact cars, and the total rental rates for luxury cars is $105 higher than it is for compact cars. What constitutes this $105? It is the higher rental cost of each luxury car (the extra $15) plus adjustments for the rent of extra/fewer luxury cars hired. That is, if n compact cars were rented and n luxury cars were rented, the extra total rental will be 15n. But if more luxury cars were rented, 105 would account for the $15 higher rent of each luxury car and also for the rent of the extra luxury cars.
Event with this information, we still should not be able to find the number of compact cars rented. Let’s find 2 cases to ensure that answer to this question is indeed E – the first one is quite easy.
We start with what we know:
The total extra money collected by renting luxury cars is $105.
105/15 = 7
Say out of 25 cars, 7 are luxury cars and 18 are compact cars. If the rent of compact cars is $0 (theoretically), the rent of luxury cars is $15 and the extra rent charged will be $105 (7*15 = 105) – this is a valid case.
Now how do we get the second case? Think about it before you read on – it will help you realize why the second case is more of a challenge.
Let’s make a slight change to our current numbers to see if they still fit:
Say out of 25 cars, 8 are luxury cars and 17 are compact cars. If the rent of compact cars is $0 and the rent of luxury cars is $15, the extra rent charged should be $15*8 = $120, but notice, 9 morecompact cars were rented than luxury cars. In reality, the extra total rent collected is $105 – the $15 reduction is because of the 9 additional compact cars. Hence, the daily rental rate of each compact car would be $15/9 = $5/3.
This would mean that the daily rental rate of each luxury car is $5/3 + $15 = $50/3
The total rental cost of luxury cars in this case would be 8 * $50/3 = $400/3
The total rental cost of compact cars in this case would be 17 * $5/3 = $85/3
The difference between the two total rental costs is $400/3 – $85/3 = 315/3 = $105
Everything checks out, so we know that there is no unique answer to this question – for any number of compact cars you use, you will come up with the same answer. Thus, Statements 1 and 2 together are not sufficient.
The strategy we used to find this second case to test is that we tweaked the numbers we were given a little and then looked for a solution. Another strategy is to try plugging in some easy numbers. For example:
Instead of using such difficult numbers, we could have tried an easier split of the cars. Say out of 25 cars, 10 are luxury and 15 are compact. If the rent of compact cars is $0 and the rent of luxury cars is $15, the extra rent charged should be 10*$15 = $150 extra, but it is actually only $105 extra, a difference of $45, due to the 5 additional compact cars. The daily rental rent of 5 extra compact cars would be $45/5 = $9. Using these numbers in the calculations above, you will see that the difference between the rental costs is, again, $105. This is a valid case, too.
Hence, there are two strategies we saw in action today:
Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube, Google+, and Twitter!
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!
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]]>The post GMAT Tip of the Week: Taking The GMAT Like It’s Nintendo Switch appeared first on Veritas Prep Blog.
]]>How?
The main feature of the Switch (and the driving factor behind its name) is its flexibility. It can be an in-home gaming system attached to a fixed TV set, but then immediately Switch to a hand-held portable system that allows you to continue your game on the go. Nintendo’s business plan is primarily based on offering flexibility…and on the GMAT, your plan should be to prove to business schools that you can offer the same.
The GMAT, of course, tests algebra skills and critical thinking skills and grammar skills, but beneath the surface it also has a preference for testing flexibility. Many problems will punish those with pure tunnel vision, but reward those who can identify that their first course of action isn’t working and who can then Switch to another plan. This often manifests itself in:
Flexibility matters on the GMAT! As an example, consider the following Data Sufficiency question:
Is x/y > 3?
1) 3x > 9y
2) y > 3y
If you’re like many, you’ll confidently address the algebra in Statement 1, divide both sides by 3 to get x > 3y, and then see that if you divide both sides by y, you can make it look exactly like the question stem: x/y > 3. And you may very well say, “Statement 1 is sufficient!” and confidently move on to Statement 2.
But when you look at Statement 2 – either conceptually or algebraically – something should stand out. For one, there’s no way that it’s sufficient because it doesn’t help you determine anything about x. And secondly, it brings up the point that “y is negative” (algebraically you’d subtract y from both sides to get 0 > 2y, then divide by 2 to get 0 > y). And here’s where, if it hasn’t already, your mind should Switch to “positive/negative number properties” mode. If you weren’t thinking about positive vs. negative properties when you considered Statement 1, this one gives you a chance to Switch your thinking and reconsider – what if y were negative? Algebraically, you’d then have to flip the sign when you divide both sides by y:
3x > 9y : Divide both sides by 3
x > 3y : Now divide both sides by y, but remember that if y is positive you keep the sign (x/y > 3), and if y is negative you flip the sign (x/y < 3).
