Sometimes, you come across some seriously interesting questions in Combinatorics. For example, this question I came across seemed like any other Combinatorics question, though it was a little cumbersome. But when I saw the answer, it got me thinking – it couldn’t have been a coincidence. There had to be a simpler logic to it and there was! I just wish I had thought of it before going the long route. So I must share it with you; you never know what might come in handy on test day!
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As noticed in the first post of Alphametics, a data sufficiency alphametic is far more complicated than a problem solving alphametic. An alphametic can have multiple solutions and establishing that it does not, is time consuming. Hence, it is less likely that you will see a DS alphametic in the actual exam.
Last week, we looked at alphametics involving addition and subtraction. The logic becomes a little more involved when the alphametic involves multiplication. When a two digit number is multiplied by another two digit number, the process of finding the result is composed of multiple levels. Today, let’s see how to handle those multiple levels. The question involves quite a few steps and observations using number properties. Hence, you are unlikely to see such a question in actual GMAT but you might see a simpler version so it’s good to be prepared.
Today, let’s learn how to solve alphametics. An alphametic is a mathematical puzzle where every letter stands for a digit from 0 – 9. The mapping of letters to numbers is one-to-one; that is, the same letter always stands for the same digit, and the same digit is always represented by the same letter.
We have discussed simple and compound interest in a previous post.
We saw that simple and compound interest (compounded annually) in the first year is the same. In the second year, the only difference is that in compound interest, you earn interest on previous year’s interest too. Hence, the total two year interest in compound interest exceeds the two year interest in case of simple interest by an amount which is interest on year 1 interest.
On the GMAT, most sentence correction questions involve compound/complex sentences with multiple phrases, clauses and modifiers. Hence it is very likely that you will see some run-on sentences on your test. In the complicated sentences that we get on the GMAT, it is very easy to overlook that we are dealing with run-on sentences.
Confess it – while watching Harvey Specter and Mike Ross on ‘Suits’, many of you have wondered how ‘cool’ it would be to be a lawyer. It’s surprising how they question every assumption, every reason and come up with an innovative solution which looks as if the magician just pulled a rabbit out of a hat.
Let’s discuss how to handle functions today. People usually perceive functions as an advanced topic mainly because of the notation. But actually, the function questions are very simplistic and can be solved with a simple process. If we ask you the value of 5x^3 where x = 3, would you be worried about what to do? We assume you won’t be. Then there should be no problem with “given f(x) = 5x^3, what is the value of f(3)?”
We know that Combinatorics and Probability are tricky topics. It is easy to misinterpret questions of these topics and get the incorrect answer – which, unfortunately, we often find in the options, giving us a false sense of accomplishment.
In many questions, we need to account for different cases one by one but we don’t really see such questions on the GMAT since we have limited time. Also, we don’t tire of repeating this again and again – GMAT questions are more reasoning based than calculation intensive. Usually, there will be an intellectual method to solve every GMAT question – a method that will help you solve it in seconds.
Today, we would like to discuss with you one of our most debated critical reasoning questions. It is an absolutely brilliant question – not just because the correct option fits in beautifully but because the other four options are also very well thought out. It is easy to write the incorrect four options such that the student community will be split between 2 options – the correct one and one of the four incorrect ones but when the jury is split between 4 or all 5 options, that’s when we know that we have come up with an absolute masterpiece. Of course, in such questions, a lot of effort is needed to convince everyone of the correct answer but it is well worth it.
Today, let’s look in detail at a relation between arithmetic mean and geometric mean of two numbers. It is one of those properties which make sense the moment someone explains to us but are very hard to arrive on our own.
When two positive numbers are equal, their Arithmetic Mean = Geometric Mean = The number itself
We all know about the role of pre-thinking in Critical Reasoning and how anticipating the answer can be supremely beneficial in not just the physical aspect of saving time in analyzing options but also the psychological aspect of promoting our self-confidence – we were thinking that the answer should look like this and that is exactly what we found! Pre-thinking puts us in the driver’s seat and we feel energized without consuming any red bull!
We often tell you that if you are short on time, you can guess intelligently on a few questions and move on. Today we will discuss what we mean by “intelligent guessing”. There are many techniques – most of them involving your reasoning skills to eliminate some options and hence generating a higher probability of an accurate guess. Let’s look at one such method to get values in the ballpark.
We know that speed is important in GMAT. We have about 2 mins per question and we always have questions in which we get stuck, waste 3-4 mins and probably still answer incorrectly. So we are always trying to go faster, rush, complete the easy ones in less time! In our bid to save time, sometimes we sacrifice accuracy. We should know that accuracy is most important. No point running through questions and completing all of them before time if at the end of it all, most of our answers are incorrect – there are no bonus points for completing the test before time, after all!
Those of you who have seen the previous version of our curriculum would know that we had tips and tricks under the heading of ‘Lazy Genius’. These used to discuss innovative shortcuts for various questions – the way very smart people would solve the question – without putting in too much effort!
As promised last week, we will look at another question which involves finding the last two digits of the product of some random numbers. In this question, along with the concepts discussed last week, we will assimilate the concept of negative remainders too discussed some weeks ago.
