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!
The post How to Solve “Unsolvable” Equations on the GMAT appeared first on Veritas Prep Blog.
]]>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!
The post Quarter Wit, Quarter Wisdom: A GMAT Quant Question That Troubles Many! appeared first on Veritas Prep Blog.
]]>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.
The post How to Use the Pythagorean Theorem With a Circle appeared first on Veritas Prep Blog.
]]>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!
The post How to Prepare for the GMAT at Home: Online GMAT Prep appeared first on Veritas Prep Blog.
]]>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.
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.
The post The Benefits of Thinking With a Growth-Mindset Mentality appeared first on Veritas Prep Blog.
]]>The post Should You Retake the GMAT? appeared first on Veritas Prep Blog.
]]>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.
The post Should You Retake the GMAT? appeared first on Veritas Prep Blog.
]]>The post Quarter Wit, Quarter Wisdom: Evaluating Nasty GMAT Answer Choices appeared first on Veritas Prep Blog.
]]>The first and only rule with these types of problems is that familiarity helps. Evaluate the answer choices that make sense to you first.
Let’s look at a few questions to understand how to do that:
Which of the following is NOT prime?
(A) 1,556,551
(B) 2,442,113
(C) 3,893,257
(D) 3,999,991
(E) 9,999,991
The first thing that comes to mind when we consider how to find prime numbers should be to “check the number N for divisibility by all prime factors until we get to the √N.” But note that here, we have four numbers that are prime and one number that is not. Also, the numbers are absolutely enormous and, hence, will be very difficult to work with. So, let’s slide down to a number that seems a bit more sane: 3,999,991 (it is very close to a number with lots of 0’s).
3,999,991 = 4,000,000 – 9
= (2000)^2 – 3^2
This is something we recognise! It’s a difference of squares, which can be written as:
= (2000 + 3) * (2000 – 3)
= 2003 * 1997
Hence, we see that 3,999,991 is a product of two factors other than 1 and itself, so it is not a prime number. We have our answer! The answer is D.
Let’s try another problem:
Which of the following is a perfect square?
(A) 649
(B) 961
(C) 1,664
(D) 2,509
(E) 100,000
Here, start by looking at the answer choices. The first one that should stand out is option E, 100,000, since multiples of 10 are always easy to handle. However, we have an odd number of zeroes here, so we know this cannot be a perfect square.
Next, we look at the answer choices that are close to the perfect squares that we intuitively know, such as 30^2 = 900, 40^2 = 1600, 50^2 = 2500. The only possible number whose perfect square could be 961 is 31 – 31^2 will end with a 1 and will be a bit greater than 900 (32^2 will end with a 4, so that cannot be the square root of 961, and the perfect squares of other greater numbers will be much greater than 900).
31^2 = (30 + 1)^2 = 900 + 1 + 2*30*1 = 961
So, we found that 961 is a perfect square and is, hence, the answer!
In case 961 were not a perfect square, we would have tried 1,664 since it is just 64 greater than 1,600. It could be the perfect square of 42, as the perfect square of 42 will end in a 4.
If 1,664 were also not a perfect square (it is not), we would have looked at 2,509. We would have known immediately that 2,509 cannot be a perfect square because it is too close to 2,500. 2,509 ends in a 9, so we may have considered 53 to be its square root, but the difference between consecutive perfect squares increases as we get to greater numbers.
(4^2 is 16 while 5^2 is 25 – the difference between them is 9. The difference between 5^2 and 6^2 will be greater than 9, and so will the difference between the perfect squares of any pair of consecutive integers greater than 6. Hence, the difference between the squares of 50 and 53 certainly cannot be 9.)
Therefore, our answer is B. Let’s try one more question:
When a certain perfect square is increased by 148, the result is another perfect square. What is the value of the original perfect square?
(A) 1,296
(B) 1,369
(C) 1,681
(D) 1,764
(E) 2,500
This question is, again, on perfect squares. We can use the same concepts here, too.
30^2 = 900
31^2 = 961 (=(30+1)^2 = 900 + 1 + 2*30)
40^2= 1,600
41^2 = 1,681 (=(40+1)^2 = 1,600 + 1 + 2*40)
50^2 = 2,500
51^2 = 2,601 (=(50+1)^2 = 2,500 + 1 + 2*50)
We know that the difference between consecutive squares increases as we go to greater numbers: going from 30^2 to 31^2 is a difference of 61, while jumping from 40^2 to 41^2 is a difference of 81.