With this in mind, Statement 1 doesn’t really tell you anything. x/y can be greater than 3 or less than 3, so all Statement 1 does is eliminate that x/y could be exactly 3. Now you have the evidence to Switch your answer. If you initially thought Statement 1 was sufficient, Statement 2 has given you a chance to reassess (thereby demonstrating flexibility in thinking) and realize that it’s not, until you know whether y is negative or positive.
Statement 2 supplies that missing piece, and the answer is thus C. But more important is the lesson – because the GMAT so values mental flexibility, it will often provide you with clues that can help you change your mind if you’re paying attention. So on the GMAT, take a lesson from Nintendo Switch: flexibility is an incredibly marketable skill, so look for clues and opportunities to Switch your line of thinking and save yourself from trap answers.
Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!
By Brian Galvin.
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]]>The post How to Solve “Unsolvable” Equations on the GMAT appeared first on Veritas Prep Blog.
]]>In this example, it relatively easy to see that the equation has no real solution. In others, it may not be so obvious, so we will need to use other strategies.
We know how to solve third degree equations. The first solution is found by trial and error – we try simple values such as -2, -1, 0, 1, 2, etc. and are usually able to find the first solution. Then the equation of third degree is split into two factors, including a quadratic. We know how to solve a quadratic, and that is how we get all three solutions, if it has any.
But what if we are unable to find the first solution to a third degree equation by trial and error? Then we should force ourselves to wonder if we even need to solve the equation at all. Let’s take a look at a sample question to better understand this idea:
Is x < 0?
(1) x^3 + x^2 + x + 2 = 0
(2) x^2 – x – 2 < 0
In this problem, x can be any real number – we have no constraints on it. Now, is x negative?
Statement 1: x^3 + x^2 + x + 2 = 0
If we try to solve this equation as we are used to doing, look at what happens:
If you plug in x = 2, you get 16 = 0
If you plug in x = 1, you get 5 = 0
If you plug in x = 0, you get 2 = 0
If you plug in x = -1, you get 1 = 0
If you plug in x = -2, you get -4 = 0
We did not find any root for the equation. What should we do now? Note that when x goes from -1 to -2, the value on the left hand side changes from 1 to -4, i.e. from a positive to a negative. So, in between -1 and -2 there will be some value of x for which the left hand side will become 0. That value of x will not be an integer, but some decimal value such as -1.3 or -1.4, etc.
Even after we find the first root, making the quadratic will be very tricky and then solving it will be another uphill task. So we should ask ourselves whether we even need to solve this equation.
Think about it – can x be positive? If x is indeed positive, x^3, x^2 and x all will be positive. Then, if we add four positive numbers (x^3, x^2, x and 2) we will get a positive sum – we cannot get 0. Obviously x cannot be 0 since that will give us 2 = 0.
This means the value of x must be negative, but what it is exactly doesn’t matter. We know that x has to be negative, and that is sufficient to answer the question.
Statement 2: x^2 – x – 2 < 0
This, we can easily solve:
x^2 – 2x + x – 2 < 0
(x – 2)*(x + 1) < 0
We know how to solve this inequality using the method discussed here.
This this will give us -1 < x < 2.
Since x can be a non-integer value too, x can be negative, 0, or positive. This statement alone is not sufficient,and therefore, the answer is A.
To evaluate Statement 1, we didn’t need to solve the equation at all. We figured out everything we wanted to know by simply using some logic.
Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube, Google+, and Twitter!
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!
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]]>The post Quarter Wit, Quarter Wisdom: A GMAT Quant Question That Troubles Many! appeared first on Veritas Prep Blog.
]]>In the same way, it is possible that a question may appear to be testing very obscure concepts, while it is really solvable by using only basic ones.
This happens with one of our own practice questions – we have often heard students exclaim that this problem isn’t relevant to the GMAT since it “tests an obscure number property”. It is a question that troubles many people, so we decided to tackle it in today’s post.
We can easily solve this problem with just some algebraic manipulation, without needing to know any obscure properties! Let’s take a look:
† and ¥ represent non-zero digits, and (†¥)² – (¥†)² is a perfect square. What is that perfect square?
