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.
Tag Archives : Quarter Wit Quarter Wisdom
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.
As pointed out by a reader, we need to complete the discussion on a question discussed in our previous ‘Advanced Number Properties’ posts so let’s do that today. Note that the discussion that follows doesn’t fall in the purview of GMAT and you needn’t know it. You will be able to solve any question without taking this post into account but that has never stopped us from letting loose our curiosity so here goes…
Let’s get back to strategies that will help us reach the coveted 51 in Quant. First, take a look at Part I and Part II of this blog series. Since the Quant section is not a Math test, you need conceptual understanding and then some ingenuity for the hard questions (since they look unique). Today we look at a Quant problem which is very easy if the method “strikes”. Else, it can be a little daunting. What we will do is look at a “brute force” method for times when the textbook method is not easily identifiable.
We will continue our Quant 48 to 51 journey in the coming weeks but today, we need to discuss an important distinction between assumptions and inferences. Most of you will be able to explain the difference between an assumption and an inference but some questions will still surprise you. After all, both assumptions and inferences deal with the same elements in the argument. The way they are worded makes all the difference.
People often ask – how do we go from 48 to 51 in Quant? This question is very hard to answer since we don’t have a step by step plan – do theory from here – do questions from there – take a test from here – read posts from there etc. Today and in the next few weeks, we will discuss how to go from 48 to 51 in Quant.
In today’s post, we will give you a question with two solutions and two different answers. You have to find out the correct answer and explain why the other is wrong. But before we do that, let’s give you some background.
Given an n sided polygon, how many diagonals will it have?
An n sided polygon has n vertices. If you join every distinct pair of vertices you will get nC2 lines. These nC2 lines account for the n sides of the polygon as well as for the diagonals.
Even after working extensively on absolute value questions, sometimes students come up with “why?” i.e. why do we have to take positive and negative values? Why do we have to consider ranges etc. They know the process but they do not understand the reason they need to follow the process. So here today, in this post, we will try to explain the reason.
We know that ‘Easy C’ is a common trap of DS questions – have you wondered whether there could be trap called ‘Easy A/B’ such that the answer would actually be (C)? Such questions also exist! The point is that whenever you feel that the question was way too simple, you might want to take a step back and review. GMAT will try every trick in the trade to delineate you. Let us show you a question which looks like an easy (A) but isn’t:
We would like to discuss a bit about conjunctions today – just whatever is relevant for GMAT. We will start by defining the kinds of conjunctions, then move on to the different ways in which they are used, and finally, we will see how they can be tested in a question.
A Conjunction is a word that connects or joins together words, phrases, clauses, or sentences. There are two kinds of conjunctions:
The famous rounding song by Joe Crone is pretty much all you need to solve the trickiest of rounding questions on GMAT:
You just slip to the side, and you look for a five.
Well if the number that you see is a five or more,
You gotta round up now, that’s for sure.
While discussing Permutations and Combinations many months back, we worked through several examples of arranging people in seats. Today we bring you an interesting question based on those concepts. It brings to the fore the tricky nature of both Data Sufficiency and Combinatorics – so much so that when the two get together, it is unlimited fun!
We are assuming you know the terms median, angle bisector and altitude but still, just to be sure, we will start our discussion today by defining them:
Median – A line segment joining a vertex of a triangle with the mid-point of the opposite side.
Angle Bisector – A line segment joining a vertex of a triangle with the opposite side such that the angle at the vertex is split into two equal parts.
We firmly believe that teaching someone is a most productive learning for oneself and every now and then, something happens that strengthens this belief of ours. It’s the questions people ask – knowingly or unknowingly – that connect strings in our mind such that we feel we have gained more from the discussion than even our students!
Once you have covered your fundamentals, we suggest you to practice advanced questions and jot down your takeaways from them. Sometimes students wonder how to find that all important “takeaway”. Today, let’s discuss how to elicit a takeaway from a question which seems to have none.
What is a takeaway? It is a small note to yourself which you would do well to remember while going for the exam. Even if you don’t remember the exact property you jotted down, knowing that such a property exists is enough. You can always try it on a couple of numbers in the test to recall the exact content.
Before we get started, be sure to take a look at Part I of this article. Number properties concepts come across as pretty easy, theoretically, but they have some of the toughest questions. Today let’s take a look at some properties of prime numbers and their sum. Note that don’t try to “learn” all the takeaways you come across for number properties – it will be very stressful. Instead, try to understand why the properties are such so that if you get a question related to some such properties, you can replicate the results effortlessly.
Don’t worry, we are not going to discuss (Even + Even = Even) and (Odd + Odd = Even) type of basic number properties in this post. What we have in mind for today is something based on this but far more advanced. Often, people complain that they thoroughly understand the theory but have difficulties applying it and hence are stuck at a score of 600. They look for practice questions and tend to ignore concepts since they already “know” them. We often ask them to go back to concepts since we believe that a strong foundation of concepts is necessary for ‘score increase’. Mind you, when we do that, we don’t mean to ask them to review the basic concepts again, we mean to ask them to deduce and work on advanced concepts. Let’s show you with the help of a question.
I am no fan of formulas, especially the un-intuitive ones but the one we are going to discuss today has proved quite useful. It is for a concept tested on GMAT Prep so it might be worth your while to remember this little formula.
When two items are sold at the same selling price, one at a profit of x% and the other at a loss of x%, there is an overall loss. The loss% = (x^2/100)%
Recall the important property that we discussed about the relation between the areas of the two similar triangles last week – if the ratio of their sides is ‘k’, the ratio of their areas will be k^2. As mentioned last week, it’s an important property and helps you easily solve otherwise difficult questions. The question I have in mind today also brings in focus the Pythagorean triplets.