All the answer choices lie in the range from 900 to 2500. In this range, the difference between consecutive squares is between 60 and 100. So, when you add 148 to a perfect square to get another perfect square in this range, we can say that the numbers must be 2 apart, such as 33 and 35 or 42 and 44, etc. Also, the numbers must lie between 30 and 40 because twice 61 is 122 and twice 81 is 162 – 148 lies somewhere in between 122 and 162.
A and B are the only two possible options.
Consider option A – it ends in a 6, so the square root must end in a 6, too. If you add 148, then it will end with a 4 (the perfect square of a number ending in 8 will end in 4). So this answer choice works.
Consider option B – it ends in a 9, so the square root must end in a 3 or a 7. When you add 148, it ends in 7. No perfect square ends in 7, so this option is out. Our answer is, therefore, A.
We hope you see how a close evaluation of the answer choices can help you solve questions of this type. Go get ’em!
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: Evaluating Nasty GMAT Answer Choices appeared first on Veritas Prep Blog.
]]>The post Kickstart Your GMAT Prep: How to Start Preparing for the GMAT appeared first on Veritas Prep Blog.
]]>Increase the Amount of Reading You Do
You may wonder how to start preparation for GMAT questions in the Verbal section. As someone who wants to pursue an MBA, you probably read finance-related materials such as newspapers and magazines – you may even be part of an online organization that gives you the latest financial news. Increasing the amount of reading you do can help you prep for Reading Comprehension questions on the exam.
By reading a variety of finance-related materials, you expose yourself to vocabulary words that may appear on the test. Also, reading financial articles and books can get you thinking like a business executive, which is the mindset you should have as you sit down to take the exam. Absorbing the information contained in finance-related materials can contribute to your performance on the GMAT, as well as serve you in your future career.
Complete Practice Questions for the GMAT
When thinking about how to start preparing for GMAT questions, you should certainly put a practice test on your to-do list. A practice GMAT serves you in several ways – for one, you’ll become familiar with the types of questions you’ll encounter on test day. Secondly, you’ll get an idea of how quickly you have to work in order to finish each section of the test before your time is up. In addition, you can use the results of your practice test to create a study schedule that allows you to dedicate the largest amount of time to your weakest subjects.
A free GMAT practice exam is available to you from Veritas Prep. We provide you with a performance analysis as well as a score report so you know what you have mastered and what needs a little work. Once you dive into your studies, it’s a good idea to take follow-up practice tests to gauge your progress.
Create and Follow a Study Schedule
Anyone who is wondering how to start their GMAT preparation must recognize the importance of a study schedule. As with most other exams, gradual study is the best path to success on the GMAT. You may want to study for two or three hours, five or even seven days per week.
The appearance of your study schedule is going to reflect the results of your practice tests. For example, say you need to sharpen your geometry and algebra skills. You may create a schedule that dedicates an hour to geometry on Tuesdays and Thursdays and an hour to algebra on Mondays and Wednesdays. If you find that you need to improve your Reading Comprehension skills, then you may carve out time on Mondays, Wednesdays, and Fridays to work on that. Creating a varied study schedule is an effective way to stay organized and keep up with your study goals.
Learn Strategies to Master the Exam
As you learn how to start your GMAT preparation, it may surprise you to discover that memorizing facts and word definitions is not the key to mastering this exam. You have to take the right approach to the GMAT by thinking like the people who created the test. You have to know how to apply the knowledge that you possess.
Our curriculum shows you what you need to do to successfully navigate your way through the questions on the GMAT. Our instructors teach you how to avoid jumping to the seemingly obvious answer and falling into traps set by the creators of the test. We have several instructional options that allow you to choose the most convenient way to start preparing for GMAT questions. We hire instructors who have teaching experience and practical experience with the GMAT. You’ll be learning from professional instructors whose scores on the GMAT put them in the 99th percentile.
If you’ve been wondering how to start preparation for GMAT questions, Veritas Prep can help. Get in touch with our offices today and begin your journey to success on the GMAT!
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!
The post Kickstart Your GMAT Prep: How to Start Preparing for the GMAT appeared first on Veritas Prep Blog.
]]>