(A) 121
(B) 361
(C) 576
(D) 961
(E) 1,089
The symbols † and ¥ are confusing to work with, so the first thing we will do is replace them with the variables A and B.
The question then becomes: A and B represent non-zero digits, and (AB)² – (BA)² is a perfect square. What is that perfect square?
As I mentioned before, we have heard students complain that this question isn’t relevant to the GMAT because it “uses an obscure number property”. Now here’s the thing – most advanced number property questions CAN be solved in a jiffy using some obscure number property such as, “If you multiply a positive integer by its 22nd multiple, the product will be divisible by …” etc. However, those questions are not actually about recalling these so-called “properties” – they are about figuring out the properties using some generic technique, such as pattern recognition.
For this question, the complaint is often that is that the question tests the property, “(x + y)*(x – y) (where x and y are two digit mirror image positive integers) is a multiple of 11 and 9.” It doesn’t! Here is how we should solve this problem, instead:
Given the term (AB)^2, where A and B are digits, how will you square this while keeping the variables A and B?
Let’s convert (AB)^2 to (10A + B)^2, because A is simply the placeholder for the tens digit of the number. If you are not sure about this, consider the following:
58 = 50 + 8 = 10*5 + 8
27 = 20 + 7 = 10*2 + 7
…etc.
Along those same lines:
AB = 10A + B
BA = 10B + A
Going back to our original question:
(AB)^2 – (BA)^2
= (10A + B)^2 – (10B + A)^2
= (10A)^2 + B^2 + 2*10A*B – (10B)^2 – A^2 – 2*10B*A
= 99A^2 – 99B^2
= 9*11*(A^2 – B^2)
We know now that the expression is a multiple of 9 and 11. We would not have known this beforehand. Now we’ll just use the answer choices to figure out the solution. Only 1,089 is a multiple of both 9 and 11, so the answer must be E.
We hope you see that this question is not as hard as it seems. Don’t get bogged down by unknown symbols – just focus on the next logical step at each stage of the problem.
Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube, Google+, and Twitter!
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!
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]]>The post GMAT Tip of the Week: As You Debate Over Answer Choices… Just Answer The Freaking Question! appeared first on Veritas Prep Blog.
]]>It’s no surprise that candidate approval ratings are low for the same reason that far too many GMAT scores are lower than candidates would hope. Why?
People don’t directly answer the question.
This is incredibly common in the debates, where the poor moderators are helpless against the talking points and stump speeches of the candidates. The public then suffers because people cannot get direct answers to the questions that matter. This is also very common on the GMAT, where students will invest the time in critical thought and calculation, and then levy an answer that just doesn’t hit the mark. Consider the example:
Donald has $520,000 in campaign money available to spend on advertising for the month of October, and his advisers are telling him that he should spend a minimum of $360,000 in the battleground states of Ohio, Florida, Virginia, and North Carolina. If he plans to spend the minimum amount in battleground states to appease his advisers, plus impress his friends by a big ad spend specific to New York City (and then he will skip advertising in the rest of the country), how much money will he have remaining if he wants 20% of his ad spend to take place in New York City?
(A) $45,000
(B) $52,000
(C) $70,000
(D) $90,000
(E) $104,000
As people begin to calculate, it’s common to try to determine all of the facets of Donald’s ad spend. If he’s spending only the $360,000 in battleground states plus the 20% he’ll spend in New York City, then $360,000 will represent 80% of his total ad spend. If $360,000 = 0.8(Total), then the total will be $450,000. That means that he’ll spend $90,000 in New York City. Which is answer choice D…but that’s not the question!
The question asked for how much of his campaign money would be left over, so the calculation you need to focus on is the $520,000 he started with minus the $450,000 he spent for a total of $70,000, answer choice C. And in a larger context, you can learn a major lesson from Wharton’s most famous alumnus: it’s not enough for your answer to be related to the question. On the GMAT, you must answer the question directly! So make sure that you:
As you watch the debate this weekend, notice (How could you not?) how absurd it is that the candidates just about never directly answer the question…and then vow to not make the same mistake on your GMAT exam.
Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!
By Brian Galvin.
The post GMAT Tip of the Week: As You Debate Over Answer Choices… Just Answer The Freaking Question! appeared first on Veritas Prep Blog.