Let’s continue the discussion of last two digits we started last week. We discussed the concept of pattern recognition and how it can help us determine the last two digits in case of numbers raised to some powers. Today we look at what happens when there is no pattern to determine! What if we are asked to determine the last two digits of the product of a bunch of numbers. We know that getting the last digit in this case is very easy – just multiply the last digits of the numbers together. But last TWO digits would seem much more complicated.
We all know how to find the last digit using cyclicity when we are given a number raised to a power. Last digit of a number depends only on the last digit of the base. You must be quite familiar with something like this –
Last Digit of Base:
0 – Last digit of expression with any power will be 0.
You must have come across questions which you thought tested one concept but later found out could be easily dealt with using another concept. Often, crafty little mixture problems belong to this category. For example:
Mark is playing poker at a casino. Mark starts playing with 140 chips, 20% of which are $100 chips and 80% of which are $20 chips. For his first bet, Mark places chips, 10% of which are $100 chips, in the center of the table. If 70% of Mark’s remaining chips are $20 chips, how much money did Mark bet?
We have discussed weighted averages in detail here but one thing we are yet to talk about is how you decide what the weights will be in weighted average problems. It is not always straight forward to identify the weights. For example, in a question such as this one,
A few weeks back, we wrote a post busting some Sentence Correction myths. Let’s continue from where we left. We discussed how we can have pronouns referring to different antecedents in different clauses of the same sentence. Let’s take another example illustrating that principle. Also, we learn how to use ‘being’ correctly in GMAT.
First, let us give you the link to the last post of this series: Post IV. It contains links to previous parts too.
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.
First, we would like to refer you back to a post we put up quite a while ago: The Holistic Approach to Mods
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.
A couple of weeks back, we looked at a 750+ level question on mean, median and range concepts of Statistics. This week, we have a 750+ level question on standard deviation concept of Statistics. We do hope you enjoy checking it out.
Before you begin, you might want to review the post that discusses standard deviation: Dealing With Standard Deviation
Today we will bust some SC myths using a question. The following are the myths:
Myth 1: Passive voice is always wrong.
Active voice is preferred over passive voice but that doesn’t make passive voice wrong.
Myth 2: The same pronoun cannot refer to two different antecedents in a sentence.
Today, we have a very interesting statistics question for you. We have already discussed statistics concepts such as mean, median, range etc in our QWQW series. Check them out here if you haven’t already done so:
Today, as promised last week, we will look at a couple of questions involving participle modifiers. We will take one question in which you should use the participle and another in which you should not.
There is a lot of confusion surrounding the topic of Participles so let’s take a look at it today.
Quite simply, participles are words formed from verbs which can be used as describing words (on the other hand, gerunds are verbs used as nouns, but that is a topic for another day!).
There are two types of participles:
We have read a lot about one way of handling complex questions – simplify them to a question you know how to solve. Here is another way – first do what you do know, and then figure out the rest!
We know that basic concepts are twisted to make advanced questions. Our aim is to break down the question into two parts – ‘the basic concept’ and ‘the complexity’. You can either deal with the complexity first and then glide through the basic concept or you can glide through the basic concept first and then face the complexity. The method you use will depend on the question. If the question seems too complex at the outset, it means you will have to deal with the complexity first. If the question seems familiar but has some extra not-so-familiar elements, it means you should get the familiar out of the way first. Let’s take a question today to see how to do that.
Most of us know that GMAT is a shrew, (euphemism for a more choice adjective that comes to mind!) and is very hard to tame. It is well established that it is able to give a pretty accurate estimate of aptitude with just a few questions, and that the only way to “deceive” it is by actually improving your aptitude! It has numerous tricks up its sleeves to uncloak a rather basic player.
Today we continue to look at ways to achieve that much desired score of 51 in Quant. Obviously, we don’t need Sheldon Cooper’s smarts to realize that for that revered high score, we must do well on the high level questions but the actual question is – how to do well on the high level questions?
Read the following sentences:
- About 70 percent of the tomatoes grown in the United States come from seeds that have been engineered in a laboratory, their DNA modified with genetic material not naturally found in tomato species.
- The defense lawyer and witnesses portrayed the accused as a victim of circumstance, his life uprooted by the media pressure to punish someone in the case.
- Researchers in Germany have unearthed 400,000-year-old wooden spears from what appears to be an ancient lakeshore hunting ground, stunning evidence that human ancestors systematically hunted big game much earlier than believed.
Which grammatical construct is represented by the underlined portions of these sentences?
This week we will look at the question on races that we gave you last week.
Question 3: A and B run a race of 2000 m. First, A gives B a head start of 200 m and beats him by 30 seconds. Next, A gives B a head start of 3 mins and is beaten by 1000 m. Find the time in minutes in which A and B can run the race separately?
Let’s discuss races today. It is a very simple concept but questions on it tend to be tricky. But if you understand how to handle them, most questions can be done easily.
A few points to remember in races:
1. Make a diagram. Draw a straight line to show the track and assume all racers are at start at 12:00. Then according to headstart, place the participants.