]]>The post How to Use the Pythagorean Theorem With a Circle appeared first on Veritas Prep Blog.
]]>Take a look at the following diagram in which a circle is centered on the origin (0,0) in the coordinate plane:
Designate a random point on the circle (x,y.) If we draw a line from the center of the circle to x,y, that line is a radius of the circle. Call it r. If we drop a line down from (x,y) to the x-axis, we’ll have a right triangle:
Note that the base of the triangle is x, and the height of the triangle is y. So now we have our Pythagorean theorem: x^2 + y^2 = r^2. This is also the equation for a circle centered on the origin on the coordinate plane. [The more general equation for a circle with a center (a,b) is (x-a)^2 + (y-b)^2 = r^2. When a circle is centered on the origin, (a,b) is simply (0,0.)]
This ends up being an immensely useful tool to use on the GMAT. Take the following question, for example:
A certain circle in the xy-plane has its center at the origin. If P is a point on the circle, what is the sum of the squares of the coordinates of P?
(1) The radius of the circle is 4
(2) The sum of the coordinates of P is 0
So let’s draw this, designating P as (x,y):
Now we draw our trust right triangle by dropping a line down from P to the x-axis, which will give us this:
We’re looking for x^2 + y^2. Hopefully, at this point, you notice what the question is going for – because we have a right triangle, x^2 + y^2 = r^2, meaning that all we need is the radius!
Statement 1 is pretty straightforward – if r = 4, we can insert this into our equation of x^2 + y^2 = r^2 to get x^2 + y^2 = 4^2. So x^2 + y^2 = 16. Clearly, this is sufficient.
Now look at Statement 2. If the sum of x and y is 0, we can say x = 1 and y = -1 or x = 2 and y = -2 or x = 100 and y = -100, etc. Each of these will yield a different value for x^2 + y^2, so this statement alone is clearly not sufficient. Our answer is A.
Takeaway: any shape can appear on the coordinate plane. If the shape in question is a circle, remember to use the Pythagorean theorem as your equation for the circle, and what would have been a challenging question becomes a tasty piece of baklava. (We are talking about principles elucidated by the ancient Greeks, after all.)
Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And be sure to follow us on Facebook, YouTube, Google+ and Twitter!
By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles written by him here.
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]]>The post Quarter Wit, Quarter Wisdom: Try to Answer This GMAT Challenge Question! appeared first on Veritas Prep Blog.
]]>Let’s take a look at the question stem:
Date of Transaction |
Type of Transaction |
June 11 |
Withdrawal of $350 |
June 16 |
Withdrawal of $500 |
June 21 |
Deposit of x dollars |
For a certain savings account, the table shows the three transactions for the month of June. The daily balance for the account was recorded at the end of each of the 30 days in June. If the daily balance was $1,000 on June 1 and if the average (arithmetic mean) of the daily balances for June was $1,000, what was the amount of the deposit on June 21?
(A) $1,000
(B) $1,150
(C) $1,200
(D) $1,450
(E) $1,600
Think about how you might answer this question:
The average of daily balances = (Balance at the end of June 1 + Balance at the end of June 2 + … + Balance at the end of June 30) / 30 = 1000
Now we have been given the only three transactions that took place:
Now we can plug in these numbers to say the average of daily balances = [1000 + 1000 + …(for 10 days, from June 1 to June 10) + 650 + 650 + … (for 5 days, from June 11 to June 15) + 150 + … (for 5 days, from June 16 to June 20) + (150 + x) + (150 + x) + … (for 10 days, from June 21 to June 30)] / 30 = 1000
One might then end up doing this calculation to find the value of x:
[(1000 * 10) + (650 * 5) + (150 * 5) + ((150 + x) * 10)] / 30 = 1000
x = $1,450
The answer is D.
But this calculation is rather tedious and time consuming. Can’t we use the deviation method we discussed for averages and weighted averages, instead? After all, we are dealing with large values here! How?
Note that we are talking about the average of certain data values. Also, we know the deviations from those data values:
Through the deviation method, we can see the shortfall = the excess:
350 * 20 + 500 * 15 = x * 10
x = 1,450 (D)
This simplifies our calculation dramatically! Though saving only one minute on a question like this may not seem like a very big deal, saving a minute on every question by using a more efficient method could be the difference between a good Quant score and a great Quant score!
Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube, Google+, and Twitter!
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 post Quarter Wit, Quarter Wisdom: Try to Answer This GMAT Challenge Question! appeared first on Veritas Prep Blog.
]]>The post How to Prepare for the GMAT at Home: Online GMAT Prep appeared first on Veritas Prep Blog.
]]>For those who are pressed for time or are worried that the GMAT will be a tough exam to prepare for, GMAT online courses may be the answer. This is an especially convenient option if you work full-time and cannot commit to attending a traditional prep class at a specific time each week. With a bit of planning, it’s entirely possible, or even preferable, to successfully complete your GMAT preparation online.
Set Up an Effective Study Environment
When you decide on online preparation for the GMAT, you must set up an environment that enables you to focus on your studies and get into a serious mindset. This means turning off the television, radio, and CD player in your study room. Also, look for other distractions around the room. Do you have a large window where you can see people and cars on the street? You may want to close the curtains during study time to avoid the temptation of people-watching.
In addition, let others in your household know when you plan to study and ask them to avoid knocking on your door during that time. Clear space on your desk so you have enough room for your computer and all of the other study materials you need. Then, you can try going it alone, or you can work your way through the thorough program of online GMAT preparation at Veritas Prep. In our online courses, we show you how to think like the test-maker! Setting up a quiet, organized study area before you start can help you to get the most out of your instruction and private study time.
Complete a Practice Exam
Completing a practice exam is a critical part of getting ready for the GMAT. Online preparation is more effective when you are aware of both your strongest and weakest subjects. At Veritas Prep, we provide you with the opportunity to take a free exam to gauge your skill level in all four sections of the test. Furthermore, we supply you with a score report and performance analysis so you have a detailed picture of the specific topics to work on. When you prepare for the GMAT with a Veritas Prep tutor, they will review your practice test results with you. We’ll help you approach each subject with practical strategies that can improve your performance on test day.
Craft a Study Schedule Based on Practice Test Results
Making an organized, logical study schedule is another key element of successful GMAT preparation online. You must decide how many hours you’re going to dedicate to GMAT study each day. For example, you may put aside four hours a day, five days a week for study. Another person may study for two hours per day, seven days a week. The study schedule you create depends on your other daily obligations.
When drafting a schedule, it’s helpful to vary the subjects you study each day. For instance, if your practice test results reveal that you need to focus your attention on Reading Comprehension as well as Algebra questions, you could assign one of those topics to Tuesdays and Thursdays and the other to Mondays and Wednesdays. This can help you to maintain interest in your GMAT studies.
Make Note of Any Puzzling Questions
It’s not uncommon for questions to come up as you are studying for the different sections of the GMAT. Online preparation with Veritas Prep means you can access one of our instructors to ask questions on any day of the week; you don’t have to wait for your next online tutoring session to get your pressing questions answered. Sometimes a simple answer to one question can provide the understanding you need to master a concept on the GMAT.
If you’d like to study online for the GMAT, we can make it happen at Veritas Prep! Each of our capable GMAT instructors achieved a score on the exam that landed them into the 99th percentile of test-takers. Simply put, we believe that our students should learn from the best! Our team of instructors at Veritas Prep is ready to help you master your online courses and ace the GMAT. Contact our offices and sign up to start studying today!
Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And be sure to follow us on Facebook, YouTube, Google+ and Twitter!
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]]>The post The Benefits of Thinking With a Growth-Mindset Mentality appeared first on Veritas Prep Blog.
]]>In a classic study, students at a middle school were interviewed and asked whether they believed that intelligence was an inherent characteristic (fixed-mindset) or that intelligence was something you can cultivate and improve through hard work (growth-mindset). It will come as no surprise that the growth-mindset group improved their grades over the course of the year by significantly more than the fixed-mindset group did. These effects became more pronounced through high school and college.
Dweck’s book is full of interesting tidbits about the history of testing. For example, Alfred Binet, one of the pioneers of IQ testing, didn’t believe that his tests measured intelligence. Rather, he saw them as a way to identify which students hadn’t properly benefited from their public school education, so that a different, more effective approach might be employed.
Put another way, the test not only wasn’t supposed to measure intelligence, it was designed on the premise that there was no such thing as fixed intelligence, – that anyone could improve and thrive if they had access to the proper tools and strategies.
I’ve written a bit about Dweck in the past, but I’m beginning to see that the implications of her research are even broader than I’d initially suspected. It should go without saying that here at Veritas Prep, we’re advocates of growth-mindset – in fact, the whole notion of test prep is rooted in a growth-mindset mentality! Moreover, I’ve noticed that this fixed vs. growth notion isn’t just applicable to performance on GMAT in general, but has implications for how test-takers attack individual questions.
Here’s a question I tackled with a tutoring student the other day:
How many positive three-digit integers are divisible by both 3 and 4?
A) 75
B) 128
C) 150
D) 225
E) 300
My student began by recognizing that if a number is divisible by both 3 and 4, it’s divisible by 12 as well, so the question was really asking how many three-digit numbers were multiples of 12. Then he looked up and told me that he didn’t know what to do.
Now, there is, of course, a way to solve this problem formally. You can find the number of elements in an evenly spaced set by using the following formula: [(High – Low)/Interval] + 1. The smallest three-digit multiple of 12 is 108 (clearly, 120 is a multiple of 12, so you can quickly see that the previous multiple of 12 is 120-12 = 108). The largest three-digit multiple of 12 is 996. (It’s divisible by 3 because 9 + 9 + 6 = 24, which is a multiple of 3. And it’s divisible by 4 because the number formed by the last two digits, 96, is divisible by 4.) So, one way to tackle this problem is to plug these numbers into the aforementioned formula to get [(996-108)/12] + 1 = (888/12) + 1 = 74 + 1 = 75.
But if you don’t know the formula, and you see this question on test day, this approach can’t help you. So rather than offer this equation, I pushed my student to think about the problem with a growth-mindset mentality. I reminded him that you don’t have to solve things formally on this test, and that he could definitely figure out a way to arrive at the correct answer based on logic and intuition. Once he stopped dwelling on the fact that he didn’t know how to do the problem formally, he used the following logic:
Between 1 and 1,000 there are 100 multiples of 10 (1,000/10 = 100). Clearly, between 100 and 999 there are fewer than 100 multiples of 12, as 12 is bigger than 10. If the correct answer is less than 100, it has to be 75, as this is the only answer choice under 100. He was able to solve a question he thought he couldn’t do in about 5 seconds. Thus, the power of the growth-mindset mentality.
Takeaway: Read Carol Dweck’s book. Work on internalizing the main ideas. Switching from a fixed-mindset mentality to a growth-mindset mentality can have a profound impact, not only on how well you perform on the GMAT, but on how ably you tackle problems in every domain of life.
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By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles written by him here.
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]]>1) Recognize the Investments Needed
Apart from the test-taking fee that you will incur for a retake, think about the hours you will need to put in to re-prepare for the GMAT, and whether this will affect the timeliness of your MBA applications. Make sure you consider whether or not you have the availability and the energy to put into this endeavor.
Often ignored, but just as important, factor in the opportunity cost of the hours you will need to spend preparing for your retake. Could you spend those efforts somewhere else to strengthen your profile? Maybe you could get involved in productive activities at work, volunteer in the community, or polish your essays.
If your application is already strong in these areas, then a GMAT retake could be a better use of your time. As such, engaging a test prep service may be the right way to go – taking a GMAT prep course or spending time with a private tutor will optimize the hours that you put into studying, and will be an investment that pays for itself in the long run.
2) Evaluate the Probability of Success
The next step would be to evaluate how likely you are to achieve your desired results. The most straightforward consideration (that requires a truly honest self-assessment) is how you have already performed on the GMAT relative to your potential:
If you believe there’s a reasonable chance that you could have done better than you did, you should seriously think about a retake.
3) Weigh the Potential Benefits
Researching the class profile of your target program, and how you compare to the school’s average GMAT score, should give you an indication as to where you stand. The standardized nature of the GMAT allows for the most straightforward and objective comparison between applicants, so ideally, you will want to score higher on the GMAT than the school’s average.
All things equal, a higher score should improve your chance of admission, and even your opportunities for scholarships. Thus, the expected value of increasing your GMAT score could be high and really worth investing in.
Knowing that you didn’t leave too many potential GMAT points on the table can also simply help you be at peace. This is an important benefit, as it will allow you to focus on the next steps in the application process, and know that you have given the GMAT your best shot.
Applying to business school? Call us at 1-800-925-7737 and speak with an MBA admissions expert today, or take our free MBA Admissions Profile Evaluation for personalized advice for your unique application situation! And as always, be sure to find us on Facebook, YouTube, Google+ and Twitter.
Written by Edison Cu, a Veritas Prep Head Consultant for INSEAD.
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